{"segments": [{"id": 1, "seek": 2294, "start": 6.76, "end": 22.94, "text": " Eventually I will give some practice problem for chapter eight. Generally speaking, there are three types of questions. The first type, multiple choice, so MCQ questions.", "tokens": [17586, 286, 486, 976, 512, 3124, 1154, 337, 7187, 3180, 13, 21082, 4124, 11, 456, 366, 1045, 3467, 295, 1651, 13, 440, 700, 2010, 11, 3866, 3922, 11, 370, 8797, 48, 1651, 13], "avg_logprob": -0.2378216885468539, "compression_ratio": 1.2761194029850746, "no_speech_prob": 0.0, "words": [{"start": 6.760000000000001, "end": 7.48, "word": " Eventually", "probability": 0.06658935546875}, {"start": 7.48, "end": 7.76, "word": " I", "probability": 0.68408203125}, {"start": 7.76, "end": 7.92, "word": " will", "probability": 0.8251953125}, {"start": 7.92, "end": 8.1, "word": " give", "probability": 0.85791015625}, {"start": 8.1, "end": 8.46, "word": " some", "probability": 0.90771484375}, {"start": 8.46, "end": 9.16, "word": " practice", "probability": 0.9326171875}, {"start": 9.16, "end": 10.02, "word": " problem", "probability": 0.77099609375}, {"start": 10.02, "end": 10.32, "word": " for", "probability": 0.927734375}, {"start": 10.32, "end": 10.72, "word": " chapter", "probability": 0.55126953125}, {"start": 10.72, "end": 11.36, "word": " eight.", "probability": 0.7890625}, {"start": 12.96, "end": 13.54, "word": " Generally", "probability": 0.66064453125}, {"start": 13.54, "end": 14.28, "word": " speaking,", "probability": 0.8779296875}, {"start": 14.52, "end": 14.66, "word": " there", "probability": 0.91015625}, {"start": 14.66, "end": 14.8, "word": " are", "probability": 0.94384765625}, {"start": 14.8, "end": 15.04, "word": " three", "probability": 0.93017578125}, {"start": 15.04, "end": 15.42, "word": " types", "probability": 0.82666015625}, {"start": 15.42, "end": 15.6, "word": " of", "probability": 0.96826171875}, {"start": 15.6, "end": 15.96, "word": " questions.", "probability": 0.95166015625}, {"start": 17.2, "end": 17.48, "word": " The", "probability": 0.89892578125}, {"start": 17.48, "end": 17.76, "word": " first", "probability": 0.8759765625}, {"start": 17.76, "end": 18.12, "word": " type,", "probability": 0.98193359375}, {"start": 19.48, "end": 19.8, "word": " multiple", "probability": 0.880859375}, {"start": 19.8, "end": 20.42, "word": " choice,", "probability": 0.81396484375}, {"start": 21.44, "end": 21.62, "word": " so", "probability": 0.8115234375}, {"start": 21.62, "end": 22.32, "word": " MCQ", "probability": 0.944091796875}, {"start": 22.32, "end": 22.94, "word": " questions.", "probability": 0.8955078125}], "temperature": 1.0}, {"id": 2, "seek": 6313, "start": 36.25, "end": 63.13, "text": " The other type of problems will be true or false. Part B, Part C, three response problems. So three types of questions. Multiple choice, we have four answers. 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And the last part, free response problems. Here we'll talk about one of these. I will cover multiple choice questions as well as true and false. Let's start with number one for multiple choice. 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No, because as we know that as the confidence level increases, the width becomes wider. So A is incorrect. Is this true? B. Wider for sample size of 100 than for a sample size of 50? 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That means the width of the interval becomes smaller and smaller. Yes, for N. Part C. Normal for 90% confidence, then for 95% confidence. That's correct. So C is the correct answer. Part D. 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So C is the correct answer. Any question? So C is the correct answer because as C level increases, the confidence interval becomes narrower. 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Let's look at the interpretation of the 99% confidence interval. Part eight. 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Here we are talking about the population mean. It says that 99% of them of these intervals would include the true population mean somewhere within their interval. It's correct. Why false? Why is it false?", "tokens": [11803, 4, 295, 552, 576, 4090, 264, 2074, 4415, 914, 4079, 1951, 641, 15035, 13, 1692, 321, 366, 1417, 466, 264, 4415, 914, 13, 467, 1619, 300, 11803, 4, 295, 552, 295, 613, 26651, 576, 4090, 264, 2074, 4415, 914, 4079, 1951, 641, 15035, 13, 467, 311, 3006, 13, 1545, 7908, 30, 1545, 307, 309, 7908, 30], "avg_logprob": -0.15153555340808014, "compression_ratio": 1.965986394557823, "no_speech_prob": 0.0, "words": [{"start": 221.69, "end": 222.15, "word": " 99", "probability": 0.66748046875}, {"start": 222.15, "end": 222.57, "word": "%", "probability": 0.87451171875}, {"start": 222.57, "end": 222.83, "word": " of", "probability": 0.931640625}, {"start": 222.83, "end": 223.07, "word": " them", "probability": 0.9091796875}, {"start": 223.07, "end": 223.37, "word": " would", "probability": 0.9150390625}, {"start": 223.37, "end": 223.83, "word": " include", "probability": 0.818359375}, {"start": 223.83, "end": 224.05, "word": " the", "probability": 0.888671875}, {"start": 224.05, "end": 224.23, "word": " true", "probability": 0.9296875}, {"start": 224.23, "end": 224.77, "word": " population", "probability": 0.9580078125}, {"start": 224.77, "end": 225.11, "word": " mean", "probability": 0.93017578125}, {"start": 225.11, "end": 225.75, "word": " somewhere", "probability": 0.89111328125}, {"start": 225.75, "end": 226.11, "word": " within", "probability": 0.92431640625}, {"start": 226.11, "end": 226.39, "word": " their", "probability": 0.94140625}, {"start": 226.39, "end": 226.79, "word": " interval.", "probability": 0.95751953125}, {"start": 229.75, "end": 230.43, "word": " Here", "probability": 0.6123046875}, {"start": 230.43, "end": 230.55, "word": " we", "probability": 0.755859375}, {"start": 230.55, "end": 230.63, "word": " are", "probability": 0.8349609375}, {"start": 230.63, "end": 230.93, "word": " talking", "probability": 0.8603515625}, {"start": 230.93, "end": 231.33, "word": " about", "probability": 0.90771484375}, {"start": 231.33, "end": 231.51, "word": " the", "probability": 0.69384765625}, {"start": 231.51, "end": 231.89, "word": " population", "probability": 0.9443359375}, {"start": 231.89, "end": 232.23, "word": " mean.", "probability": 0.93212890625}, {"start": 232.95, "end": 233.21, "word": " It", "probability": 0.9375}, {"start": 233.21, "end": 233.53, "word": " says", "probability": 0.87744140625}, {"start": 233.53, "end": 233.87, "word": " that", "probability": 0.65283203125}, {"start": 233.87, "end": 234.75, "word": " 99", "probability": 0.927734375}, {"start": 234.75, "end": 235.37, "word": "%", "probability": 0.98486328125}, {"start": 235.37, "end": 235.55, "word": " of", "probability": 0.96630859375}, {"start": 235.55, "end": 235.81, "word": " them", "probability": 0.82470703125}, {"start": 235.81, "end": 236.03, "word": " of", "probability": 0.5634765625}, {"start": 236.03, "end": 236.25, "word": " these", "probability": 0.697265625}, {"start": 236.25, "end": 236.81, "word": " intervals", "probability": 0.869140625}, {"start": 236.81, "end": 237.89, "word": " would", "probability": 0.767578125}, {"start": 237.89, "end": 238.29, "word": " include", "probability": 0.82666015625}, {"start": 238.29, "end": 238.59, "word": " the", "probability": 0.9052734375}, {"start": 238.59, "end": 238.81, "word": " true", "probability": 0.97265625}, {"start": 238.81, "end": 239.35, "word": " population", "probability": 0.9443359375}, {"start": 239.35, "end": 239.73, "word": " mean", "probability": 0.96484375}, {"start": 239.73, "end": 240.45, "word": " somewhere", "probability": 0.8916015625}, {"start": 240.45, "end": 240.79, "word": " within", "probability": 0.9150390625}, {"start": 240.79, "end": 241.05, "word": " their", "probability": 0.9453125}, {"start": 241.05, "end": 241.37, "word": " interval.", "probability": 0.955078125}, {"start": 242.41, "end": 243.09, "word": " It's", "probability": 0.595947265625}, {"start": 243.09, "end": 243.37, "word": " correct.", "probability": 0.9130859375}, {"start": 243.57, "end": 243.75, "word": " Why", "probability": 0.8837890625}, {"start": 243.75, "end": 244.11, "word": " false?", "probability": 0.86669921875}, {"start": 244.87, "end": 245.25, "word": " Why", "probability": 0.89501953125}, {"start": 245.25, "end": 245.37, "word": " is", "probability": 0.92919921875}, {"start": 245.37, "end": 245.49, "word": " it", "probability": 0.9404296875}, {"start": 245.49, "end": 245.81, "word": " false?", "probability": 0.93359375}], "temperature": 1.0}, {"id": 10, "seek": 27477, "start": 247.62, "end": 274.78, "text": " This is correct answer, because it's mentioned that 99% of these confidence intervals will contain the true population mean somewhere within their interval. So A is correct. Let's look at B. 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Again, it's mentioned that 99% confidence that we have selected sample whose interval does include. So it's correct. So C is both of the above and D none of the above. So C is the correct answer. So sometimes maybe there is only one answer. Maybe in other problems, it might be two answers are correct. So for this one, B and C.", "tokens": [2743, 11, 341, 472, 307, 3006, 13, 3764, 11, 309, 311, 2835, 300, 11803, 4, 6687, 300, 321, 362, 8209, 6889, 6104, 15035, 775, 4090, 13, 407, 309, 311, 3006, 13, 407, 383, 307, 1293, 295, 264, 3673, 293, 413, 6022, 295, 264, 3673, 13, 407, 383, 307, 264, 3006, 1867, 13, 407, 2171, 1310, 456, 307, 787, 472, 1867, 13, 2704, 294, 661, 2740, 11, 309, 1062, 312, 732, 6338, 366, 3006, 13, 407, 337, 341, 472, 11, 363, 293, 383, 13], "avg_logprob": -0.20107887064417204, "compression_ratio": 1.679245283018868, "no_speech_prob": 0.0, "words": [{"start": 275.94, "end": 276.46, "word": " Also,", "probability": 0.755859375}, {"start": 276.72, "end": 277.04, "word": " this", "probability": 0.94287109375}, {"start": 277.04, "end": 277.3, "word": " one", "probability": 0.9326171875}, {"start": 277.3, "end": 277.46, "word": " is", "probability": 0.94482421875}, {"start": 277.46, "end": 277.8, "word": " correct.", "probability": 0.8681640625}, {"start": 278.86, 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Number three, which of the following is not true about the student's T distribution? Here, we are talking about the not true statement about the student T distribution, A. 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That's correct because we mentioned last time that T distribution, the tail is fatter than the Z normal. So that means it has more data in the tails and less data in the center. So that's correct.", "tokens": [293, 1570, 294, 264, 3056, 813, 775, 264, 2710, 7316, 13, 663, 311, 3006, 570, 321, 2835, 1036, 565, 300, 314, 7316, 11, 264, 6838, 307, 283, 1161, 813, 264, 1176, 2710, 13, 407, 300, 1355, 309, 575, 544, 1412, 294, 264, 28537, 293, 1570, 1412, 294, 264, 3056, 13, 407, 300, 311, 3006, 13], "avg_logprob": -0.18136160980377877, "compression_ratio": 1.7465753424657535, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 332.98, "end": 333.34, "word": " and", "probability": 0.334716796875}, {"start": 333.34, "end": 333.62, "word": " less", "probability": 0.900390625}, {"start": 333.62, "end": 333.84, "word": " in", "probability": 0.93115234375}, {"start": 333.84, "end": 334.02, "word": " the", "probability": 0.92236328125}, {"start": 334.02, "end": 334.36, "word": " center", "probability": 0.91845703125}, {"start": 334.36, "end": 334.88, "word": " than", "probability": 0.82373046875}, {"start": 334.88, "end": 335.18, "word": " does", "probability": 0.85791015625}, {"start": 335.18, "end": 335.44, "word": " the", "probability": 0.8935546875}, {"start": 335.44, "end": 335.78, "word": " normal", "probability": 0.87548828125}, {"start": 335.78, "end": 336.48, "word": " distribution.", "probability": 0.83203125}, {"start": 336.66, "end": 336.88, "word": " That's", "probability": 0.862060546875}, {"start": 336.88, "end": 337.18, "word": " correct", "probability": 0.90771484375}, {"start": 337.18, "end": 337.68, "word": " because", "probability": 0.64111328125}, {"start": 337.68, "end": 338.32, "word": " we", "probability": 0.8828125}, {"start": 338.32, "end": 338.58, "word": " mentioned", "probability": 0.84130859375}, {"start": 338.58, "end": 338.86, "word": " last", "probability": 0.85888671875}, {"start": 338.86, "end": 339.26, "word": " time", "probability": 0.88818359375}, {"start": 339.26, "end": 339.92, "word": " that", "probability": 0.875}, {"start": 339.92, "end": 340.68, "word": " T", "probability": 0.30517578125}, {"start": 340.68, "end": 341.3, "word": " distribution,", "probability": 0.69482421875}, {"start": 341.74, "end": 341.88, "word": " the", "probability": 0.8857421875}, {"start": 341.88, "end": 342.3, "word": " tail", "probability": 0.8056640625}, {"start": 342.3, "end": 343.54, "word": " is", "probability": 0.5791015625}, {"start": 343.54, "end": 344.16, "word": " fatter", "probability": 0.8828125}, {"start": 344.16, "end": 344.64, "word": " than", "probability": 0.94140625}, {"start": 344.64, "end": 345.5, "word": " the", "probability": 0.89404296875}, {"start": 345.5, "end": 345.64, "word": " Z", "probability": 0.8095703125}, {"start": 345.64, "end": 346.02, "word": " normal.", "probability": 0.7548828125}, {"start": 346.38, "end": 346.48, "word": " So", "probability": 0.88623046875}, {"start": 346.48, "end": 346.7, "word": " that", "probability": 0.86376953125}, {"start": 346.7, "end": 346.92, "word": " means", "probability": 0.93359375}, {"start": 346.92, "end": 347.08, "word": " it", "probability": 0.9248046875}, {"start": 347.08, "end": 347.3, "word": " has", "probability": 0.94189453125}, {"start": 347.3, "end": 347.58, "word": " more", "probability": 0.939453125}, {"start": 347.58, "end": 348.0, "word": " data", "probability": 0.94384765625}, {"start": 348.0, "end": 348.56, "word": " in", "probability": 0.94140625}, {"start": 348.56, "end": 348.7, "word": " the", "probability": 0.92529296875}, {"start": 348.7, "end": 349.06, "word": " tails", "probability": 0.8056640625}, {"start": 349.06, "end": 349.68, "word": " and", "probability": 0.83642578125}, {"start": 349.68, "end": 349.98, "word": " less", "probability": 0.9326171875}, {"start": 349.98, "end": 350.36, "word": " data", "probability": 0.9267578125}, {"start": 350.36, "end": 350.54, "word": " in", "probability": 0.943359375}, {"start": 350.54, "end": 350.7, "word": " the", "probability": 0.91943359375}, {"start": 350.7, "end": 350.96, "word": " center.", "probability": 0.90771484375}, {"start": 351.88, "end": 352.1, "word": " So", "probability": 0.95458984375}, {"start": 352.1, "end": 352.34, "word": " that's", "probability": 0.948486328125}, {"start": 352.34, "end": 352.72, "word": " correct.", "probability": 0.900390625}], "temperature": 1.0}, {"id": 14, "seek": 38326, "start": 358.0, "end": 383.26, "text": " It is used to construct confidence intervals for the population mean when the population standard deviation is known. No, we use z instead of t, so this one is incorrect about t. It is well-shaped and symmetrical, so that's true, so we are looking for the incorrect statement. 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That's true. So which one? P. So P is incorrect. So number four. Extra. Can you explain the average total compensation of CEOs in the service industry? 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Which of the following interpretations is correct? Part number A.", "tokens": [23399, 4, 6687, 15035, 390, 15598, 281, 312, 1848, 11205, 16, 11, 1848, 17, 4550, 11, 1848, 20419, 11309, 11, 293, 1848, 37078, 13, 3013, 295, 264, 3480, 37547, 307, 3006, 30, 4100, 1230, 316, 13], "avg_logprob": -0.29919763191326243, "compression_ratio": 1.1382113821138211, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 416.36, "end": 416.82, "word": " 97", "probability": 0.40966796875}, {"start": 416.82, "end": 417.48, "word": "%", "probability": 0.6455078125}, {"start": 417.48, "end": 418.02, "word": " confidence", "probability": 0.92578125}, {"start": 418.02, "end": 418.72, "word": " interval", "probability": 0.962890625}, {"start": 418.72, "end": 419.8, "word": " was", "probability": 0.86279296875}, {"start": 419.8, "end": 420.5, "word": " calculated", "probability": 0.9560546875}, {"start": 420.5, "end": 421.2, "word": " to", "probability": 0.94482421875}, {"start": 421.2, "end": 421.7, "word": " be", "probability": 0.9443359375}, {"start": 421.7, "end": 426.04, "word": " $281,", "probability": 0.4589436848958333}, {"start": 427.04, "end": 429.02, "word": " $260,", "probability": 0.7288411458333334}, {"start": 430.06, "end": 433.78, "word": " $5836,", "probability": 0.7646484375}, {"start": 434.8, "end": 435.02, "word": " and", "probability": 0.8427734375}, {"start": 435.02, "end": 436.0, "word": " $180.", "probability": 0.928955078125}, {"start": 437.22, "end": 437.6, "word": " Which", "probability": 0.8525390625}, {"start": 437.6, "end": 437.88, "word": " of", "probability": 0.95703125}, {"start": 437.88, "end": 438.12, "word": " the", "probability": 0.91845703125}, {"start": 438.12, "end": 438.5, "word": " following", "probability": 0.82373046875}, {"start": 438.5, "end": 439.3, "word": " interpretations", "probability": 0.8291015625}, {"start": 439.3, "end": 440.0, "word": " is", "probability": 0.93505859375}, {"start": 440.0, "end": 440.52, "word": " correct?", "probability": 0.8837890625}, {"start": 442.56, "end": 443.06, "word": " Part", "probability": 0.7109375}, {"start": 443.06, "end": 443.36, "word": " number", "probability": 0.93212890625}, {"start": 443.36, "end": 443.6, "word": " A.", "probability": 0.5556640625}], "temperature": 1.0}, {"id": 17, "seek": 47207, "start": 444.37, "end": 472.07, "text": " It says 97% of the sample data compensation value between these two values, correct or incorrect statement. Because it says 97% of the sample data. For the confidence center value, we are looking for the average, not for the population, not for the sample. So A is incorrect.", "tokens": [467, 1619, 23399, 4, 295, 264, 6889, 1412, 19644, 2158, 1296, 613, 732, 4190, 11, 3006, 420, 18424, 5629, 13, 1436, 309, 1619, 23399, 4, 295, 264, 6889, 1412, 13, 1171, 264, 6687, 3056, 2158, 11, 321, 366, 1237, 337, 264, 4274, 11, 406, 337, 264, 4415, 11, 406, 337, 264, 6889, 13, 407, 316, 307, 18424, 13], "avg_logprob": -0.18008475081395295, "compression_ratio": 1.6932515337423313, "no_speech_prob": 0.0, "words": [{"start": 444.37, "end": 444.65, "word": " It", "probability": 0.5625}, {"start": 444.65, "end": 445.15, "word": " says", "probability": 0.8681640625}, {"start": 445.15, "end": 445.91, "word": " 97", "probability": 0.83935546875}, {"start": 445.91, "end": 446.67, "word": "%", "probability": 0.904296875}, {"start": 446.67, "end": 447.09, "word": " of", "probability": 0.93212890625}, {"start": 447.09, "end": 447.31, "word": " the", "probability": 0.91748046875}, {"start": 447.31, "end": 447.61, "word": " sample", "probability": 0.82080078125}, {"start": 447.61, "end": 448.31, "word": " data", "probability": 0.92724609375}, {"start": 448.31, "end": 449.79, "word": " compensation", "probability": 0.352294921875}, {"start": 449.79, "end": 450.41, "word": " value", "probability": 0.978515625}, {"start": 450.41, "end": 451.93, "word": " between", "probability": 0.85888671875}, {"start": 451.93, "end": 452.29, "word": " these", "probability": 0.85888671875}, {"start": 452.29, "end": 452.45, "word": " two", "probability": 0.921875}, {"start": 452.45, "end": 452.85, "word": " values,", "probability": 0.97314453125}, {"start": 454.27, "end": 454.79, "word": " correct", "probability": 0.91259765625}, {"start": 454.79, "end": 455.03, "word": " or", "probability": 0.9658203125}, {"start": 455.03, "end": 455.47, "word": " incorrect", "probability": 0.9482421875}, {"start": 455.47, "end": 455.91, "word": " statement.", "probability": 0.92236328125}, {"start": 456.49, "end": 457.07, "word": " Because", "probability": 0.9306640625}, {"start": 457.07, "end": 457.31, "word": " it", "probability": 0.939453125}, {"start": 457.31, "end": 457.67, "word": " says", "probability": 0.880859375}, {"start": 457.67, "end": 458.97, "word": " 97", "probability": 0.93994140625}, {"start": 458.97, "end": 459.47, "word": "%", "probability": 0.99560546875}, {"start": 459.47, "end": 461.05, "word": " of", "probability": 0.96630859375}, {"start": 461.05, "end": 461.29, "word": " the", "probability": 0.923828125}, {"start": 461.29, "end": 461.61, "word": " sample", "probability": 0.8779296875}, {"start": 461.61, "end": 462.71, "word": " data.", "probability": 0.91845703125}, {"start": 463.59, "end": 463.83, "word": " For", "probability": 0.94921875}, {"start": 463.83, "end": 463.99, "word": " the", "probability": 0.89404296875}, {"start": 463.99, "end": 464.31, "word": " confidence", "probability": 0.5908203125}, {"start": 464.31, "end": 464.71, "word": " center", "probability": 0.76806640625}, {"start": 464.71, "end": 464.93, "word": " value,", "probability": 0.7158203125}, {"start": 465.03, "end": 465.11, "word": " we", "probability": 0.9140625}, {"start": 465.11, "end": 465.21, "word": " are", "probability": 0.931640625}, {"start": 465.21, "end": 465.51, "word": " looking", "probability": 0.9140625}, {"start": 465.51, "end": 466.03, "word": " for", "probability": 0.94775390625}, {"start": 466.03, "end": 466.77, "word": " the", "probability": 0.8095703125}, {"start": 466.77, "end": 467.21, "word": " average,", "probability": 0.76953125}, {"start": 468.15, "end": 468.31, "word": " not", "probability": 0.7177734375}, {"start": 468.31, "end": 468.51, "word": " for", "probability": 0.94775390625}, {"start": 468.51, "end": 468.67, "word": " the", "probability": 0.91455078125}, {"start": 468.67, "end": 469.83, "word": " population,", "probability": 0.8232421875}, {"start": 470.01, "end": 470.11, "word": " not", "probability": 0.93017578125}, {"start": 470.11, "end": 470.27, "word": " for", "probability": 0.94287109375}, {"start": 470.27, "end": 470.41, "word": " the", "probability": 0.923828125}, {"start": 470.41, "end": 470.69, "word": " sample.", "probability": 0.89453125}, {"start": 471.13, "end": 471.39, "word": " So", "probability": 0.966796875}, {"start": 471.39, "end": 471.59, "word": " A", "probability": 0.57861328125}, {"start": 471.59, "end": 471.69, "word": " is", "probability": 0.9375}, {"start": 471.69, "end": 472.07, "word": " incorrect.", "probability": 0.93310546875}], "temperature": 1.0}, {"id": 18, "seek": 50127, "start": 472.85, "end": 501.27, "text": " Because A, it says here 97% of the sampling total. Sample total, we are looking for the average of the population. So A is incorrect statement. B, we are 97% confident that the mean of the sample. So it's false. Because the confidence about the entire population is about the population mean. 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So D is the correct statement. So for the confidence interval, we are looking for population, number one. Number two, the average of that population. So D is the correct answer. Let's go back to part A. In part A, it says sample total. So this is incorrect. Next one. The mean of the sample. We are looking for the mean of the population. So B is incorrect. 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So this one is incorrect. Finally here, we are 97% confident that the average total. So this one is true of all. So here we have population and the average of that population. So it makes sense that this is the correct answer. 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Confidence interval was used to estimate the proportion of statistics students that are females. A random sample of 72 statistics students generated the following 90% confidence interval, 0.438 and 0.640.", "tokens": [5118, 1732, 11, 6687, 15035, 13, 11701, 2778, 15035, 390, 1143, 281, 12539, 264, 16068, 295, 12523, 1731, 300, 366, 21529, 13, 316, 4974, 6889, 295, 18731, 12523, 1731, 10833, 264, 3480, 4289, 4, 6687, 15035, 11, 1958, 13, 19, 12625, 293, 1958, 13, 21, 5254, 13], "avg_logprob": -0.21468098678936562, "compression_ratio": 1.5933333333333333, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 599.69, "end": 600.03, "word": " Number", "probability": 0.61767578125}, {"start": 600.03, "end": 600.37, "word": " five,", "probability": 0.76220703125}, {"start": 600.49, "end": 600.87, "word": " confidence", "probability": 0.662109375}, {"start": 600.87, "end": 601.41, "word": " interval.", "probability": 0.96630859375}, {"start": 602.67, "end": 603.29, "word": " Confidence", "probability": 0.773193359375}, {"start": 603.29, "end": 603.85, "word": " interval", "probability": 0.96484375}, {"start": 603.85, "end": 604.29, "word": " was", "probability": 0.93896484375}, {"start": 604.29, "end": 604.67, "word": " used", "probability": 0.9228515625}, {"start": 604.67, "end": 604.93, "word": " to", "probability": 0.95751953125}, {"start": 604.93, "end": 605.35, "word": " estimate", "probability": 0.91064453125}, {"start": 605.35, "end": 605.71, "word": " the", "probability": 0.8828125}, {"start": 605.71, "end": 606.35, "word": " proportion", "probability": 0.83740234375}, {"start": 606.35, "end": 606.61, "word": " of", "probability": 0.9677734375}, {"start": 606.61, "end": 607.27, "word": " statistics", "probability": 0.62939453125}, {"start": 607.27, "end": 607.83, "word": " students", "probability": 0.76904296875}, {"start": 607.83, "end": 608.15, "word": " that", "probability": 0.904296875}, {"start": 608.15, "end": 608.47, "word": " are", "probability": 0.94384765625}, {"start": 608.47, "end": 609.17, "word": " females.", "probability": 0.92822265625}, {"start": 609.81, "end": 609.95, "word": " A", "probability": 0.6845703125}, {"start": 609.95, "end": 610.17, "word": " random", "probability": 0.85498046875}, {"start": 610.17, "end": 610.55, "word": " sample", "probability": 0.73291015625}, {"start": 610.55, "end": 610.95, "word": " of", "probability": 0.96875}, {"start": 610.95, "end": 612.79, "word": " 72", "probability": 0.6240234375}, {"start": 612.79, "end": 614.25, "word": " statistics", "probability": 0.86083984375}, {"start": 614.25, "end": 614.85, "word": " students", "probability": 0.84375}, {"start": 614.85, "end": 615.77, "word": " generated", "probability": 0.8642578125}, {"start": 615.77, "end": 616.17, "word": " the", "probability": 0.8505859375}, {"start": 616.17, "end": 616.49, "word": " following", "probability": 0.865234375}, {"start": 616.49, "end": 617.11, "word": " 90", "probability": 0.84033203125}, {"start": 617.11, "end": 617.49, "word": "%", "probability": 0.90283203125}, {"start": 617.49, "end": 617.99, "word": " confidence", "probability": 0.97216796875}, {"start": 617.99, "end": 618.61, "word": " interval,", "probability": 0.9501953125}, {"start": 619.39, "end": 619.71, "word": " 0", "probability": 0.359619140625}, {"start": 619.71, "end": 622.97, "word": ".438", "probability": 0.93505859375}, {"start": 622.97, "end": 624.21, "word": " and", "probability": 0.43505859375}, {"start": 624.21, "end": 624.97, "word": " 0", "probability": 0.873046875}, {"start": 624.97, "end": 628.15, "word": ".640.", "probability": 0.7085774739583334}], "temperature": 1.0}, {"id": 23, "seek": 65335, "start": 628.51, "end": 653.35, "text": " 42, based on the interval above the population proportion of females equals to 0.6. So here we have confidence interval for the female proportion ranges between 0.438 up to 0.642. Based on this interval.", "tokens": [14034, 11, 2361, 322, 264, 15035, 3673, 264, 4415, 16068, 295, 21529, 6915, 281, 1958, 13, 21, 13, 407, 510, 321, 362, 6687, 15035, 337, 264, 6556, 16068, 22526, 1296, 1958, 13, 19, 12625, 493, 281, 1958, 13, 21, 15628, 13, 18785, 322, 341, 15035, 13], "avg_logprob": -0.2337101108216225, "compression_ratio": 1.5, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 628.51, "end": 628.97, "word": " 42,", "probability": 0.267578125}, {"start": 629.51, "end": 630.03, "word": " based", "probability": 0.84228515625}, {"start": 630.03, "end": 630.21, "word": " on", "probability": 0.947265625}, {"start": 630.21, "end": 630.35, "word": " the", "probability": 0.91845703125}, {"start": 630.35, "end": 630.69, "word": " interval", "probability": 0.87939453125}, {"start": 630.69, "end": 631.23, "word": " above", "probability": 0.93603515625}, {"start": 631.23, "end": 631.67, "word": " the", "probability": 0.83056640625}, {"start": 631.67, "end": 632.89, "word": " population", "probability": 0.93896484375}, {"start": 632.89, "end": 633.59, "word": " proportion", "probability": 0.82275390625}, {"start": 633.59, "end": 634.21, "word": " of", "probability": 0.890625}, {"start": 634.21, "end": 634.63, "word": " females", "probability": 0.92919921875}, {"start": 634.63, "end": 635.19, "word": " equals", "probability": 0.84814453125}, {"start": 635.19, "end": 636.13, "word": " to", "probability": 0.8232421875}, {"start": 636.13, "end": 636.85, "word": " 0", "probability": 0.3525390625}, {"start": 636.85, "end": 637.57, "word": ".6.", "probability": 0.957275390625}, {"start": 637.71, "end": 637.87, "word": " So", "probability": 0.58349609375}, {"start": 637.87, "end": 638.09, "word": " here", "probability": 0.75439453125}, {"start": 638.09, "end": 638.23, "word": " we", "probability": 0.79541015625}, {"start": 638.23, "end": 638.65, "word": " have", "probability": 0.93701171875}, {"start": 638.65, "end": 639.65, "word": " confidence", "probability": 0.478759765625}, {"start": 639.65, "end": 640.09, "word": " interval", "probability": 0.955078125}, {"start": 640.09, "end": 642.01, "word": " for", "probability": 0.8369140625}, {"start": 642.01, "end": 642.15, "word": " the", "probability": 0.916015625}, {"start": 642.15, "end": 643.63, "word": " female", "probability": 0.85205078125}, {"start": 643.63, "end": 644.31, "word": " proportion", "probability": 0.81494140625}, {"start": 644.31, "end": 646.11, "word": " ranges", "probability": 0.38330078125}, {"start": 646.11, "end": 646.65, "word": " between", "probability": 0.86083984375}, {"start": 646.65, "end": 647.55, "word": " 0", "probability": 0.96923828125}, {"start": 647.55, "end": 648.25, "word": ".438", "probability": 0.8951822916666666}, {"start": 648.25, "end": 649.41, "word": " up", "probability": 0.96044921875}, {"start": 649.41, "end": 649.53, "word": " to", "probability": 0.9560546875}, {"start": 649.53, "end": 649.73, "word": " 0", "probability": 0.97900390625}, {"start": 649.73, "end": 650.49, "word": ".642.", "probability": 0.9627278645833334}, {"start": 651.51, "end": 651.93, "word": " Based", "probability": 0.2403564453125}, {"start": 651.93, "end": 652.75, "word": " on", "probability": 0.94873046875}, {"start": 652.75, "end": 652.99, "word": " this", "probability": 0.92041015625}, {"start": 652.99, "end": 653.35, "word": " interval.", "probability": 0.96337890625}], "temperature": 1.0}, {"id": 24, "seek": 68093, "start": 654.21, "end": 680.93, "text": " Is the population proportion of females equal 60%? So here we have from this point all the way up to 0.6. Is the population proportion of females equal to 0.6? No. The answer is no, but know what? Number A. No, and we are 90% sure of it.", "tokens": [1119, 264, 4415, 16068, 295, 21529, 2681, 4060, 4, 30, 407, 510, 321, 362, 490, 341, 935, 439, 264, 636, 493, 281, 1958, 13, 21, 13, 1119, 264, 4415, 16068, 295, 21529, 2681, 281, 1958, 13, 21, 30, 883, 13, 440, 1867, 307, 572, 11, 457, 458, 437, 30, 5118, 316, 13, 883, 11, 293, 321, 366, 4289, 4, 988, 295, 309, 13], "avg_logprob": -0.20629883324727416, "compression_ratio": 1.5454545454545454, "no_speech_prob": 0.0, "words": [{"start": 654.21, "end": 654.55, "word": " Is", "probability": 0.6005859375}, {"start": 654.55, "end": 654.69, "word": " the", "probability": 0.88330078125}, {"start": 654.69, "end": 655.11, "word": " population", "probability": 0.88671875}, {"start": 655.11, "end": 655.65, "word": " proportion", "probability": 0.7744140625}, {"start": 655.65, "end": 656.37, "word": " of", "probability": 0.951171875}, {"start": 656.37, "end": 657.05, "word": " females", "probability": 0.8779296875}, {"start": 657.05, "end": 657.51, "word": " equal", "probability": 0.708984375}, {"start": 657.51, "end": 658.29, "word": " 60", "probability": 0.480712890625}, {"start": 658.29, "end": 658.77, "word": "%?", "probability": 0.86083984375}, {"start": 663.41, "end": 664.01, "word": " So", "probability": 0.73779296875}, {"start": 664.01, "end": 664.19, "word": " here", "probability": 0.7509765625}, {"start": 664.19, "end": 664.33, "word": " we", "probability": 0.8798828125}, {"start": 664.33, "end": 664.57, "word": " have", "probability": 0.93896484375}, {"start": 664.57, "end": 664.95, "word": " from", "probability": 0.7998046875}, {"start": 664.95, "end": 665.37, "word": " this", "probability": 0.939453125}, {"start": 665.37, "end": 665.77, "word": " point", "probability": 0.95849609375}, {"start": 665.77, "end": 666.09, "word": " all", "probability": 0.818359375}, {"start": 666.09, "end": 666.25, "word": " the", "probability": 0.9111328125}, {"start": 666.25, "end": 666.39, "word": " way", "probability": 0.9541015625}, {"start": 666.39, "end": 666.55, "word": " up", "probability": 0.92041015625}, {"start": 666.55, "end": 666.69, "word": " to", "probability": 0.9599609375}, {"start": 666.69, "end": 666.91, "word": " 0", "probability": 0.37646484375}, {"start": 666.91, "end": 667.31, "word": ".6.", "probability": 0.98486328125}, {"start": 668.03, "end": 668.29, "word": " Is", "probability": 0.95947265625}, {"start": 668.29, "end": 668.47, "word": " the", "probability": 0.91015625}, {"start": 668.47, "end": 668.87, "word": " population", "probability": 0.93994140625}, {"start": 668.87, "end": 669.47, "word": " proportion", "probability": 0.8525390625}, {"start": 669.47, "end": 669.73, "word": " of", "probability": 0.9638671875}, {"start": 669.73, "end": 670.13, "word": " females", "probability": 0.92041015625}, {"start": 670.13, "end": 670.61, "word": " equal", "probability": 0.9111328125}, {"start": 670.61, "end": 670.83, "word": " to", "probability": 0.8271484375}, {"start": 670.83, "end": 670.99, "word": " 0", "probability": 0.96337890625}, {"start": 670.99, "end": 671.41, "word": ".6?", "probability": 0.998779296875}, {"start": 673.05, "end": 673.65, "word": " No.", "probability": 0.71484375}, {"start": 674.41, "end": 674.67, "word": " The", "probability": 0.853515625}, {"start": 674.67, "end": 674.93, "word": " answer", "probability": 0.953125}, {"start": 674.93, "end": 675.19, "word": " is", "probability": 0.94921875}, {"start": 675.19, "end": 675.45, "word": " no,", "probability": 0.7412109375}, {"start": 675.51, "end": 675.69, "word": " but", "probability": 0.923828125}, {"start": 675.69, "end": 675.95, "word": " know", "probability": 0.43408203125}, {"start": 675.95, "end": 676.25, "word": " what?", "probability": 0.9521484375}, {"start": 676.85, "end": 677.09, "word": " Number", "probability": 0.67431640625}, {"start": 677.09, "end": 677.27, "word": " A.", "probability": 0.50341796875}, {"start": 677.91, "end": 678.33, "word": " No,", "probability": 0.82080078125}, {"start": 678.47, "end": 678.71, "word": " and", "probability": 0.92578125}, {"start": 678.71, "end": 678.87, "word": " we", "probability": 0.9521484375}, {"start": 678.87, "end": 679.05, "word": " are", "probability": 0.845703125}, {"start": 679.05, "end": 679.51, "word": " 90", "probability": 0.888671875}, {"start": 679.51, "end": 680.25, "word": "%", "probability": 0.95263671875}, {"start": 680.25, "end": 680.57, "word": " sure", "probability": 0.486328125}, {"start": 680.57, "end": 680.71, "word": " of", "probability": 0.93212890625}, {"start": 680.71, "end": 680.93, "word": " it.", "probability": 0.88232421875}], "temperature": 1.0}, {"id": 25, "seek": 70490, "start": 683.64, "end": 704.9, "text": " No, the proportion is 54.17. See, maybe 60% is a believable value of population proportion based on information about it. He said yes, and we are 90% sure of it. So which one is correct? Farah. Which one is correct?", "tokens": [883, 11, 264, 16068, 307, 20793, 13, 7773, 13, 3008, 11, 1310, 4060, 4, 307, 257, 1351, 17915, 2158, 295, 4415, 16068, 2361, 322, 1589, 466, 309, 13, 634, 848, 2086, 11, 293, 321, 366, 4289, 4, 988, 295, 309, 13, 407, 597, 472, 307, 3006, 30, 9067, 545, 13, 3013, 472, 307, 3006, 30], "avg_logprob": -0.21679687313735485, "compression_ratio": 1.411764705882353, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 683.64, "end": 684.06, "word": " No,", "probability": 0.5673828125}, {"start": 684.2, "end": 684.32, "word": " the", "probability": 0.8955078125}, {"start": 684.32, "end": 684.8, "word": " proportion", "probability": 0.79345703125}, {"start": 684.8, "end": 685.22, "word": " is", "probability": 0.9443359375}, {"start": 685.22, "end": 685.88, "word": " 54", "probability": 0.95703125}, {"start": 685.88, "end": 686.78, "word": ".17.", "probability": 0.960693359375}, {"start": 688.14, "end": 688.74, "word": " See,", "probability": 0.4384765625}, {"start": 689.24, "end": 689.64, "word": " maybe", "probability": 0.9228515625}, {"start": 689.64, "end": 690.34, "word": " 60", "probability": 0.85302734375}, {"start": 690.34, "end": 690.58, "word": "%", "probability": 0.833984375}, {"start": 690.58, "end": 691.04, "word": " is", "probability": 0.94384765625}, {"start": 691.04, "end": 691.2, "word": " a", "probability": 0.96044921875}, {"start": 691.2, "end": 691.62, "word": " believable", "probability": 0.905029296875}, {"start": 691.62, "end": 692.08, "word": " value", "probability": 0.89794921875}, {"start": 692.08, "end": 692.32, "word": " of", "probability": 0.52197265625}, {"start": 692.32, "end": 692.76, "word": " population", "probability": 0.8779296875}, {"start": 692.76, "end": 693.24, "word": " proportion", "probability": 0.82861328125}, {"start": 693.24, "end": 693.62, "word": " based", "probability": 0.8115234375}, {"start": 693.62, "end": 693.76, "word": " on", "probability": 0.9228515625}, {"start": 693.76, "end": 694.26, "word": " information", "probability": 0.434814453125}, {"start": 694.26, "end": 694.62, "word": " about", "probability": 0.85498046875}, {"start": 694.62, "end": 694.94, "word": " it.", "probability": 0.603515625}, {"start": 695.74, "end": 695.96, "word": " He", "probability": 0.5830078125}, {"start": 695.96, "end": 696.24, "word": " said", "probability": 0.29150390625}, {"start": 696.24, "end": 696.58, "word": " yes,", "probability": 0.673828125}, {"start": 696.72, "end": 696.92, "word": " and", "probability": 0.92919921875}, {"start": 696.92, "end": 697.1, "word": " we", "probability": 0.92724609375}, {"start": 697.1, "end": 697.32, "word": " are", "probability": 0.853515625}, {"start": 697.32, "end": 697.66, "word": " 90", "probability": 0.95654296875}, {"start": 697.66, "end": 698.08, "word": "%", "probability": 0.97802734375}, {"start": 698.08, "end": 698.38, "word": " sure", "probability": 0.89990234375}, {"start": 698.38, "end": 698.54, "word": " of", "probability": 0.7763671875}, {"start": 698.54, "end": 698.68, "word": " it.", "probability": 0.90625}, {"start": 698.96, "end": 699.18, "word": " So", "probability": 0.8974609375}, {"start": 699.18, "end": 699.4, "word": " which", "probability": 0.8134765625}, {"start": 699.4, "end": 699.62, "word": " one", "probability": 0.9326171875}, {"start": 699.62, "end": 699.82, "word": " is", "probability": 0.943359375}, {"start": 699.82, "end": 700.22, "word": " correct?", "probability": 0.89892578125}, {"start": 702.58, "end": 703.26, "word": " Farah.", "probability": 0.7294921875}, {"start": 704.02, "end": 704.3, "word": " Which", "probability": 0.82666015625}, {"start": 704.3, "end": 704.46, "word": " one", "probability": 0.92724609375}, {"start": 704.46, "end": 704.6, "word": " is", "probability": 0.93896484375}, {"start": 704.6, "end": 704.9, "word": " correct?", "probability": 0.89599609375}], "temperature": 1.0}, {"id": 26, "seek": 73906, "start": 710.0, "end": 739.06, "text": " B says the proportion is 54. 54 if we take the average of these two values, the answer is 54. But the true proportion is not the average of the two endpoints. So B is incorrect. If you look at A, the answer is no. 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Now C, maybe. So C is the correct statement, maybe 60% is believable value of the population proportion based on the information about. So C is the correct answer. 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{"start": 831.88, "end": 832.1, "word": " minus", "probability": 0.986328125}, {"start": 832.1, "end": 832.34, "word": " 8", "probability": 0.986328125}, {"start": 832.34, "end": 833.28, "word": "%", "probability": 0.693359375}, {"start": 833.28, "end": 833.72, "word": " using", "probability": 0.732421875}, {"start": 833.72, "end": 834.2, "word": " 95", "probability": 0.98046875}, {"start": 834.2, "end": 834.46, "word": "%", "probability": 0.60546875}, {"start": 834.46, "end": 834.72, "word": " confidence.", "probability": 0.97607421875}], "temperature": 1.0}, {"id": 31, "seek": 86642, "start": 838.64, "end": 866.42, "text": " The formula first, n equals z squared c plus one. We have pi, one minus pi divided by e squared. Now, pi is not given. So in this case either we use a sinus sample in order to estimate the sample proportion,", "tokens": [440, 8513, 700, 11, 297, 6915, 710, 8889, 269, 1804, 472, 13, 492, 362, 3895, 11, 472, 3175, 3895, 6666, 538, 308, 8889, 13, 823, 11, 3895, 307, 406, 2212, 13, 407, 294, 341, 1389, 2139, 321, 764, 257, 41503, 6889, 294, 1668, 281, 12539, 264, 6889, 16068, 11], "avg_logprob": -0.348124994635582, "compression_ratio": 1.4344827586206896, "no_speech_prob": 0.0, "words": [{"start": 838.64, "end": 839.36, "word": " The", "probability": 0.440185546875}, {"start": 839.36, "end": 840.08, "word": " formula", "probability": 0.90234375}, {"start": 840.08, "end": 840.44, "word": " first,", "probability": 0.322998046875}, {"start": 840.54, "end": 840.72, "word": " n", "probability": 0.4892578125}, {"start": 840.72, "end": 841.44, "word": " equals", "probability": 0.70849609375}, {"start": 841.44, "end": 843.36, "word": " z", "probability": 0.72265625}, {"start": 843.36, "end": 843.98, "word": " squared", "probability": 0.7587890625}, {"start": 843.98, "end": 844.98, "word": " c", "probability": 0.1668701171875}, {"start": 844.98, "end": 845.26, "word": " plus", "probability": 0.84619140625}, {"start": 845.26, "end": 845.36, "word": " one.", "probability": 0.513671875}, {"start": 848.74, "end": 849.06, "word": " We", "probability": 0.58203125}, {"start": 849.06, "end": 849.34, "word": " have", "probability": 0.94775390625}, {"start": 849.34, "end": 849.82, "word": " pi,", "probability": 0.3984375}, {"start": 850.6, "end": 851.08, "word": " one", "probability": 0.87353515625}, {"start": 851.08, "end": 851.44, "word": " minus", "probability": 0.98583984375}, {"start": 851.44, "end": 851.76, "word": " pi", "probability": 0.92138671875}, {"start": 851.76, "end": 852.2, "word": " divided", "probability": 0.681640625}, {"start": 852.2, "end": 852.56, "word": " by", "probability": 0.97509765625}, {"start": 852.56, "end": 853.9, "word": " e", "probability": 0.58056640625}, {"start": 853.9, "end": 854.24, "word": " squared.", "probability": 0.79931640625}, {"start": 855.74, "end": 856.04, "word": " Now,", "probability": 0.955078125}, {"start": 856.14, "end": 856.3, "word": " pi", "probability": 0.8798828125}, {"start": 856.3, "end": 856.46, "word": " is", "probability": 0.9404296875}, {"start": 856.46, "end": 856.66, "word": " not", "probability": 0.94677734375}, {"start": 856.66, "end": 856.92, "word": " given.", "probability": 0.890625}, {"start": 859.34, "end": 860.06, "word": " So", "probability": 0.86279296875}, {"start": 860.06, "end": 860.2, "word": " in", "probability": 0.5927734375}, {"start": 860.2, "end": 860.36, "word": " this", "probability": 0.94775390625}, {"start": 860.36, "end": 860.58, "word": " case", "probability": 0.90380859375}, {"start": 860.58, "end": 860.9, "word": " either", "probability": 0.54931640625}, {"start": 860.9, "end": 861.12, "word": " we", "probability": 0.955078125}, {"start": 861.12, "end": 861.56, "word": " use", "probability": 0.88720703125}, {"start": 861.56, "end": 862.5, "word": " a", "probability": 0.83544921875}, {"start": 862.5, "end": 862.74, "word": " sinus", "probability": 0.11285400390625}, {"start": 862.74, "end": 863.12, "word": " sample", "probability": 0.88330078125}, {"start": 863.12, "end": 863.36, "word": " in", "probability": 0.93408203125}, {"start": 863.36, "end": 863.58, "word": " order", "probability": 0.9228515625}, {"start": 863.58, "end": 863.88, "word": " to", "probability": 0.96875}, {"start": 863.88, "end": 864.44, "word": " estimate", "probability": 0.9326171875}, {"start": 864.44, "end": 864.82, "word": " the", "probability": 0.92333984375}, {"start": 864.82, "end": 865.88, "word": " sample", "probability": 0.410888671875}, {"start": 865.88, "end": 866.42, "word": " proportion,", "probability": 0.78955078125}], "temperature": 1.0}, {"id": 32, "seek": 89192, "start": 867.24, "end": 891.92, "text": " Or use Pi to be 0.5. So in this case we have to use Pi 1 half. If you remember last time I gave you this equation. Z alpha over 2 divided by 2 squared. So we have this equation. Because Pi is not given, just use Pi to be 1 half. Or you may use this equation.", "tokens": [1610, 764, 17741, 281, 312, 1958, 13, 20, 13, 407, 294, 341, 1389, 321, 362, 281, 764, 17741, 502, 1922, 13, 759, 291, 1604, 1036, 565, 286, 2729, 291, 341, 5367, 13, 1176, 8961, 670, 568, 6666, 538, 568, 8889, 13, 407, 321, 362, 341, 5367, 13, 1436, 17741, 307, 406, 2212, 11, 445, 764, 17741, 281, 312, 502, 1922, 13, 1610, 291, 815, 764, 341, 5367, 13], "avg_logprob": -0.2323369504748911, "compression_ratio": 1.608695652173913, "no_speech_prob": 0.0, "words": [{"start": 867.24, "end": 867.58, "word": " Or", "probability": 0.65771484375}, {"start": 867.58, "end": 867.88, "word": " use", "probability": 0.74169921875}, {"start": 867.88, "end": 868.1, "word": " Pi", "probability": 0.54931640625}, {"start": 868.1, "end": 868.28, "word": " to", "probability": 0.9501953125}, {"start": 868.28, "end": 868.5, "word": " be", "probability": 0.93408203125}, {"start": 868.5, "end": 869.24, "word": " 0", "probability": 0.671875}, {"start": 869.24, "end": 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In this case, here we are talking about 95%. So what's the value of Z? 196. 2 times E. E is 8%. So 196 divided by 2 times E, the quantity squared. 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So approximately 150. So 150 is the correct answer. So again, here we used pi to be 1 half because P is not given. And simple calculation results in 150 for the sample size. So P is the correct answer, 7.", "tokens": [8451, 13, 407, 10447, 8451, 13, 407, 8451, 307, 264, 3006, 1867, 13, 407, 797, 11, 510, 321, 1143, 3895, 281, 312, 502, 1922, 570, 430, 307, 406, 2212, 13, 400, 2199, 17108, 3542, 294, 8451, 337, 264, 6889, 2744, 13, 407, 430, 307, 264, 3006, 1867, 11, 1614, 13], "avg_logprob": -0.18857231034952052, "compression_ratio": 1.4383561643835616, "no_speech_prob": 0.0, "words": [{"start": 923.22, "end": 923.98, "word": " 150.", "probability": 0.494140625}, {"start": 924.78, "end": 925.54, "word": " So", "probability": 0.93115234375}, {"start": 925.54, "end": 926.1, "word": " approximately", "probability": 0.81396484375}, {"start": 926.1, "end": 928.72, "word": " 150.", "probability": 0.8359375}, {"start": 929.16, "end": 929.46, "word": " So", "probability": 0.91796875}, {"start": 929.46, "end": 929.76, "word": " 150", "probability": 0.869140625}, {"start": 929.76, "end": 930.06, "word": " is", "probability": 0.9462890625}, {"start": 930.06, "end": 930.2, "word": " the", "probability": 0.91162109375}, {"start": 930.2, "end": 930.64, "word": " correct", "probability": 0.9208984375}, {"start": 930.64, "end": 931.7, "word": " answer.", "probability": 0.95849609375}, {"start": 932.34, "end": 932.8, "word": " So", "probability": 0.947265625}, {"start": 932.8, "end": 933.06, "word": " again,", "probability": 0.91650390625}, {"start": 933.28, "end": 933.34, "word": " here", "probability": 0.85595703125}, {"start": 933.34, "end": 933.52, "word": " we", "probability": 0.84375}, {"start": 933.52, "end": 933.9, "word": " used", "probability": 0.77490234375}, {"start": 933.9, "end": 935.32, "word": " pi", "probability": 0.755859375}, {"start": 935.32, "end": 936.26, "word": " to", "probability": 0.9541015625}, {"start": 936.26, "end": 936.5, "word": " be", "probability": 0.93212890625}, {"start": 936.5, "end": 936.9, "word": " 1", "probability": 0.6396484375}, {"start": 936.9, "end": 937.16, "word": " half", "probability": 0.007434844970703125}, {"start": 937.16, "end": 937.54, "word": " because", "probability": 0.6337890625}, {"start": 937.54, "end": 938.46, "word": " P", "probability": 0.3466796875}, {"start": 938.46, "end": 938.6, "word": " is", "probability": 0.9462890625}, {"start": 938.6, "end": 938.78, "word": " not", "probability": 0.94677734375}, {"start": 938.78, "end": 939.02, "word": " given.", "probability": 0.9052734375}, {"start": 941.06, "end": 941.46, "word": " And", "probability": 0.9453125}, {"start": 941.46, "end": 941.94, "word": " simple", "probability": 0.9013671875}, {"start": 941.94, "end": 942.48, "word": " calculation", "probability": 0.91064453125}, {"start": 942.48, "end": 943.94, "word": " results", "probability": 0.916015625}, {"start": 943.94, "end": 945.02, "word": " in", "probability": 0.9150390625}, {"start": 945.02, "end": 945.62, "word": " 150", "probability": 0.89404296875}, {"start": 945.62, "end": 946.2, "word": " for", "probability": 0.921875}, {"start": 946.2, "end": 946.34, "word": " the", "probability": 0.73046875}, {"start": 946.34, "end": 946.58, "word": " sample", "probability": 0.85546875}, {"start": 946.58, "end": 946.96, "word": " size.", "probability": 0.8447265625}, {"start": 947.3, "end": 947.6, "word": " So", "probability": 0.96630859375}, {"start": 947.6, "end": 947.8, "word": " P", "probability": 0.67822265625}, {"start": 947.8, "end": 948.02, "word": " is", "probability": 0.9501953125}, {"start": 948.02, "end": 948.18, "word": " the", "probability": 0.91162109375}, {"start": 948.18, "end": 948.52, "word": " correct", "probability": 0.90673828125}, {"start": 948.52, "end": 948.98, "word": " answer,", "probability": 0.9580078125}, {"start": 949.54, "end": 949.82, "word": " 7.", "probability": 0.5009765625}], "temperature": 1.0}, {"id": 35, "seek": 97796, "start": 955.22, "end": 977.96, "text": " Number seven. Number seven. When determining the sample size necessarily for estimating the true population mean, which factor is not considered when sampling with replacement? 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Now, the population size, the population size is not in this quantity, so A is the correct answer. B, the population standard deviation, sigma is here. C, the level of confidence desired in the estimate, we have Z.", "tokens": [823, 11, 597, 5952, 307, 406, 4888, 562, 21179, 1553, 3364, 14419, 30, 823, 11, 264, 4415, 2744, 11, 264, 4415, 2744, 307, 406, 294, 341, 11275, 11, 370, 316, 307, 264, 3006, 1867, 13, 363, 11, 264, 4415, 3832, 25163, 11, 12771, 307, 510, 13, 383, 11, 264, 1496, 295, 6687, 14721, 294, 264, 12539, 11, 321, 362, 1176, 13], "avg_logprob": -0.22316028562284285, "compression_ratio": 1.6010928961748634, "no_speech_prob": 0.0, "words": [{"start": 998.82, "end": 999.34, "word": " Now,", "probability": 0.066650390625}, {"start": 1000.68, "end": 1000.88, "word": " which", "probability": 0.865234375}, {"start": 1000.88, "end": 1001.5, "word": " factor", "probability": 0.8154296875}, {"start": 1001.5, "end": 1001.92, "word": " is", "probability": 0.93017578125}, {"start": 1001.92, "end": 1002.14, "word": " not", "probability": 0.923828125}, {"start": 1002.14, "end": 1002.7, "word": " considered", "probability": 0.771484375}, {"start": 1002.7, "end": 1002.96, "word": " when", "probability": 0.86474609375}, {"start": 1002.96, "end": 1003.46, "word": " sampling", "probability": 0.95654296875}, {"start": 1003.46, "end": 1004.48, "word": " without", "probability": 0.4814453125}, {"start": 1004.48, "end": 1004.8, "word": " weight", "probability": 0.41064453125}, {"start": 1004.8, "end": 1005.2, "word": " replacement?", "probability": 0.85595703125}, {"start": 1006.14, "end": 1006.38, "word": " Now,", "probability": 0.62548828125}, {"start": 1006.58, "end": 1006.8, "word": " the", "probability": 0.8046875}, {"start": 1006.8, "end": 1007.12, "word": " population", "probability": 0.97607421875}, {"start": 1007.12, "end": 1007.66, "word": " size,", "probability": 0.8564453125}, {"start": 1007.74, "end": 1007.86, "word": " the", "probability": 0.7939453125}, {"start": 1007.86, "end": 1008.18, "word": " population", "probability": 0.94580078125}, {"start": 1008.18, "end": 1008.74, "word": " size", "probability": 0.84375}, {"start": 1008.74, "end": 1008.96, "word": " is", "probability": 0.939453125}, {"start": 1008.96, "end": 1009.26, "word": " not", "probability": 0.9462890625}, {"start": 1009.26, "end": 1010.72, "word": " in", "probability": 0.9150390625}, {"start": 1010.72, "end": 1010.94, "word": " this", "probability": 0.93359375}, {"start": 1010.94, "end": 1011.46, "word": " quantity,", "probability": 0.97900390625}, {"start": 1011.6, "end": 1011.76, "word": " so", "probability": 0.93212890625}, {"start": 1011.76, "end": 1011.94, "word": " A", "probability": 0.62353515625}, {"start": 1011.94, "end": 1012.12, "word": " is", "probability": 0.94873046875}, {"start": 1012.12, "end": 1012.26, "word": " the", "probability": 0.90869140625}, {"start": 1012.26, "end": 1012.52, "word": " correct", "probability": 0.90478515625}, {"start": 1012.52, "end": 1012.92, "word": " answer.", "probability": 0.9521484375}, {"start": 1013.62, "end": 1013.84, "word": " B,", "probability": 0.96533203125}, {"start": 1013.94, "end": 1014.02, "word": " the", "probability": 0.890625}, {"start": 1014.02, "end": 1014.42, "word": " population", "probability": 0.95458984375}, {"start": 1014.42, "end": 1014.68, "word": " standard", "probability": 0.86279296875}, {"start": 1014.68, "end": 1015.14, "word": " deviation,", "probability": 0.88818359375}, {"start": 1015.52, "end": 1015.7, "word": " sigma", "probability": 0.8203125}, {"start": 1015.7, "end": 1015.88, "word": " is", "probability": 0.84765625}, {"start": 1015.88, "end": 1016.14, "word": " here.", "probability": 0.85205078125}, {"start": 1017.5, "end": 1017.92, "word": " C,", "probability": 0.98388671875}, {"start": 1018.2, "end": 1018.32, "word": " the", "probability": 0.908203125}, {"start": 1018.32, "end": 1018.56, "word": " level", "probability": 0.84228515625}, {"start": 1018.56, "end": 1018.82, "word": " of", "probability": 0.884765625}, {"start": 1018.82, "end": 1019.36, "word": " confidence", "probability": 0.97265625}, {"start": 1019.36, "end": 1020.2, "word": " desired", "probability": 0.8232421875}, {"start": 1020.2, "end": 1020.44, "word": " in", "probability": 0.9365234375}, {"start": 1020.44, "end": 1020.54, "word": " the", "probability": 0.90625}, {"start": 1020.54, "end": 1020.92, "word": " estimate,", "probability": 0.84375}, {"start": 1021.08, "end": 1021.16, "word": " we", "probability": 0.86865234375}, {"start": 1021.16, "end": 1021.3, "word": " have", "probability": 0.94775390625}, {"start": 1021.3, "end": 1021.52, "word": " Z.", "probability": 0.82373046875}], "temperature": 1.0}, {"id": 37, "seek": 103363, "start": 1022.69, "end": 1033.63, "text": " The allowable or tolerable seminar, we have it here. So eight is the correct answer. 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It turns out to be one of them. I'm not sure if I'm on the right track. To make more use of it as a reference for the update.", "tokens": [9391, 1744, 356, 11, 286, 478, 3442, 281, 1879, 322, 264, 3431, 300, 291, 434, 1364, 322, 586, 13, 467, 4523, 484, 281, 312, 472, 295, 552, 13, 286, 478, 406, 988, 498, 286, 478, 322, 264, 558, 2837, 13, 1407, 652, 544, 764, 295, 309, 382, 257, 6408, 337, 264, 5623, 13], "avg_logprob": -0.729745399068903, "compression_ratio": 1.4137931034482758, "no_speech_prob": 3.516674041748047e-06, "words": [{"start": 1040.02, "end": 1040.46, "word": " Supposedly,", "probability": 0.4037679036458333}, {"start": 1040.56, "end": 1040.62, "word": " I'm", "probability": 0.36907958984375}, {"start": 1040.62, "end": 1040.96, "word": " supposed", "probability": 0.83447265625}, {"start": 1040.96, "end": 1041.2, "word": " to", "probability": 0.91064453125}, {"start": 1041.2, "end": 1041.72, "word": " focus", "probability": 0.130859375}, {"start": 1041.72, "end": 1042.14, "word": " on", "probability": 0.8427734375}, {"start": 1042.14, "end": 1042.24, "word": " the", "probability": 0.33935546875}, {"start": 1042.24, "end": 1042.6, "word": " companies", "probability": 0.45166015625}, {"start": 1042.6, "end": 1042.8, "word": " that", "probability": 0.3828125}, {"start": 1042.8, "end": 1043.02, "word": " you're", "probability": 0.3883056640625}, {"start": 1043.02, "end": 1043.2, "word": " working", "probability": 0.396240234375}, {"start": 1043.2, "end": 1043.58, "word": " on", "probability": 0.521484375}, {"start": 1043.58, "end": 1043.98, "word": " now.", "probability": 0.6025390625}, {"start": 1044.28, "end": 1044.36, "word": " It", "probability": 0.54150390625}, {"start": 1044.36, "end": 1044.62, "word": " turns", "probability": 0.62109375}, {"start": 1044.62, "end": 1044.88, "word": " out", "probability": 0.880859375}, {"start": 1044.88, "end": 1045.1, "word": " to", "probability": 0.94873046875}, {"start": 1045.1, "end": 1045.34, "word": " be", "probability": 0.94482421875}, {"start": 1045.34, "end": 1045.64, "word": " one", "probability": 0.57763671875}, {"start": 1045.64, "end": 1045.78, "word": " of", "probability": 0.443115234375}, {"start": 1045.78, "end": 1046.14, "word": " them.", "probability": 0.82568359375}, {"start": 1046.62, "end": 1047.06, "word": " I'm", "probability": 0.4764404296875}, {"start": 1047.06, "end": 1047.26, "word": " not", "probability": 0.328125}, {"start": 1047.26, "end": 1047.26, "word": " sure", "probability": 0.8662109375}, {"start": 1047.26, "end": 1047.52, "word": " if", "probability": 0.32373046875}, {"start": 1047.52, "end": 1047.7, "word": " I'm", "probability": 0.775390625}, {"start": 1047.7, "end": 1047.8, "word": " on", "probability": 0.2386474609375}, {"start": 1047.8, "end": 1047.98, "word": " the", "probability": 0.482666015625}, {"start": 1047.98, "end": 1048.14, "word": " right", "probability": 0.85791015625}, {"start": 1048.14, "end": 1048.36, "word": " track.", "probability": 0.623046875}, {"start": 1048.42, "end": 1048.58, "word": " To", "probability": 0.366943359375}, {"start": 1048.58, "end": 1048.78, "word": " make", "probability": 0.9453125}, {"start": 1048.78, "end": 1049.02, "word": " more", "probability": 0.89111328125}, {"start": 1049.02, "end": 1049.24, "word": " use", "probability": 0.849609375}, {"start": 1049.24, "end": 1049.38, "word": " of", "probability": 0.90673828125}, {"start": 1049.38, "end": 1049.54, "word": " it", "probability": 0.16748046875}, {"start": 1049.54, "end": 1049.68, "word": " as", "probability": 0.27001953125}, {"start": 1049.68, "end": 1049.78, "word": " a", "probability": 0.57861328125}, {"start": 1049.78, "end": 1050.32, "word": " reference", "probability": 0.888671875}, {"start": 1050.32, "end": 1050.68, "word": " for", "probability": 0.8798828125}, {"start": 1050.68, "end": 1051.04, "word": " the", "probability": 0.77294921875}, {"start": 1051.04, "end": 1051.78, "word": " update.", "probability": 0.05145263671875}], "temperature": 1.0}, {"id": 39, "seek": 108466, "start": 1063.82, "end": 1084.66, "text": " Now, which of the following will result in a reduced interval width? So here we are talking about reducing the width of the interval. Number one. 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So this is the error state. Now, based on this equation, if we increase the sample size, the error will decrease. That means we reduce the interval with it. So A is the correct answer. Look at B. 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Increase the population mean, it doesn't matter actually, so it's not correct. Increase the sample mean also. So C and D are incorrect totally, so B is incorrect, so E is the correct answer. 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0.8818359375}, {"start": 1136.17, "end": 1136.39, "word": " correct", "probability": 0.8544921875}, {"start": 1136.39, "end": 1136.65, "word": " answer.", "probability": 0.93603515625}, {"start": 1137.25, "end": 1137.51, "word": " So", "probability": 0.95703125}, {"start": 1137.51, "end": 1137.67, "word": " the", "probability": 0.8720703125}, {"start": 1137.67, "end": 1137.95, "word": " correct", "probability": 0.90673828125}, {"start": 1137.95, "end": 1138.45, "word": " answer", "probability": 0.9599609375}, {"start": 1138.45, "end": 1139.37, "word": " is", "probability": 0.94677734375}, {"start": 1139.37, "end": 1139.63, "word": " A,", "probability": 0.62646484375}, {"start": 1140.27, "end": 1140.63, "word": " nine.", "probability": 0.70849609375}], "temperature": 1.0}, {"id": 42, "seek": 117522, "start": 1147.14, "end": 1175.22, "text": " A major department store chain is interested in estimating the average amount each credit and customers spent on their first visit to the chain's new store in the mall. 15 credit cards accounts were randomly sampled and analyzed with the following results. So here we have this information about the 15 data points. We have x bar.", "tokens": [316, 2563, 5882, 3531, 5021, 307, 3102, 294, 8017, 990, 264, 4274, 2372, 1184, 5397, 293, 4581, 4418, 322, 641, 700, 3441, 281, 264, 5021, 311, 777, 3531, 294, 264, 16026, 13, 2119, 5397, 5632, 9402, 645, 16979, 3247, 15551, 293, 28181, 365, 264, 3480, 3542, 13, 407, 510, 321, 362, 341, 1589, 466, 264, 2119, 1412, 2793, 13, 492, 362, 2031, 2159, 13], "avg_logprob": -0.1762019230769231, "compression_ratio": 1.5395348837209302, "no_speech_prob": 0.0, "words": [{"start": 1147.14, "end": 1147.4, "word": " A", "probability": 0.85302734375}, {"start": 1147.4, "end": 1147.64, "word": " major", "probability": 0.9248046875}, {"start": 1147.64, "end": 1148.18, "word": " department", "probability": 0.95751953125}, {"start": 1148.18, "end": 1148.8, "word": " store", "probability": 0.89013671875}, {"start": 1148.8, "end": 1149.54, "word": " chain", "probability": 0.85791015625}, {"start": 1149.54, "end": 1149.76, "word": " is", "probability": 0.93017578125}, {"start": 1149.76, "end": 1150.24, "word": " interested", "probability": 0.85791015625}, {"start": 1150.24, "end": 1150.5, "word": " in", "probability": 0.93359375}, {"start": 1150.5, "end": 1150.84, "word": " estimating", "probability": 0.879150390625}, {"start": 1150.84, "end": 1151.02, "word": " the", "probability": 0.9091796875}, {"start": 1151.02, "end": 1151.28, "word": " average", "probability": 0.81982421875}, {"start": 1151.28, "end": 1151.76, "word": " amount", "probability": 0.8837890625}, {"start": 1151.76, "end": 1152.84, "word": " each", "probability": 0.61181640625}, {"start": 1152.84, "end": 1153.28, "word": " credit", "probability": 0.93017578125}, {"start": 1153.28, "end": 1153.56, "word": " and", "probability": 0.83447265625}, {"start": 1153.56, "end": 1154.2, "word": " customers", "probability": 0.7880859375}, {"start": 1154.2, "end": 1155.04, "word": " spent", "probability": 0.78466796875}, {"start": 1155.04, "end": 1155.26, "word": " on", "probability": 0.92431640625}, {"start": 1155.26, "end": 1155.5, "word": " their", "probability": 0.951171875}, {"start": 1155.5, "end": 1155.88, "word": " first", "probability": 0.8798828125}, {"start": 1155.88, "end": 1156.2, "word": " visit", "probability": 0.93359375}, {"start": 1156.2, "end": 1156.4, "word": " to", "probability": 0.95703125}, {"start": 1156.4, "end": 1156.56, "word": " the", "probability": 0.9150390625}, {"start": 1156.56, "end": 1156.98, "word": " chain's", "probability": 0.9072265625}, {"start": 1156.98, "end": 1157.22, "word": " new", "probability": 0.92529296875}, {"start": 1157.22, "end": 1157.58, "word": " store", "probability": 0.85009765625}, {"start": 1157.58, "end": 1157.8, "word": " in", "probability": 0.755859375}, {"start": 1157.8, "end": 1157.96, "word": " the", "probability": 0.6220703125}, {"start": 1157.96, "end": 1158.2, "word": " mall.", "probability": 0.8515625}, {"start": 1159.68, "end": 1160.28, "word": " 15", "probability": 0.52978515625}, {"start": 1160.28, "end": 1160.76, "word": " credit", "probability": 0.869140625}, {"start": 1160.76, "end": 1161.38, "word": " cards", "probability": 0.8173828125}, {"start": 1161.38, "end": 1162.96, "word": " accounts", "probability": 0.58740234375}, {"start": 1162.96, "end": 1163.28, "word": " were", "probability": 0.85205078125}, {"start": 1163.28, "end": 1163.64, "word": " randomly", "probability": 0.64892578125}, {"start": 1163.64, "end": 1164.56, "word": " sampled", "probability": 0.80126953125}, {"start": 1164.56, "end": 1165.34, "word": " and", "probability": 0.865234375}, {"start": 1165.34, "end": 1165.92, "word": " analyzed", "probability": 0.86865234375}, {"start": 1165.92, "end": 1166.54, "word": " with", "probability": 0.89453125}, {"start": 1166.54, "end": 1166.7, "word": " the", "probability": 0.90625}, {"start": 1166.7, "end": 1167.0, "word": " following", "probability": 0.8974609375}, {"start": 1167.0, "end": 1167.66, "word": " results.", "probability": 0.8388671875}, {"start": 1167.82, "end": 1167.96, "word": " So", "probability": 0.94189453125}, {"start": 1167.96, "end": 1168.16, "word": " here", "probability": 0.82275390625}, {"start": 1168.16, "end": 1168.32, "word": " we", "probability": 0.78076171875}, {"start": 1168.32, "end": 1168.6, "word": " have", "probability": 0.94287109375}, {"start": 1168.6, "end": 1169.32, "word": " this", "probability": 0.92578125}, {"start": 1169.32, "end": 1169.82, "word": " information", "probability": 0.84814453125}, {"start": 1169.82, "end": 1170.18, "word": " about", "probability": 0.90087890625}, {"start": 1170.18, "end": 1170.44, "word": " the", "probability": 0.65625}, {"start": 1170.44, "end": 1170.94, "word": " 15", "probability": 0.97607421875}, {"start": 1170.94, "end": 1172.34, "word": " data", "probability": 0.94140625}, {"start": 1172.34, "end": 1172.8, "word": " points.", "probability": 0.91552734375}, {"start": 1172.92, "end": 1173.02, "word": " We", "probability": 0.955078125}, {"start": 1173.02, "end": 1173.42, "word": " have", "probability": 0.94189453125}, {"start": 1173.42, "end": 1174.88, "word": " x", "probability": 0.72265625}, {"start": 1174.88, "end": 1175.22, "word": " bar.", "probability": 0.72119140625}], "temperature": 1.0}, {"id": 43, "seek": 120501, "start": 1178.55, "end": 1205.01, "text": " of $50.5. And S squared, the sample variance is 400. Construct 95 confidence interval for the average amount it's credit card customer spent on their first visit to the chain. It's a new store. It's in the mall, assuming the amount spent follows a normal distribution.", "tokens": [295, 1848, 2803, 13, 20, 13, 400, 318, 8889, 11, 264, 6889, 21977, 307, 8423, 13, 8574, 1757, 13420, 6687, 15035, 337, 264, 4274, 2372, 309, 311, 5397, 2920, 5474, 4418, 322, 641, 700, 3441, 281, 264, 5021, 13, 467, 311, 257, 777, 3531, 13, 467, 311, 294, 264, 16026, 11, 11926, 264, 2372, 4418, 10002, 257, 2710, 7316, 13], "avg_logprob": -0.27228484388257634, "compression_ratio": 1.4308510638297873, "no_speech_prob": 0.0, "words": [{"start": 1178.55, "end": 1178.65, "word": " of", "probability": 0.06646728515625}, {"start": 1178.65, "end": 1179.11, "word": " $50", "probability": 0.564697265625}, {"start": 1179.11, "end": 1182.15, "word": ".5.", "probability": 0.88427734375}, {"start": 1183.47, "end": 1184.21, "word": " And", "probability": 0.87109375}, {"start": 1184.21, "end": 1184.57, "word": " S", "probability": 0.7666015625}, {"start": 1184.57, "end": 1184.97, "word": " squared,", "probability": 0.72314453125}, {"start": 1185.75, "end": 1185.95, "word": " the", "probability": 0.85693359375}, {"start": 1185.95, "end": 1186.27, "word": " sample", "probability": 0.86328125}, {"start": 1186.27, "end": 1186.65, "word": " variance", "probability": 0.42333984375}, {"start": 1186.65, "end": 1186.87, "word": " is", "probability": 0.81982421875}, {"start": 1186.87, "end": 1187.39, "word": " 400.", "probability": 0.9775390625}, {"start": 1189.89, "end": 1190.63, "word": " Construct", "probability": 0.934814453125}, {"start": 1190.63, "end": 1190.93, "word": " 95", "probability": 0.9033203125}, {"start": 1190.93, "end": 1191.47, "word": " confidence", "probability": 0.92919921875}, {"start": 1191.47, "end": 1191.99, "word": " interval", "probability": 0.74755859375}, {"start": 1191.99, "end": 1192.29, "word": " for", "probability": 0.9287109375}, {"start": 1192.29, "end": 1192.43, "word": " the", "probability": 0.90673828125}, {"start": 1192.43, "end": 1192.75, "word": " average", "probability": 0.8212890625}, {"start": 1192.75, "end": 1193.23, "word": " amount", "probability": 0.9033203125}, {"start": 1193.23, "end": 1193.67, "word": " it's", "probability": 0.6512451171875}, {"start": 1193.67, "end": 1193.97, "word": " credit", "probability": 0.87451171875}, {"start": 1193.97, "end": 1194.33, "word": " card", "probability": 0.89794921875}, {"start": 1194.33, "end": 1194.81, "word": " customer", "probability": 0.43310546875}, {"start": 1194.81, "end": 1195.21, "word": " spent", "probability": 0.583984375}, {"start": 1195.21, "end": 1195.39, "word": " on", "probability": 0.79296875}, {"start": 1195.39, "end": 1195.57, "word": " their", "probability": 0.9501953125}, {"start": 1195.57, "end": 1196.09, "word": " first", "probability": 0.8828125}, {"start": 1196.09, "end": 1196.91, "word": " visit", "probability": 0.94091796875}, {"start": 1196.91, "end": 1198.99, "word": " to", "probability": 0.537109375}, {"start": 1198.99, "end": 1199.15, "word": " the", "probability": 0.91064453125}, {"start": 1199.15, "end": 1199.55, "word": " chain.", "probability": 0.92822265625}, {"start": 1200.09, "end": 1200.21, "word": " It's", "probability": 0.873046875}, {"start": 1200.21, "end": 1200.31, "word": " a", "probability": 0.88037109375}, {"start": 1200.31, "end": 1200.55, "word": " new", "probability": 0.9013671875}, {"start": 1200.55, "end": 1200.93, "word": " store.", "probability": 0.77392578125}, {"start": 1201.05, "end": 1201.23, "word": " It's", "probability": 0.885009765625}, {"start": 1201.23, "end": 1201.43, "word": " in", "probability": 0.91796875}, {"start": 1201.43, "end": 1201.53, "word": " the", "probability": 0.91845703125}, {"start": 1201.53, "end": 1201.71, "word": " mall,", "probability": 0.86962890625}, {"start": 1201.83, "end": 1202.23, "word": " assuming", "probability": 0.88232421875}, {"start": 1202.23, "end": 1202.97, "word": " the", "probability": 0.90673828125}, {"start": 1202.97, "end": 1203.27, "word": " amount", "probability": 0.8505859375}, {"start": 1203.27, "end": 1203.65, "word": " spent", "probability": 0.8974609375}, {"start": 1203.65, "end": 1204.09, "word": " follows", "probability": 0.89453125}, {"start": 1204.09, "end": 1204.31, "word": " a", "probability": 0.98876953125}, {"start": 1204.31, "end": 1204.53, "word": " normal", "probability": 0.89453125}, {"start": 1204.53, "end": 1205.01, "word": " distribution.", "probability": 0.85693359375}], "temperature": 1.0}, {"id": 44, "seek": 123401, "start": 1208.09, "end": 1234.01, "text": " In this case, we should use T instead of Z. So the formula should be X bar plus or minus T, alpha over 2S over root N. So X bar is 50.5. T, we should use the T table. In this case, here we are talking about 95%.", "tokens": [682, 341, 1389, 11, 321, 820, 764, 314, 2602, 295, 1176, 13, 407, 264, 8513, 820, 312, 1783, 2159, 1804, 420, 3175, 314, 11, 8961, 670, 568, 50, 670, 5593, 426, 13, 407, 1783, 2159, 307, 2625, 13, 20, 13, 314, 11, 321, 820, 764, 264, 314, 3199, 13, 682, 341, 1389, 11, 510, 321, 366, 1417, 466, 13420, 6856], "avg_logprob": -0.17315573379641674, "compression_ratio": 1.4421768707482994, "no_speech_prob": 0.0, "words": [{"start": 1208.09, "end": 1208.57, "word": " In", "probability": 0.1702880859375}, {"start": 1208.57, "end": 1209.05, "word": " this", "probability": 0.94482421875}, {"start": 1209.05, "end": 1209.25, "word": " case,", "probability": 0.91455078125}, {"start": 1209.29, "end": 1209.39, "word": " we", "probability": 0.94287109375}, {"start": 1209.39, "end": 1209.57, "word": " should", "probability": 0.96142578125}, {"start": 1209.57, "end": 1209.99, "word": " use", "probability": 0.892578125}, {"start": 1209.99, "end": 1211.53, "word": " T", "probability": 0.705078125}, {"start": 1211.53, "end": 1212.25, "word": " instead", "probability": 0.82177734375}, {"start": 1212.25, "end": 1212.39, "word": " of", "probability": 0.96435546875}, {"start": 1212.39, "end": 1212.57, "word": " Z.", "probability": 0.5625}, {"start": 1212.81, "end": 1212.95, "word": " So", "probability": 0.94970703125}, {"start": 1212.95, "end": 1213.15, "word": " the", "probability": 0.734375}, {"start": 1213.15, "end": 1213.51, "word": " formula", "probability": 0.92626953125}, {"start": 1213.51, "end": 1213.85, "word": " should", "probability": 0.96484375}, {"start": 1213.85, "end": 1214.05, "word": " be", "probability": 0.94970703125}, {"start": 1214.05, "end": 1214.19, "word": " X", "probability": 0.62890625}, {"start": 1214.19, "end": 1214.33, "word": " bar", "probability": 0.837890625}, {"start": 1214.33, "end": 1214.57, "word": " plus", "probability": 0.9697265625}, {"start": 1214.57, "end": 1214.75, "word": " or", "probability": 0.9375}, {"start": 1214.75, "end": 1214.97, "word": " minus", "probability": 0.9873046875}, {"start": 1214.97, "end": 1215.37, "word": " T,", "probability": 0.98828125}, {"start": 1216.01, "end": 1216.31, "word": " alpha", "probability": 0.79833984375}, {"start": 1216.31, "end": 1216.55, "word": " over", "probability": 0.91259765625}, {"start": 1216.55, "end": 1216.95, "word": " 2S", "probability": 0.7626953125}, {"start": 1216.95, "end": 1217.19, "word": " over", "probability": 0.88720703125}, {"start": 1217.19, "end": 1217.39, "word": " root", "probability": 0.9326171875}, {"start": 1217.39, "end": 1217.61, "word": " N.", "probability": 0.91552734375}, {"start": 1223.11, "end": 1223.59, "word": " So", "probability": 0.953125}, {"start": 1223.59, "end": 1223.83, "word": " X", "probability": 0.8505859375}, {"start": 1223.83, "end": 1224.17, "word": " bar", "probability": 0.93212890625}, {"start": 1224.17, "end": 1225.13, "word": " is", "probability": 0.9375}, {"start": 1225.13, "end": 1225.41, "word": " 50", "probability": 0.89794921875}, {"start": 1225.41, "end": 1225.99, "word": ".5.", "probability": 0.99267578125}, {"start": 1226.29, "end": 1226.53, "word": " T,", "probability": 0.9462890625}, {"start": 1226.63, "end": 1226.83, "word": " we", "probability": 0.8603515625}, {"start": 1226.83, "end": 1227.01, "word": " should", "probability": 0.970703125}, {"start": 1227.01, "end": 1227.31, "word": " use", "probability": 0.884765625}, {"start": 1227.31, "end": 1227.59, "word": " the", "probability": 0.89013671875}, {"start": 1227.59, "end": 1228.19, "word": " T", "probability": 0.974609375}, {"start": 1228.19, "end": 1228.51, "word": " table.", "probability": 0.72265625}, {"start": 1229.17, "end": 1229.35, "word": " In", "probability": 0.9619140625}, {"start": 1229.35, "end": 1229.55, "word": " this", "probability": 0.94384765625}, {"start": 1229.55, "end": 1229.89, "word": " case,", "probability": 0.9091796875}, {"start": 1229.99, "end": 1230.17, "word": " here", "probability": 0.8408203125}, {"start": 1230.17, "end": 1230.31, "word": " we", "probability": 0.720703125}, {"start": 1230.31, "end": 1230.43, "word": " are", "probability": 0.921875}, {"start": 1230.43, "end": 1230.77, "word": " talking", "probability": 0.85302734375}, {"start": 1230.77, "end": 1231.49, "word": " about", "probability": 0.908203125}, {"start": 1231.49, "end": 1234.01, "word": " 95%.", "probability": 0.86181640625}], "temperature": 1.0}, {"id": 45, "seek": 126384, "start": 1236.83, "end": 1263.85, "text": " So that means alpha is 5%, alpha over 2, 0, 2, 5. So now we are looking for 2, 0, 2, 5, and degrees of freedom. N is 15. It says that 15 credit cards. So 15 credit cards accounts for random samples. So N equals 15. So since N is 15,", "tokens": [407, 300, 1355, 8961, 307, 1025, 8923, 8961, 670, 568, 11, 1958, 11, 568, 11, 1025, 13, 407, 586, 321, 366, 1237, 337, 568, 11, 1958, 11, 568, 11, 1025, 11, 293, 5310, 295, 5645, 13, 426, 307, 2119, 13, 467, 1619, 300, 2119, 5397, 5632, 13, 407, 2119, 5397, 5632, 9402, 337, 4974, 10938, 13, 407, 426, 6915, 2119, 13, 407, 1670, 426, 307, 2119, 11], "avg_logprob": -0.23851103226051612, "compression_ratio": 1.5129870129870129, "no_speech_prob": 0.0, "words": [{"start": 1236.83, "end": 1237.07, "word": " So", "probability": 0.87744140625}, {"start": 1237.07, "end": 1237.31, "word": " that", "probability": 0.826171875}, {"start": 1237.31, "end": 1237.63, "word": " means", "probability": 0.908203125}, {"start": 1237.63, "end": 1238.15, "word": " alpha", "probability": 0.80224609375}, {"start": 1238.15, "end": 1239.35, "word": " is", "probability": 0.9150390625}, {"start": 1239.35, "end": 1240.19, "word": " 5%,", "probability": 0.63427734375}, {"start": 1240.19, "end": 1241.45, "word": " alpha", "probability": 0.86279296875}, {"start": 1241.45, "end": 1241.67, "word": " over", "probability": 0.896484375}, {"start": 1241.67, "end": 1241.93, "word": " 2,", "probability": 0.77978515625}, {"start": 1242.03, "end": 1242.33, "word": " 0,", "probability": 0.90380859375}, {"start": 1242.75, "end": 1243.75, "word": " 2,", "probability": 0.444580078125}, {"start": 1243.83, "end": 1244.13, "word": " 5.", "probability": 0.958984375}, {"start": 1244.77, "end": 1245.37, "word": " So", "probability": 0.91796875}, {"start": 1245.37, "end": 1245.53, "word": " now", "probability": 0.91015625}, {"start": 1245.53, "end": 1245.65, "word": " we", "probability": 0.8291015625}, {"start": 1245.65, "end": 1245.75, "word": " are", "probability": 0.90673828125}, {"start": 1245.75, "end": 1245.99, "word": " looking", "probability": 0.8798828125}, {"start": 1245.99, "end": 1246.25, "word": " for", "probability": 0.94580078125}, {"start": 1246.25, "end": 1246.55, "word": " 2,", "probability": 0.88916015625}, {"start": 1246.85, "end": 1247.19, "word": " 0,", "probability": 0.98876953125}, {"start": 1247.27, "end": 1247.39, "word": " 2,", "probability": 0.92822265625}, {"start": 1247.39, "end": 1248.21, "word": " 5,", "probability": 0.9814453125}, {"start": 1248.41, "end": 1248.67, "word": " and", "probability": 0.82568359375}, {"start": 1248.67, "end": 1248.93, "word": " degrees", "probability": 0.947265625}, {"start": 1248.93, "end": 1249.13, "word": " of", "probability": 0.97021484375}, {"start": 1249.13, "end": 1249.55, "word": " freedom.", "probability": 0.93896484375}, {"start": 1250.93, "end": 1251.27, "word": " N", "probability": 0.7275390625}, {"start": 1251.27, "end": 1251.45, "word": " is", "probability": 0.9423828125}, {"start": 1251.45, "end": 1251.93, "word": " 15.", "probability": 0.9638671875}, {"start": 1252.09, "end": 1252.29, "word": " It", "probability": 0.603515625}, {"start": 1252.29, "end": 1252.53, "word": " says", "probability": 0.900390625}, {"start": 1252.53, "end": 1252.95, "word": " that", "probability": 0.93017578125}, {"start": 1252.95, "end": 1254.21, "word": " 15", "probability": 0.90673828125}, {"start": 1254.21, "end": 1254.67, "word": " credit", "probability": 0.87744140625}, {"start": 1254.67, "end": 1255.17, "word": " cards.", "probability": 0.4765625}, {"start": 1255.77, "end": 1255.77, "word": " So", "probability": 0.89404296875}, {"start": 1255.77, "end": 1256.51, "word": " 15", "probability": 0.92431640625}, {"start": 1256.51, "end": 1257.25, "word": " credit", "probability": 0.7626953125}, {"start": 1257.25, "end": 1257.45, "word": " cards", "probability": 0.84619140625}, {"start": 1257.45, "end": 1257.81, "word": " accounts", "probability": 0.6162109375}, {"start": 1257.81, "end": 1258.03, "word": " for", "probability": 0.86962890625}, {"start": 1258.03, "end": 1258.27, "word": " random", "probability": 0.367431640625}, {"start": 1258.27, "end": 1258.79, "word": " samples.", "probability": 0.209716796875}, {"start": 1258.99, "end": 1259.11, "word": " So", "probability": 0.9541015625}, {"start": 1259.11, "end": 1259.27, "word": " N", "probability": 0.638671875}, {"start": 1259.27, "end": 1259.59, "word": " equals", "probability": 0.87841796875}, {"start": 1259.59, "end": 1260.23, "word": " 15.", "probability": 0.97314453125}, {"start": 1261.51, "end": 1261.99, "word": " So", "probability": 0.95751953125}, {"start": 1261.99, "end": 1262.93, "word": " since", "probability": 0.83251953125}, {"start": 1262.93, "end": 1263.17, "word": " N", "probability": 0.9580078125}, {"start": 1263.17, "end": 1263.33, "word": " is", "probability": 0.94970703125}, {"start": 1263.33, "end": 1263.85, "word": " 15,", "probability": 0.974609375}], "temperature": 1.0}, {"id": 46, "seek": 129308, "start": 1264.39, "end": 1293.09, "text": " Degrees of freedom is 14. Now we may use the normal, the T table in order to find the value of T in the upper tier actually. So what's the value if you have the table? So look at degrees of freedom 14 under the probability of 0 to 5.", "tokens": [413, 1146, 4856, 295, 5645, 307, 3499, 13, 823, 321, 815, 764, 264, 2710, 11, 264, 314, 3199, 294, 1668, 281, 915, 264, 2158, 295, 314, 294, 264, 6597, 12362, 767, 13, 407, 437, 311, 264, 2158, 498, 291, 362, 264, 3199, 30, 407, 574, 412, 5310, 295, 5645, 3499, 833, 264, 8482, 295, 1958, 281, 1025, 13], "avg_logprob": -0.2503972356602297, "compression_ratio": 1.4904458598726114, "no_speech_prob": 0.0, "words": [{"start": 1264.39, "end": 1265.05, "word": " Degrees", "probability": 0.627197265625}, {"start": 1265.05, "end": 1265.25, "word": " of", "probability": 0.955078125}, {"start": 1265.25, "end": 1265.47, "word": " freedom", "probability": 0.87548828125}, {"start": 1265.47, "end": 1265.71, "word": " is", "probability": 0.7021484375}, {"start": 1265.71, "end": 1266.09, "word": " 14.", "probability": 0.80029296875}, {"start": 1267.03, "end": 1267.27, "word": " Now", "probability": 0.8828125}, {"start": 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1271.91, "word": " the", "probability": 0.90771484375}, {"start": 1271.91, "end": 1272.27, "word": " value", "probability": 0.97509765625}, {"start": 1272.27, "end": 1272.71, "word": " of", "probability": 0.9658203125}, {"start": 1272.71, "end": 1273.15, "word": " T", "probability": 0.9638671875}, {"start": 1273.15, "end": 1276.25, "word": " in", "probability": 0.6181640625}, {"start": 1276.25, "end": 1276.41, "word": " the", "probability": 0.919921875}, {"start": 1276.41, "end": 1276.61, "word": " upper", "probability": 0.70068359375}, {"start": 1276.61, "end": 1276.89, "word": " tier", "probability": 0.89990234375}, {"start": 1276.89, "end": 1277.33, "word": " actually.", "probability": 0.73291015625}, {"start": 1277.99, "end": 1278.13, "word": " So", "probability": 0.94873046875}, {"start": 1278.13, "end": 1278.29, "word": " what's", "probability": 0.873291015625}, {"start": 1278.29, "end": 1278.43, "word": " the", "probability": 0.9169921875}, {"start": 1278.43, "end": 1278.81, 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" 14", "probability": 0.81982421875}, {"start": 1286.93, "end": 1288.71, "word": " under", "probability": 0.41064453125}, {"start": 1288.71, "end": 1289.27, "word": " the", "probability": 0.75341796875}, {"start": 1289.27, "end": 1289.85, "word": " probability", "probability": 0.94970703125}, {"start": 1289.85, "end": 1290.49, "word": " of", "probability": 0.96630859375}, {"start": 1290.49, "end": 1292.51, "word": " 0", "probability": 0.818359375}, {"start": 1292.51, "end": 1292.71, "word": " to", "probability": 0.93505859375}, {"start": 1292.71, "end": 1293.09, "word": " 5.", "probability": 0.98828125}], "temperature": 1.0}, {"id": 47, "seek": 130917, "start": 1300.19, "end": 1309.17, "text": " So again, we are looking for degrees of freedom equal 14 under 2.5%.", "tokens": [407, 797, 11, 321, 366, 1237, 337, 5310, 295, 5645, 2681, 3499, 833, 568, 13, 20, 6856], "avg_logprob": -0.1514756911330753, "compression_ratio": 0.9452054794520548, "no_speech_prob": 0.0, "words": [{"start": 1300.1899999999998, "end": 1301.11, "word": " So", "probability": 0.372314453125}, {"start": 1301.11, "end": 1302.03, "word": " again,", "probability": 0.81591796875}, {"start": 1302.49, "end": 1303.61, "word": " we", "probability": 0.9501953125}, {"start": 1303.61, "end": 1303.73, "word": " are", "probability": 0.931640625}, {"start": 1303.73, "end": 1303.97, "word": " looking", "probability": 0.9189453125}, {"start": 1303.97, "end": 1304.33, "word": " for", "probability": 0.9541015625}, {"start": 1304.33, "end": 1304.63, "word": " degrees", "probability": 0.95703125}, {"start": 1304.63, "end": 1304.81, "word": " of", "probability": 0.9599609375}, {"start": 1304.81, "end": 1305.05, "word": " freedom", "probability": 0.94580078125}, {"start": 1305.05, "end": 1305.33, "word": " equal", "probability": 0.8720703125}, {"start": 1305.33, "end": 1305.95, "word": " 14", "probability": 0.90771484375}, {"start": 1305.95, "end": 1307.15, "word": " under", "probability": 0.5498046875}, {"start": 1307.15, "end": 1308.25, "word": " 2", "probability": 0.9482421875}, {"start": 1308.25, "end": 1309.17, "word": ".5%.", "probability": 0.9573567708333334}], "temperature": 1.0}, {"id": 48, "seek": 135035, "start": 1324.85, "end": 1350.35, "text": " 0.5 plus or minus 2.1448. S squared is given 400. Take square root of this quantity 20 over root n over root 15. And the answer, just simple calculation will give", "tokens": [1958, 13, 20, 1804, 420, 3175, 568, 13, 7271, 13318, 13, 318, 8889, 307, 2212, 8423, 13, 3664, 3732, 5593, 295, 341, 11275, 945, 670, 5593, 297, 670, 5593, 2119, 13, 400, 264, 1867, 11, 445, 2199, 17108, 486, 976], "avg_logprob": -0.3546112921179795, "compression_ratio": 1.2635658914728682, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1324.85, "end": 1325.15, "word": " 0", "probability": 0.1478271484375}, {"start": 1325.15, "end": 1325.69, "word": ".5", "probability": 0.96728515625}, {"start": 1325.69, "end": 1326.05, "word": " plus", "probability": 0.7587890625}, {"start": 1326.05, "end": 1326.29, "word": " or", "probability": 0.93603515625}, {"start": 1326.29, "end": 1326.73, "word": " minus", "probability": 0.986328125}, {"start": 1326.73, "end": 1331.39, "word": " 2", "probability": 0.677734375}, {"start": 1331.39, "end": 1333.35, "word": ".1448.", "probability": 0.9376627604166666}, {"start": 1333.99, "end": 1334.57, "word": " S", "probability": 0.6962890625}, {"start": 1334.57, "end": 1335.39, "word": " squared", "probability": 0.599609375}, {"start": 1335.39, "end": 1335.57, "word": " is", "probability": 0.92626953125}, {"start": 1335.57, "end": 1335.85, "word": " given", "probability": 0.83154296875}, {"start": 1335.85, "end": 1336.61, "word": " 400.", "probability": 0.54638671875}, {"start": 1337.05, "end": 1337.55, "word": " Take", "probability": 0.335693359375}, {"start": 1337.55, "end": 1337.95, "word": " square", "probability": 0.71044921875}, {"start": 1337.95, "end": 1338.21, "word": " root", "probability": 0.89453125}, {"start": 1338.21, "end": 1338.39, "word": " of", "probability": 0.798828125}, {"start": 1338.39, "end": 1338.55, "word": " this", "probability": 0.92626953125}, {"start": 1338.55, "end": 1339.11, "word": " quantity", "probability": 0.97705078125}, {"start": 1339.11, "end": 1340.03, "word": " 20", "probability": 0.54736328125}, {"start": 1340.03, "end": 1340.97, "word": " over", "probability": 0.7412109375}, {"start": 1340.97, "end": 1341.27, "word": " root", "probability": 0.86474609375}, {"start": 1341.27, "end": 1341.55, "word": " n", "probability": 0.57568359375}, {"start": 1341.55, "end": 1342.71, "word": " over", "probability": 0.60302734375}, {"start": 1342.71, "end": 1343.17, "word": " root", "probability": 0.54052734375}, {"start": 1343.17, "end": 1344.33, "word": " 15.", "probability": 0.919921875}, {"start": 1345.15, "end": 1345.43, "word": " And", "probability": 0.89404296875}, {"start": 1345.43, "end": 1345.57, "word": " the", "probability": 0.79736328125}, {"start": 1345.57, "end": 1345.99, "word": " answer,", "probability": 0.95849609375}, {"start": 1347.59, "end": 1347.97, "word": " just", "probability": 0.69189453125}, {"start": 1347.97, "end": 1348.31, "word": " simple", "probability": 0.8349609375}, {"start": 1348.31, "end": 1348.85, "word": " calculation", "probability": 0.921875}, {"start": 1348.85, "end": 1349.97, "word": " will", "probability": 0.55712890625}, {"start": 1349.97, "end": 1350.35, "word": " give", "probability": 0.88916015625}], "temperature": 1.0}, {"id": 49, "seek": 138011, "start": 1354.25, "end": 1380.11, "text": " This result, so D is the correct answer. So the answer should be 50.5 plus or minus 11.08. So D is the correct answer. So this one is straightforward calculation, gives part D to be the correct answer. Any question? 11, 10?", "tokens": [639, 1874, 11, 370, 413, 307, 264, 3006, 1867, 13, 407, 264, 1867, 820, 312, 2625, 13, 20, 1804, 420, 3175, 2975, 13, 16133, 13, 407, 413, 307, 264, 3006, 1867, 13, 407, 341, 472, 307, 15325, 17108, 11, 2709, 644, 413, 281, 312, 264, 3006, 1867, 13, 2639, 1168, 30, 2975, 11, 1266, 30], "avg_logprob": -0.18596540737364972, "compression_ratio": 1.5342465753424657, "no_speech_prob": 0.0, "words": [{"start": 1354.25, "end": 1354.97, "word": " This", "probability": 0.5302734375}, {"start": 1354.97, "end": 1355.33, "word": " result,", "probability": 0.68505859375}, {"start": 1355.73, "end": 1355.93, "word": " so", "probability": 0.89794921875}, {"start": 1355.93, "end": 1356.27, "word": " D", "probability": 0.51953125}, {"start": 1356.27, "end": 1356.45, "word": " is", "probability": 0.94775390625}, {"start": 1356.45, "end": 1356.61, "word": " the", "probability": 0.87109375}, {"start": 1356.61, "end": 1356.87, "word": " correct", "probability": 0.9072265625}, {"start": 1356.87, "end": 1357.29, "word": " answer.", "probability": 0.94091796875}, {"start": 1357.83, "end": 1358.21, "word": " So", "probability": 0.939453125}, {"start": 1358.21, "end": 1358.41, "word": " the", "probability": 0.740234375}, {"start": 1358.41, "end": 1358.71, "word": " answer", "probability": 0.9482421875}, {"start": 1358.71, "end": 1359.05, "word": " should", "probability": 0.96875}, {"start": 1359.05, "end": 1359.31, "word": " be", "probability": 0.953125}, {"start": 1359.31, "end": 1359.79, "word": " 50", "probability": 0.80029296875}, {"start": 1359.79, "end": 1360.51, "word": ".5", "probability": 0.9794921875}, {"start": 1360.51, "end": 1360.81, "word": " plus", "probability": 0.654296875}, {"start": 1360.81, "end": 1361.01, "word": " or", "probability": 0.93310546875}, {"start": 1361.01, "end": 1361.39, "word": " minus", "probability": 0.98291015625}, {"start": 1361.39, "end": 1362.51, "word": " 11", "probability": 0.923828125}, {"start": 1362.51, "end": 1364.23, "word": ".08.", "probability": 0.943359375}, {"start": 1364.81, "end": 1365.29, "word": " So", "probability": 0.95068359375}, {"start": 1365.29, "end": 1365.55, "word": " D", "probability": 0.8486328125}, {"start": 1365.55, "end": 1365.87, "word": " is", "probability": 0.951171875}, {"start": 1365.87, "end": 1366.05, "word": " the", "probability": 0.87939453125}, {"start": 1366.05, "end": 1366.39, "word": " correct", "probability": 0.908203125}, {"start": 1366.39, "end": 1367.23, "word": " answer.", "probability": 0.9560546875}, {"start": 1367.93, "end": 1368.19, "word": " So", "probability": 0.94677734375}, {"start": 1368.19, "end": 1368.35, "word": " this", "probability": 0.9091796875}, {"start": 1368.35, "end": 1368.51, "word": " one", "probability": 0.8876953125}, {"start": 1368.51, "end": 1368.65, "word": " is", "probability": 0.89111328125}, {"start": 1368.65, "end": 1369.17, "word": " straightforward", "probability": 0.7763671875}, {"start": 1369.17, "end": 1369.93, "word": " calculation,", "probability": 0.916015625}, {"start": 1370.71, "end": 1371.07, "word": " gives", "probability": 0.85107421875}, {"start": 1371.07, "end": 1371.93, "word": " part", "probability": 0.447021484375}, {"start": 1371.93, "end": 1372.21, "word": " D", "probability": 0.9443359375}, {"start": 1372.21, "end": 1372.39, "word": " to", "probability": 0.95947265625}, {"start": 1372.39, "end": 1372.53, "word": " be", "probability": 0.94384765625}, {"start": 1372.53, "end": 1372.69, "word": " the", "probability": 0.90771484375}, {"start": 1372.69, "end": 1372.99, "word": " correct", "probability": 0.89306640625}, {"start": 1372.99, "end": 1373.41, "word": " answer.", "probability": 0.94775390625}, {"start": 1375.19, "end": 1375.43, "word": " Any", "probability": 0.89599609375}, {"start": 1375.43, "end": 1375.75, "word": " question?", "probability": 0.7578125}, {"start": 1378.51, "end": 1379.23, "word": " 11,", "probability": 0.7177734375}, {"start": 1379.69, "end": 1380.11, "word": " 10?", "probability": 0.798828125}], "temperature": 1.0}, {"id": 50, "seek": 141195, "start": 1383.11, "end": 1411.95, "text": " Private colleges and universities rely on money contributed by individuals and corporations for their operating expenses. Much of this money is put into a fund called an endowment, and the college spends only the interest earned by the fund. Now, here we have a recent", "tokens": [30386, 15272, 293, 11779, 10687, 322, 1460, 18434, 538, 5346, 293, 17676, 337, 641, 7447, 15506, 13, 12313, 295, 341, 1460, 307, 829, 666, 257, 2374, 1219, 364, 917, 47966, 11, 293, 264, 3859, 25620, 787, 264, 1179, 12283, 538, 264, 2374, 13, 823, 11, 510, 321, 362, 257, 5162], "avg_logprob": -0.1766237704192891, "compression_ratio": 1.5197740112994351, "no_speech_prob": 0.0, "words": [{"start": 1383.11, "end": 1383.59, "word": " Private", "probability": 0.64111328125}, {"start": 1383.59, "end": 1384.73, "word": " colleges", "probability": 0.89208984375}, {"start": 1384.73, "end": 1385.71, "word": " and", "probability": 0.93408203125}, {"start": 1385.71, "end": 1386.25, "word": " universities", "probability": 0.9052734375}, {"start": 1386.25, "end": 1386.75, "word": " rely", "probability": 0.91162109375}, {"start": 1386.75, "end": 1387.03, "word": " on", "probability": 0.95166015625}, {"start": 1387.03, "end": 1387.25, "word": " money", "probability": 0.90283203125}, {"start": 1387.25, "end": 1387.95, "word": " contributed", "probability": 0.54345703125}, {"start": 1387.95, "end": 1390.33, "word": " by", "probability": 0.9365234375}, {"start": 1390.33, "end": 1391.17, "word": " individuals", "probability": 0.69482421875}, {"start": 1391.17, "end": 1391.73, "word": " and", "probability": 0.54931640625}, {"start": 1391.73, "end": 1392.29, "word": " corporations", "probability": 0.84326171875}, {"start": 1392.29, "end": 1392.73, "word": " for", "probability": 0.93115234375}, {"start": 1392.73, "end": 1393.01, "word": " their", "probability": 0.95166015625}, {"start": 1393.01, "end": 1393.53, "word": " operating", "probability": 0.99072265625}, {"start": 1393.53, "end": 1394.19, "word": " expenses.", "probability": 0.9638671875}, {"start": 1396.13, "end": 1397.01, "word": " Much", "probability": 0.8994140625}, {"start": 1397.01, "end": 1397.21, "word": " of", "probability": 0.96533203125}, {"start": 1397.21, "end": 1397.45, "word": " this", "probability": 0.93701171875}, {"start": 1397.45, "end": 1397.71, "word": " money", "probability": 0.92578125}, {"start": 1397.71, "end": 1397.95, "word": " is", "probability": 0.92578125}, {"start": 1397.95, "end": 1398.17, "word": " put", "probability": 0.931640625}, {"start": 1398.17, "end": 1398.89, "word": " into", "probability": 0.85302734375}, {"start": 1398.89, "end": 1400.49, "word": " a", "probability": 0.9794921875}, {"start": 1400.49, "end": 1400.71, "word": " fund", "probability": 0.9248046875}, {"start": 1400.71, "end": 1401.21, "word": " called", "probability": 0.89794921875}, {"start": 1401.21, "end": 1402.71, "word": " an", "probability": 0.75048828125}, {"start": 1402.71, "end": 1403.17, "word": " endowment,", "probability": 0.6072998046875}, {"start": 1403.69, "end": 1403.93, "word": " and", "probability": 0.9228515625}, {"start": 1403.93, "end": 1404.09, "word": " the", "probability": 0.8515625}, {"start": 1404.09, "end": 1404.35, "word": " college", "probability": 0.7255859375}, {"start": 1404.35, "end": 1404.77, "word": " spends", "probability": 0.9287109375}, {"start": 1404.77, "end": 1405.17, "word": " only", "probability": 0.7421875}, {"start": 1405.17, "end": 1405.95, "word": " the", "probability": 0.892578125}, {"start": 1405.95, "end": 1406.57, "word": " interest", "probability": 0.8876953125}, {"start": 1406.57, "end": 1406.93, "word": " earned", "probability": 0.8916015625}, {"start": 1406.93, "end": 1407.27, "word": " by", "probability": 0.97900390625}, {"start": 1407.27, "end": 1407.53, "word": " the", "probability": 0.91552734375}, {"start": 1407.53, "end": 1407.85, "word": " fund.", "probability": 0.931640625}, {"start": 1409.61, "end": 1410.27, "word": " Now,", "probability": 0.931640625}, {"start": 1410.71, "end": 1411.03, "word": " here", "probability": 0.859375}, {"start": 1411.03, "end": 1411.21, "word": " we", "probability": 0.896484375}, {"start": 1411.21, "end": 1411.39, "word": " have", "probability": 0.94482421875}, {"start": 1411.39, "end": 1411.55, "word": " a", "probability": 0.9638671875}, {"start": 1411.55, "end": 1411.95, "word": " recent", "probability": 0.92578125}], "temperature": 1.0}, {"id": 51, "seek": 143785, "start": 1412.25, "end": 1437.85, "text": " It says that a recent survey of eight private colleges in the United States revealed the following endowment in millions of dollars. So we have this data. So it's raw data. Summary statistics yield export to be 180. 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"text": " But here, the mean and standard deviation are given. So just use this information anyway. Calculate 95 confidence interval for the mean endowment of all private colleges in the United States, assuming a normal distribution for the endowment. Here we have 95%. Now what's the sample size? It says that eight.", "tokens": [583, 510, 11, 264, 914, 293, 3832, 25163, 366, 2212, 13, 407, 445, 764, 341, 1589, 4033, 13, 3511, 2444, 473, 13420, 6687, 15035, 337, 264, 914, 917, 47966, 295, 439, 4551, 15272, 294, 264, 2824, 3040, 11, 11926, 257, 2710, 7316, 337, 264, 917, 47966, 13, 1692, 321, 362, 13420, 6856, 823, 437, 311, 264, 6889, 2744, 30, 467, 1619, 300, 3180, 13], "avg_logprob": -0.16009615384615383, "compression_ratio": 1.4597156398104265, "no_speech_prob": 0.0, "words": [{"start": 1457.04, "end": 1457.34, "word": " But", "probability": 0.73828125}, {"start": 1457.34, "end": 1457.58, "word": " here,", "probability": 0.828125}, {"start": 1457.8, "end": 1457.96, "word": " the", "probability": 0.88037109375}, {"start": 1457.96, "end": 1458.24, "word": " mean", "probability": 0.96435546875}, {"start": 1458.24, "end": 1459.46, "word": " and", "probability": 0.787109375}, {"start": 1459.46, "end": 1459.86, "word": " standard", "probability": 0.90478515625}, {"start": 1459.86, "end": 1460.26, "word": " deviation", "probability": 0.94580078125}, {"start": 1460.26, "end": 1460.72, "word": " are", "probability": 0.9375}, {"start": 1460.72, "end": 1461.04, "word": " given.", "probability": 0.9052734375}, {"start": 1461.6, "end": 1461.96, "word": " So", "probability": 0.96240234375}, {"start": 1461.96, "end": 1462.2, "word": " just", "probability": 0.76220703125}, {"start": 1462.2, "end": 1462.48, "word": " use", "probability": 0.86962890625}, {"start": 1462.48, "end": 1462.72, "word": " this", "probability": 0.9462890625}, {"start": 1462.72, "end": 1463.2, "word": " information", "probability": 0.8369140625}, {"start": 1463.2, "end": 1463.54, "word": " anyway.", "probability": 0.452880859375}, {"start": 1464.0, "end": 1464.5, "word": " Calculate", "probability": 0.98095703125}, {"start": 1464.5, "end": 1465.1, "word": " 95", "probability": 0.97900390625}, {"start": 1465.1, "end": 1465.76, "word": " confidence", "probability": 0.958984375}, {"start": 1465.76, "end": 1466.24, "word": " interval", "probability": 0.8603515625}, {"start": 1466.24, "end": 1467.26, "word": " for", "probability": 0.92138671875}, {"start": 1467.26, "end": 1467.48, "word": " the", "probability": 0.92333984375}, {"start": 1467.48, "end": 1467.72, "word": " mean", "probability": 0.9638671875}, {"start": 1467.72, "end": 1468.18, "word": " endowment", "probability": 0.777099609375}, {"start": 1468.18, "end": 1468.66, "word": " of", "probability": 0.96142578125}, {"start": 1468.66, "end": 1468.94, "word": " all", "probability": 0.94189453125}, {"start": 1468.94, "end": 1469.32, "word": " private", "probability": 0.85888671875}, {"start": 1469.32, "end": 1469.78, "word": " colleges", "probability": 0.9072265625}, {"start": 1469.78, "end": 1470.02, "word": " in", "probability": 0.93701171875}, {"start": 1470.02, "end": 1470.14, "word": " the", "probability": 0.87109375}, {"start": 1470.14, "end": 1470.38, "word": " United", "probability": 0.9208984375}, {"start": 1470.38, "end": 1470.86, "word": " States,", "probability": 0.9443359375}, {"start": 1472.4, "end": 1472.86, "word": " assuming", "probability": 0.88232421875}, {"start": 1472.86, "end": 1473.1, "word": " a", "probability": 0.994140625}, {"start": 1473.1, "end": 1473.44, "word": " normal", "probability": 0.87841796875}, {"start": 1473.44, "end": 1474.04, "word": " distribution", "probability": 0.88330078125}, {"start": 1474.04, "end": 1474.52, "word": " for", "probability": 0.951171875}, {"start": 1474.52, "end": 1474.72, "word": " the", "probability": 0.89892578125}, {"start": 1474.72, "end": 1475.08, "word": " endowment.", "probability": 0.935302734375}, {"start": 1475.28, "end": 1475.6, "word": " Here", "probability": 0.7646484375}, {"start": 1475.6, "end": 1475.76, "word": " we", "probability": 0.6396484375}, {"start": 1475.76, "end": 1476.08, "word": " have", "probability": 0.94873046875}, {"start": 1476.08, "end": 1479.3, "word": " 95%.", "probability": 0.7568359375}, {"start": 1479.3, "end": 1482.6, "word": " Now", "probability": 0.9580078125}, {"start": 1482.6, "end": 1482.84, "word": " what's", "probability": 0.75244140625}, {"start": 1482.84, "end": 1482.98, "word": " the", "probability": 0.92919921875}, {"start": 1482.98, "end": 1483.18, "word": " sample", "probability": 0.92578125}, {"start": 1483.18, "end": 1483.66, "word": " size?", "probability": 0.86083984375}, {"start": 1485.38, "end": 1485.64, "word": " It", "probability": 0.814453125}, {"start": 1485.64, "end": 1485.88, "word": " says", "probability": 0.6640625}, {"start": 1485.88, "end": 1486.12, "word": " that", "probability": 0.86328125}, {"start": 1486.12, "end": 1486.5, "word": " eight.", "probability": 0.56396484375}], "temperature": 1.0}, {"id": 54, "seek": 151346, "start": 1487.6, "end": 1513.46, "text": " So N is eight. So again, simple calculation. So explore, plus or minus T, S over root N. So use the same idea for the previous one. And the answer for number 10 is part D. So D is the correct answer. So again,", "tokens": [407, 426, 307, 3180, 13, 407, 797, 11, 2199, 17108, 13, 407, 6839, 11, 1804, 420, 3175, 314, 11, 318, 670, 5593, 426, 13, 407, 764, 264, 912, 1558, 337, 264, 3894, 472, 13, 400, 264, 1867, 337, 1230, 1266, 307, 644, 413, 13, 407, 413, 307, 264, 3006, 1867, 13, 407, 797, 11], "avg_logprob": -0.21463068236004224, "compression_ratio": 1.4482758620689655, "no_speech_prob": 0.0, "words": [{"start": 1487.6, "end": 1488.08, "word": " So", "probability": 0.79736328125}, {"start": 1488.08, "end": 1488.48, "word": " N", "probability": 0.289306640625}, {"start": 1488.48, "end": 1489.4, "word": " is", "probability": 0.908203125}, {"start": 1489.4, "end": 1489.74, "word": " eight.", "probability": 0.5126953125}, {"start": 1490.58, "end": 1490.9, "word": " So", "probability": 0.939453125}, {"start": 1490.9, "end": 1491.18, "word": " again,", "probability": 0.89013671875}, {"start": 1491.34, "end": 1491.68, "word": " simple", "probability": 0.92431640625}, {"start": 1491.68, "end": 1492.34, "word": " calculation.", "probability": 0.9248046875}, {"start": 1493.74, "end": 1493.9, "word": " So", "probability": 0.92431640625}, {"start": 1493.9, "end": 1494.4, "word": " explore,", "probability": 0.317626953125}, {"start": 1494.98, "end": 1495.42, "word": " plus", "probability": 0.83154296875}, {"start": 1495.42, "end": 1495.56, "word": " or", "probability": 0.94580078125}, {"start": 1495.56, "end": 1495.82, "word": " minus", "probability": 0.990234375}, {"start": 1495.82, "end": 1496.2, "word": " T,", "probability": 0.81494140625}, {"start": 1496.42, "end": 1496.64, "word": " S", "probability": 0.8544921875}, {"start": 1496.64, "end": 1497.06, "word": " over", "probability": 0.87255859375}, {"start": 1497.06, "end": 1498.24, "word": " root", "probability": 0.8818359375}, {"start": 1498.24, "end": 1498.46, "word": " N.", "probability": 0.97216796875}, {"start": 1499.22, "end": 1499.46, "word": " So", "probability": 0.94873046875}, {"start": 1499.46, "end": 1499.68, "word": " use", "probability": 0.7705078125}, {"start": 1499.68, "end": 1499.92, "word": " the", "probability": 0.9150390625}, {"start": 1499.92, "end": 1500.34, "word": " same", "probability": 0.9091796875}, {"start": 1500.34, "end": 1501.52, "word": " idea", "probability": 0.9140625}, {"start": 1501.52, "end": 1501.84, "word": " for", "probability": 0.70703125}, {"start": 1501.84, "end": 1501.98, "word": " the", "probability": 0.9189453125}, {"start": 1501.98, "end": 1502.3, "word": " previous", "probability": 0.845703125}, {"start": 1502.3, "end": 1502.7, "word": " one.", "probability": 0.9287109375}, {"start": 1503.38, "end": 1503.7, "word": " And", "probability": 0.94873046875}, {"start": 1503.7, "end": 1503.82, "word": " the", "probability": 0.79296875}, {"start": 1503.82, "end": 1504.2, "word": " answer", "probability": 0.96044921875}, {"start": 1504.2, "end": 1505.92, "word": " for", "probability": 0.89208984375}, {"start": 1505.92, "end": 1506.22, "word": " number", "probability": 0.935546875}, {"start": 1506.22, "end": 1506.64, "word": " 10", "probability": 0.85693359375}, {"start": 1506.64, "end": 1508.54, "word": " is", "probability": 0.86474609375}, {"start": 1508.54, "end": 1508.9, "word": " part", "probability": 0.7705078125}, {"start": 1508.9, "end": 1509.22, "word": " D.", "probability": 0.96142578125}, {"start": 1509.48, "end": 1509.68, "word": " So", "probability": 0.95654296875}, {"start": 1509.68, "end": 1509.84, "word": " D", "probability": 0.9443359375}, {"start": 1509.84, "end": 1510.02, "word": " is", "probability": 0.94775390625}, {"start": 1510.02, "end": 1510.16, "word": " the", "probability": 0.91259765625}, {"start": 1510.16, "end": 1510.42, "word": " correct", "probability": 0.90576171875}, {"start": 1510.42, "end": 1510.84, "word": " answer.", "probability": 0.947265625}, {"start": 1512.62, "end": 1513.12, "word": " So", "probability": 0.95751953125}, {"start": 1513.12, "end": 1513.46, "word": " again,", "probability": 0.91552734375}], "temperature": 1.0}, {"id": 55, "seek": 153126, "start": 1514.48, "end": 1531.26, "text": " For eleven, D is the correct answer. For ten, D is the correct answer. Next. So this one is similar to the one we just did. Eleven.", "tokens": [1171, 21090, 11, 413, 307, 264, 3006, 1867, 13, 1171, 2064, 11, 413, 307, 264, 3006, 1867, 13, 3087, 13, 407, 341, 472, 307, 2531, 281, 264, 472, 321, 445, 630, 13, 48548, 13], "avg_logprob": -0.2018973239830562, "compression_ratio": 1.4193548387096775, "no_speech_prob": 0.0, "words": [{"start": 1514.48, "end": 1514.84, "word": " For", "probability": 0.61328125}, {"start": 1514.84, "end": 1515.3, "word": " eleven,", "probability": 0.439453125}, {"start": 1516.24, "end": 1516.44, "word": " D", "probability": 0.48388671875}, {"start": 1516.44, "end": 1516.88, "word": " is", "probability": 0.947265625}, {"start": 1516.88, "end": 1517.04, "word": " the", "probability": 0.8701171875}, {"start": 1517.04, "end": 1517.38, "word": " correct", "probability": 0.89990234375}, {"start": 1517.38, "end": 1517.76, "word": " answer.", "probability": 0.42138671875}, {"start": 1518.2, "end": 1518.34, "word": " For", "probability": 0.716796875}, {"start": 1518.34, "end": 1518.56, "word": " ten,", "probability": 0.8017578125}, {"start": 1518.8, "end": 1518.92, "word": " D", "probability": 0.9580078125}, {"start": 1518.92, "end": 1519.04, "word": " is", "probability": 0.94970703125}, {"start": 1519.04, "end": 1519.16, "word": " the", "probability": 0.89404296875}, {"start": 1519.16, "end": 1519.4, "word": " correct", "probability": 0.90234375}, {"start": 1519.4, "end": 1519.72, "word": " answer.", "probability": 0.9619140625}, {"start": 1521.2, "end": 1521.8, "word": " Next.", "probability": 0.875}, {"start": 1522.4, "end": 1522.68, "word": " So", "probability": 0.8173828125}, {"start": 1522.68, "end": 1522.88, "word": " this", "probability": 0.80517578125}, {"start": 1522.88, "end": 1523.08, "word": " one", "probability": 0.9150390625}, {"start": 1523.08, "end": 1523.26, "word": " is", "probability": 0.951171875}, {"start": 1523.26, "end": 1523.64, "word": " similar", "probability": 0.943359375}, {"start": 1523.64, "end": 1523.88, "word": " to", "probability": 0.9677734375}, {"start": 1523.88, "end": 1523.98, "word": " the", "probability": 0.9111328125}, {"start": 1523.98, "end": 1524.12, "word": " one", "probability": 0.92626953125}, {"start": 1524.12, "end": 1524.28, "word": " we", "probability": 0.93115234375}, {"start": 1524.28, "end": 1524.7, "word": " just", "probability": 0.8984375}, {"start": 1524.7, "end": 1526.28, "word": " did.", "probability": 0.89306640625}, {"start": 1530.66, "end": 1531.26, "word": " Eleven.", "probability": 0.822265625}], "temperature": 1.0}, {"id": 56, "seek": 156486, "start": 1547.14, "end": 1564.86, "text": " Here it says that rather than examine the records of all students, the dean took a random sample of size 200. So we have large university. Here we took representative sample of size 200.", "tokens": [1692, 309, 1619, 300, 2831, 813, 17496, 264, 7724, 295, 439, 1731, 11, 264, 31120, 1890, 257, 4974, 6889, 295, 2744, 2331, 13, 407, 321, 362, 2416, 5454, 13, 1692, 321, 1890, 12424, 6889, 295, 2744, 2331, 13], "avg_logprob": -0.21955128663625473, "compression_ratio": 1.4274809160305344, "no_speech_prob": 0.0, "words": [{"start": 1547.1399999999999, "end": 1547.86, "word": " Here", "probability": 0.264404296875}, {"start": 1547.86, "end": 1548.58, "word": " it", "probability": 0.77734375}, {"start": 1548.58, "end": 1548.84, "word": " says", "probability": 0.890625}, {"start": 1548.84, "end": 1549.14, "word": " that", "probability": 0.88232421875}, {"start": 1549.14, "end": 1549.5, "word": " rather", "probability": 0.8408203125}, {"start": 1549.5, "end": 1549.86, "word": " than", "probability": 0.9443359375}, {"start": 1549.86, "end": 1550.36, "word": " examine", "probability": 0.935546875}, {"start": 1550.36, "end": 1550.72, "word": " the", "probability": 0.91552734375}, {"start": 1550.72, "end": 1551.14, "word": " records", "probability": 0.90185546875}, {"start": 1551.14, "end": 1551.46, "word": " of", "probability": 0.9658203125}, {"start": 1551.46, "end": 1551.82, "word": " all", "probability": 0.9384765625}, {"start": 1551.82, "end": 1552.6, "word": " students,", "probability": 0.921875}, {"start": 1552.88, "end": 1554.02, "word": " the", "probability": 0.6748046875}, {"start": 1554.02, "end": 1554.34, "word": " dean", "probability": 0.8125}, {"start": 1554.34, "end": 1555.04, "word": " took", "probability": 0.921875}, {"start": 1555.04, "end": 1555.26, "word": " a", "probability": 0.54248046875}, {"start": 1555.26, "end": 1555.54, "word": " random", "probability": 0.64404296875}, {"start": 1555.54, "end": 1555.98, "word": " sample", "probability": 0.87451171875}, {"start": 1555.98, "end": 1556.22, "word": " of", "probability": 0.96435546875}, {"start": 1556.22, "end": 1556.5, "word": " size", "probability": 0.8173828125}, {"start": 1556.5, "end": 1556.98, "word": " 200.", "probability": 0.92578125}, {"start": 1557.72, "end": 1558.0, "word": " So", "probability": 0.95068359375}, {"start": 1558.0, "end": 1558.12, "word": " we", "probability": 0.8603515625}, {"start": 1558.12, "end": 1558.34, "word": " have", "probability": 0.9462890625}, {"start": 1558.34, "end": 1558.84, "word": " large", "probability": 0.58447265625}, {"start": 1558.84, "end": 1559.5, "word": " university.", "probability": 0.80712890625}, {"start": 1560.84, "end": 1561.1, "word": " Here", "probability": 0.849609375}, {"start": 1561.1, "end": 1561.34, "word": " we", "probability": 0.87109375}, {"start": 1561.34, "end": 1562.2, "word": " took", "probability": 0.90478515625}, {"start": 1562.2, "end": 1562.88, "word": " representative", "probability": 0.88818359375}, {"start": 1562.88, "end": 1563.76, "word": " sample", "probability": 0.8720703125}, {"start": 1563.76, "end": 1564.08, "word": " of", "probability": 0.96826171875}, {"start": 1564.08, "end": 1564.38, "word": " size", "probability": 0.8251953125}, {"start": 1564.38, "end": 1564.86, "word": " 200.", "probability": 0.935546875}], "temperature": 1.0}, {"id": 57, "seek": 159626, "start": 1586.98, "end": 1596.26, "text": " How many students would be to be assembled? It says that if the dean wanted to estimate the proportion of all students,", "tokens": [1012, 867, 1731, 576, 312, 281, 312, 24204, 30, 467, 1619, 300, 498, 264, 31120, 1415, 281, 12539, 264, 16068, 295, 439, 1731, 11], "avg_logprob": -0.22546875, "compression_ratio": 1.2244897959183674, "no_speech_prob": 0.0, "words": [{"start": 1586.9799999999998, "end": 1587.62, "word": " How", "probability": 0.136962890625}, {"start": 1587.62, "end": 1588.26, "word": " many", "probability": 0.900390625}, {"start": 1588.26, "end": 1588.98, "word": " students", "probability": 0.97216796875}, {"start": 1588.98, "end": 1589.28, "word": " would", "probability": 0.8837890625}, {"start": 1589.28, "end": 1589.64, "word": " be", "probability": 0.91455078125}, {"start": 1589.64, "end": 1589.96, "word": " to", "probability": 0.88037109375}, {"start": 1589.96, "end": 1590.22, "word": " be", "probability": 0.96240234375}, {"start": 1590.22, "end": 1590.58, "word": " assembled?", "probability": 0.392333984375}, {"start": 1591.58, "end": 1591.9, "word": " It", "probability": 0.92333984375}, {"start": 1591.9, "end": 1592.1, "word": " says", "probability": 0.841796875}, {"start": 1592.1, "end": 1592.32, "word": " that", "probability": 0.90966796875}, {"start": 1592.32, "end": 1592.5, "word": " if", "probability": 0.84375}, {"start": 1592.5, "end": 1592.66, "word": " the", "probability": 0.85546875}, {"start": 1592.66, "end": 1592.84, "word": " dean", "probability": 0.9169921875}, {"start": 1592.84, "end": 1593.3, "word": " wanted", "probability": 0.88134765625}, {"start": 1593.3, "end": 1593.74, "word": " to", "probability": 0.96630859375}, {"start": 1593.74, "end": 1594.22, "word": " estimate", "probability": 0.9306640625}, {"start": 1594.22, "end": 1594.54, "word": " the", "probability": 0.91748046875}, {"start": 1594.54, "end": 1594.98, "word": " proportion", "probability": 0.8369140625}, {"start": 1594.98, "end": 1595.28, "word": " of", "probability": 0.96923828125}, {"start": 1595.28, "end": 1595.54, "word": " all", "probability": 0.94189453125}, {"start": 1595.54, "end": 1596.26, "word": " students,", "probability": 0.75439453125}], "temperature": 1.0}, {"id": 58, "seek": 162578, "start": 1597.0, "end": 1625.78, "text": " The saving financial aid to within 3% with 99% probability. How many students would need to be sampled? So we have the formula, if you remember, n equals z y 1 minus y divided by e. So we have z squared. 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Now in this problem, it says that Dean selected 200 students, and he finds that out of this number, 118 of them are receiving financial aid. So based on this information, we can compute B. So B is x over n. It's 118 divided by 200. 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That means the proportion, the sample proportion, is 118 divided by 200, which is 0.59. So we have to use this information instead of pi. So n equals, now it's about 99%.", "tokens": [407, 294, 341, 1389, 11, 484, 295, 2331, 1731, 11, 2975, 23, 295, 552, 366, 10040, 4669, 9418, 13, 663, 1355, 264, 16068, 11, 264, 6889, 16068, 11, 307, 2975, 23, 6666, 538, 2331, 11, 597, 307, 1958, 13, 19600, 13, 407, 321, 362, 281, 764, 341, 1589, 2602, 295, 3895, 13, 407, 297, 6915, 11, 586, 309, 311, 466, 11803, 6856], "avg_logprob": -0.16319445012107728, "compression_ratio": 1.4124293785310735, "no_speech_prob": 0.0, "words": [{"start": 1661.09, "end": 1661.35, "word": " So", "probability": 0.89111328125}, {"start": 1661.35, "end": 1661.47, "word": " in", "probability": 0.8212890625}, {"start": 1661.47, "end": 1661.63, "word": " this", "probability": 0.94677734375}, {"start": 1661.63, "end": 1662.03, "word": " case,", "probability": 0.91015625}, {"start": 1662.73, "end": 1663.55, "word": " out", "probability": 0.87890625}, {"start": 1663.55, "end": 1663.83, "word": " of", "probability": 0.970703125}, {"start": 1663.83, "end": 1664.45, "word": " 200", "probability": 0.8916015625}, {"start": 1664.45, "end": 1665.09, "word": " students,", "probability": 0.97265625}, {"start": 1665.27, "end": 1665.81, "word": " 118", "probability": 0.912109375}, {"start": 1665.81, "end": 1666.05, "word": " of", "probability": 0.95703125}, {"start": 1666.05, "end": 1666.31, "word": " them", "probability": 0.89794921875}, {"start": 1666.31, "end": 1666.61, "word": " are", "probability": 0.939453125}, {"start": 1666.61, "end": 1666.97, "word": " receiving", "probability": 0.91748046875}, {"start": 1666.97, "end": 1667.45, "word": " financial", "probability": 0.87939453125}, {"start": 1667.45, "end": 1667.77, "word": " aid.", "probability": 0.9384765625}, {"start": 1668.63, "end": 1669.09, "word": " That", "probability": 0.8544921875}, {"start": 1669.09, "end": 1669.37, "word": " means", "probability": 0.92626953125}, {"start": 1669.37, "end": 1669.63, "word": " the", "probability": 0.857421875}, {"start": 1669.63, "end": 1670.15, "word": " proportion,", "probability": 0.76025390625}, {"start": 1670.67, "end": 1670.99, "word": " the", "probability": 0.89306640625}, {"start": 1670.99, "end": 1671.29, "word": " sample", "probability": 0.77783203125}, {"start": 1671.29, "end": 1671.85, "word": " proportion,", "probability": 0.8076171875}, {"start": 1672.83, "end": 1673.03, "word": " is", "probability": 0.94189453125}, {"start": 1673.03, "end": 1673.47, "word": " 118", "probability": 0.94384765625}, {"start": 1673.47, "end": 1673.73, "word": " divided", "probability": 0.7490234375}, {"start": 1673.73, "end": 1673.91, "word": " by", "probability": 0.97314453125}, {"start": 1673.91, "end": 1674.31, "word": " 200,", "probability": 0.92724609375}, {"start": 1674.49, "end": 1674.69, "word": " which", "probability": 0.9453125}, {"start": 1674.69, "end": 1674.93, "word": " is", "probability": 0.94189453125}, {"start": 1674.93, "end": 1675.17, "word": " 0", "probability": 0.84619140625}, {"start": 1675.17, "end": 1675.71, "word": ".59.", "probability": 0.9951171875}, {"start": 1676.21, "end": 1676.67, "word": " So", "probability": 0.95654296875}, {"start": 1676.67, "end": 1676.81, "word": " we", "probability": 0.9287109375}, {"start": 1676.81, "end": 1676.99, "word": " have", "probability": 0.9462890625}, {"start": 1676.99, "end": 1677.13, "word": " to", "probability": 0.96826171875}, {"start": 1677.13, "end": 1677.35, "word": " use", "probability": 0.8740234375}, {"start": 1677.35, "end": 1677.69, "word": " this", "probability": 0.95166015625}, {"start": 1677.69, "end": 1678.33, "word": " information", "probability": 0.830078125}, {"start": 1678.33, "end": 1680.35, "word": " instead", "probability": 0.8134765625}, {"start": 1680.35, "end": 1680.67, "word": " of", "probability": 0.9677734375}, {"start": 1680.67, "end": 1680.97, "word": " pi.", "probability": 0.350830078125}, {"start": 1682.67, "end": 1683.17, "word": " So", "probability": 0.890625}, {"start": 1683.17, "end": 1683.37, "word": " n", "probability": 0.6630859375}, {"start": 1683.37, "end": 1683.83, "word": " equals,", "probability": 0.93359375}, {"start": 1688.05, "end": 1688.41, "word": " now", "probability": 0.75537109375}, {"start": 1688.41, "end": 1688.57, "word": " it's", "probability": 0.929931640625}, {"start": 1688.57, "end": 1688.79, "word": " about", "probability": 0.9208984375}, {"start": 1688.79, "end": 1689.55, "word": " 99%.", "probability": 0.4798583984375}], "temperature": 1.0}, {"id": 61, "seek": 171272, "start": 1691.72, "end": 1712.72, "text": " 2.85. Exactly, it's one of these. We have 2.57 and 8. It says 99%. So here we have 99%. So what's left?", "tokens": [568, 13, 19287, 13, 7587, 11, 309, 311, 472, 295, 613, 13, 492, 362, 568, 13, 19004, 293, 1649, 13, 467, 1619, 11803, 6856, 407, 510, 321, 362, 11803, 6856, 407, 437, 311, 1411, 30], "avg_logprob": -0.2816840137044589, "compression_ratio": 1.0612244897959184, "no_speech_prob": 0.0, "words": [{"start": 1691.72, "end": 1691.96, "word": " 2", "probability": 0.353271484375}, {"start": 1691.96, "end": 1692.48, "word": ".85.", "probability": 0.79052734375}, {"start": 1693.26, "end": 1693.84, "word": " Exactly,", "probability": 0.31005859375}, {"start": 1694.16, "end": 1694.4, "word": " it's", "probability": 0.885986328125}, {"start": 1694.4, "end": 1694.96, "word": " one", "probability": 0.87060546875}, {"start": 1694.96, "end": 1695.12, "word": " of", "probability": 0.9677734375}, {"start": 1695.12, "end": 1695.36, "word": " these.", "probability": 0.86181640625}, {"start": 1696.0, "end": 1696.26, "word": " We", "probability": 0.830078125}, {"start": 1696.26, "end": 1696.56, "word": " have", "probability": 0.94970703125}, {"start": 1696.56, "end": 1696.94, "word": " 2", "probability": 0.9541015625}, {"start": 1696.94, "end": 1698.14, "word": ".57", "probability": 0.887451171875}, {"start": 1698.14, "end": 1701.38, "word": " and", "probability": 0.69287109375}, {"start": 1701.38, "end": 1701.74, "word": " 8.", "probability": 0.55419921875}, {"start": 1704.08, "end": 1704.8, "word": " It", "probability": 0.83251953125}, {"start": 1704.8, "end": 1705.1, "word": " says", "probability": 0.857421875}, {"start": 1705.1, "end": 1707.14, "word": " 99%.", "probability": 0.6357421875}, {"start": 1707.14, "end": 1710.22, "word": " So", "probability": 0.91796875}, {"start": 1710.22, "end": 1710.4, "word": " here", "probability": 0.79443359375}, {"start": 1710.4, "end": 1710.58, "word": " we", "probability": 0.8076171875}, {"start": 1710.58, "end": 1710.72, "word": " have", "probability": 0.94873046875}, {"start": 1710.72, "end": 1711.6, "word": " 99%.", "probability": 0.873046875}, {"start": 1711.6, "end": 1712.26, "word": " So", "probability": 0.91845703125}, {"start": 1712.26, "end": 1712.5, "word": " what's", "probability": 0.927490234375}, {"start": 1712.5, "end": 1712.72, "word": " left?", "probability": 0.931640625}], "temperature": 1.0}, {"id": 62, "seek": 174322, "start": 1722.18, "end": 1743.22, "text": " 0.5 percent, this area. 0.5 to the right and 0.5 to the left, so 005. Now if you look at 2.5 under 7, the answer is 0051, the other one 0049. So either this one or the other value, so 2.57.", "tokens": [1958, 13, 20, 3043, 11, 341, 1859, 13, 1958, 13, 20, 281, 264, 558, 293, 1958, 13, 20, 281, 264, 1411, 11, 370, 7143, 20, 13, 823, 498, 291, 574, 412, 568, 13, 20, 833, 1614, 11, 264, 1867, 307, 7143, 18682, 11, 264, 661, 472, 7143, 14938, 13, 407, 2139, 341, 472, 420, 264, 661, 2158, 11, 370, 568, 13, 19004, 13], "avg_logprob": -0.21594238048419356, "compression_ratio": 1.4179104477611941, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1722.18, "end": 1722.34, "word": " 0", "probability": 0.486572265625}, {"start": 1722.34, "end": 1722.74, "word": ".5", "probability": 0.970703125}, {"start": 1722.74, "end": 1723.12, "word": " percent,", "probability": 0.27197265625}, {"start": 1723.62, "end": 1723.8, "word": " this", "probability": 0.837890625}, {"start": 1723.8, "end": 1724.14, "word": " area.", "probability": 0.873046875}, {"start": 1725.72, "end": 1725.96, "word": " 0", "probability": 0.82666015625}, {"start": 1725.96, "end": 1726.26, "word": ".5", "probability": 0.994873046875}, {"start": 1726.26, "end": 1726.44, "word": " to", "probability": 0.95703125}, {"start": 1726.44, "end": 1726.56, "word": " the", "probability": 0.9130859375}, {"start": 1726.56, "end": 1726.74, "word": " right", "probability": 0.904296875}, {"start": 1726.74, "end": 1726.9, "word": " and", "probability": 0.72021484375}, {"start": 1726.9, "end": 1727.08, "word": " 0", "probability": 0.97509765625}, {"start": 1727.08, "end": 1727.32, "word": ".5", "probability": 0.99853515625}, {"start": 1727.32, "end": 1727.48, "word": " to", "probability": 0.96533203125}, {"start": 1727.48, "end": 1727.6, "word": " the", "probability": 0.92041015625}, {"start": 1727.6, "end": 1727.76, "word": " left,", "probability": 0.92626953125}, {"start": 1728.0, "end": 1728.0, "word": " so", "probability": 0.93310546875}, {"start": 1728.0, "end": 1729.44, "word": " 005.", "probability": 0.6776123046875}, {"start": 1730.48, "end": 1730.96, "word": " Now", "probability": 0.9482421875}, {"start": 1730.96, "end": 1731.12, "word": " if", "probability": 0.5966796875}, {"start": 1731.12, "end": 1731.2, "word": " you", "probability": 0.9248046875}, {"start": 1731.2, "end": 1731.36, "word": " look", "probability": 0.96728515625}, {"start": 1731.36, "end": 1731.52, "word": " at", "probability": 0.9609375}, {"start": 1731.52, "end": 1731.8, "word": " 2", "probability": 0.970703125}, {"start": 1731.8, "end": 1732.28, "word": ".5", "probability": 0.9287109375}, {"start": 1732.28, "end": 1732.5, "word": " under", "probability": 0.417724609375}, {"start": 1732.5, "end": 1732.86, "word": " 7,", "probability": 0.63916015625}, {"start": 1733.1, "end": 1733.26, "word": " the", "probability": 0.89453125}, {"start": 1733.26, "end": 1733.58, "word": " answer", "probability": 0.951171875}, {"start": 1733.58, "end": 1733.84, "word": " is", "probability": 0.9453125}, {"start": 1733.84, "end": 1735.58, "word": " 0051,", "probability": 0.86083984375}, {"start": 1735.98, "end": 1736.08, "word": " the", "probability": 0.74560546875}, {"start": 1736.08, "end": 1736.28, "word": " other", "probability": 0.8857421875}, {"start": 1736.28, "end": 1736.5, "word": " one", "probability": 0.8984375}, {"start": 1736.5, "end": 1737.28, "word": " 0049.", "probability": 0.83203125}, {"start": 1739.84, "end": 1740.24, "word": " So", "probability": 0.8359375}, {"start": 1740.24, "end": 1740.46, "word": " either", "probability": 0.8564453125}, {"start": 1740.46, "end": 1740.78, "word": " this", "probability": 0.94677734375}, {"start": 1740.78, "end": 1741.0, "word": " one", "probability": 0.9306640625}, {"start": 1741.0, "end": 1741.22, "word": " or", "probability": 0.9130859375}, {"start": 1741.22, "end": 1741.4, "word": " the", "probability": 0.58251953125}, {"start": 1741.4, "end": 1741.62, "word": " other", "probability": 0.8720703125}, {"start": 1741.62, "end": 1742.02, "word": " value,", "probability": 0.5380859375}, {"start": 1742.14, "end": 1742.3, "word": " so", "probability": 0.9189453125}, {"start": 1742.3, "end": 1742.6, "word": " 2", "probability": 0.98681640625}, {"start": 1742.6, "end": 1743.22, "word": ".57.", "probability": 0.9892578125}], "temperature": 1.0}, {"id": 63, "seek": 177272, "start": 1744.3, "end": 1772.72, "text": " or 2.58, it's better to take the average of these two. Because 005 lies exactly between these two values. So the score in this case, either 2.75 or 2.78, or the average. And the exact one, 2.7, I'm sorry, 2.576.", "tokens": [420, 568, 13, 20419, 11, 309, 311, 1101, 281, 747, 264, 4274, 295, 613, 732, 13, 1436, 7143, 20, 9134, 2293, 1296, 613, 732, 4190, 13, 407, 264, 6175, 294, 341, 1389, 11, 2139, 568, 13, 11901, 420, 568, 13, 30693, 11, 420, 264, 4274, 13, 400, 264, 1900, 472, 11, 568, 13, 22, 11, 286, 478, 2597, 11, 568, 13, 19004, 21, 13], "avg_logprob": -0.16622596153846153, "compression_ratio": 1.4228187919463087, "no_speech_prob": 0.0, "words": [{"start": 1744.3, "end": 1744.6, "word": " or", "probability": 0.37744140625}, {"start": 1744.6, "end": 1744.84, "word": " 2", "probability": 0.986328125}, {"start": 1744.84, "end": 1745.54, "word": ".58,", "probability": 0.989501953125}, {"start": 1745.86, "end": 1746.06, "word": " it's", "probability": 0.9345703125}, {"start": 1746.06, "end": 1746.26, "word": " better", "probability": 0.9140625}, {"start": 1746.26, "end": 1746.48, "word": " to", "probability": 0.95849609375}, {"start": 1746.48, "end": 1746.74, "word": " take", "probability": 0.86474609375}, {"start": 1746.74, "end": 1746.9, "word": " the", "probability": 0.896484375}, {"start": 1746.9, "end": 1747.22, "word": " average", "probability": 0.7900390625}, {"start": 1747.22, "end": 1747.42, "word": " of", "probability": 0.94775390625}, {"start": 1747.42, "end": 1747.6, "word": " these", "probability": 0.85009765625}, {"start": 1747.6, "end": 1747.86, "word": " two.", "probability": 0.8916015625}, {"start": 1748.26, "end": 1748.82, "word": " Because", "probability": 0.92626953125}, {"start": 1748.82, "end": 1749.96, "word": " 005", "probability": 0.84619140625}, {"start": 1749.96, "end": 1750.88, "word": " lies", "probability": 0.90966796875}, {"start": 1750.88, "end": 1751.56, "word": " exactly", "probability": 0.908203125}, {"start": 1751.56, "end": 1752.76, "word": " between", "probability": 0.86572265625}, {"start": 1752.76, "end": 1753.12, "word": " these", "probability": 0.8603515625}, {"start": 1753.12, "end": 1753.32, "word": " two", "probability": 0.92529296875}, {"start": 1753.32, "end": 1753.64, "word": " values.", "probability": 0.94189453125}, {"start": 1753.8, "end": 1754.18, "word": " So", "probability": 0.9423828125}, {"start": 1754.18, "end": 1755.84, "word": " the", "probability": 0.27587890625}, {"start": 1755.84, "end": 1756.24, "word": " score", "probability": 0.8525390625}, {"start": 1756.24, "end": 1756.44, "word": " in", "probability": 0.72265625}, {"start": 1756.44, "end": 1756.62, "word": " this", "probability": 0.9443359375}, {"start": 1756.62, "end": 1756.98, "word": " case,", "probability": 0.89013671875}, {"start": 1758.0, "end": 1758.24, "word": " either", "probability": 0.8916015625}, {"start": 1758.24, "end": 1758.56, "word": " 2", "probability": 0.99072265625}, {"start": 1758.56, "end": 1759.16, "word": ".75", "probability": 0.992919921875}, {"start": 1759.16, "end": 1760.78, "word": " or", "probability": 0.83935546875}, {"start": 1760.78, "end": 1762.14, "word": " 2", "probability": 0.99169921875}, {"start": 1762.14, "end": 1762.7, "word": ".78,", "probability": 0.996826171875}, {"start": 1763.82, "end": 1765.06, "word": " or", "probability": 0.9169921875}, {"start": 1765.06, "end": 1765.24, "word": " the", "probability": 0.9130859375}, {"start": 1765.24, "end": 1765.7, "word": " average.", "probability": 0.7880859375}, {"start": 1766.58, "end": 1766.96, "word": " And", "probability": 0.94970703125}, {"start": 1766.96, "end": 1767.14, "word": " the", "probability": 0.90380859375}, {"start": 1767.14, "end": 1767.56, "word": " exact", "probability": 0.93896484375}, {"start": 1767.56, "end": 1767.92, "word": " one,", "probability": 0.93701171875}, {"start": 1769.18, "end": 1769.36, "word": " 2", "probability": 0.97265625}, {"start": 1769.36, "end": 1770.08, "word": ".7,", "probability": 0.929931640625}, {"start": 1770.64, "end": 1770.88, "word": " I'm", "probability": 0.98193359375}, {"start": 1770.88, "end": 1771.06, "word": " sorry,", "probability": 0.837890625}, {"start": 1771.36, "end": 1771.64, "word": " 2", "probability": 0.9970703125}, {"start": 1771.64, "end": 1772.72, "word": ".576.", "probability": 0.8821614583333334}], "temperature": 1.0}, {"id": 64, "seek": 180202, "start": 1773.66, "end": 1802.02, "text": " The exact answer. It's better to use the average if you don't remember the exact answer. So it's the exact one. But 2.575 is okay. Now just use this equation, 2.575 times square, times 59.", "tokens": [440, 1900, 1867, 13, 467, 311, 1101, 281, 764, 264, 4274, 498, 291, 500, 380, 1604, 264, 1900, 1867, 13, 407, 309, 311, 264, 1900, 472, 13, 583, 568, 13, 20, 11901, 307, 1392, 13, 823, 445, 764, 341, 5367, 11, 568, 13, 20, 11901, 1413, 3732, 11, 1413, 24624, 13], "avg_logprob": -0.19531250114624316, "compression_ratio": 1.4104477611940298, "no_speech_prob": 0.0, "words": [{"start": 1773.66, "end": 1773.94, "word": " The", "probability": 0.214111328125}, {"start": 1773.94, "end": 1774.34, "word": " exact", "probability": 0.9287109375}, {"start": 1774.34, "end": 1774.68, "word": " answer.", "probability": 0.939453125}, {"start": 1778.0, "end": 1778.8, "word": " It's", "probability": 0.906494140625}, {"start": 1778.8, "end": 1779.02, "word": " better", "probability": 0.91015625}, {"start": 1779.02, "end": 1779.2, "word": " to", "probability": 0.95361328125}, {"start": 1779.2, "end": 1779.4, "word": " use", "probability": 0.87939453125}, {"start": 1779.4, "end": 1779.52, "word": " the", "probability": 0.88134765625}, {"start": 1779.52, "end": 1779.92, "word": " average", "probability": 0.79296875}, {"start": 1779.92, "end": 1780.32, "word": " if", "probability": 0.81298828125}, {"start": 1780.32, "end": 1780.46, "word": " you", "probability": 0.9599609375}, {"start": 1780.46, "end": 1780.7, "word": " don't", "probability": 0.971435546875}, {"start": 1780.7, "end": 1781.18, "word": " remember", "probability": 0.86279296875}, {"start": 1781.18, "end": 1783.34, "word": " the", "probability": 0.75927734375}, {"start": 1783.34, "end": 1783.84, "word": " exact", "probability": 0.94384765625}, {"start": 1783.84, "end": 1784.28, "word": " answer.", "probability": 0.95654296875}, {"start": 1784.94, "end": 1785.16, "word": " So", "probability": 0.9150390625}, {"start": 1785.16, "end": 1785.32, "word": " it's", "probability": 0.775634765625}, {"start": 1785.32, "end": 1785.5, "word": " the", "probability": 0.9189453125}, {"start": 1785.5, "end": 1785.82, "word": " exact", "probability": 0.9404296875}, {"start": 1785.82, "end": 1786.1, "word": " one.", "probability": 0.93359375}, {"start": 1787.48, "end": 1787.74, "word": " But", "probability": 0.76123046875}, {"start": 1787.74, "end": 1787.92, "word": " 2", "probability": 0.943359375}, {"start": 1787.92, "end": 1788.9, "word": ".575", "probability": 0.9443359375}, {"start": 1788.9, "end": 1789.64, "word": " is", "probability": 0.931640625}, {"start": 1789.64, "end": 1789.92, "word": " okay.", "probability": 0.77978515625}, {"start": 1791.3, "end": 1791.56, "word": " Now", "probability": 0.88623046875}, {"start": 1791.56, "end": 1791.82, "word": " just", "probability": 0.68017578125}, {"start": 1791.82, "end": 1792.14, "word": " use", "probability": 0.87060546875}, {"start": 1792.14, "end": 1792.66, "word": " this", "probability": 0.947265625}, {"start": 1792.66, "end": 1793.12, "word": " equation,", "probability": 0.97607421875}, {"start": 1793.3, "end": 1793.44, "word": " 2", "probability": 0.9912109375}, {"start": 1793.44, "end": 1795.6, "word": ".575", "probability": 0.97314453125}, {"start": 1795.6, "end": 1798.0, "word": " times", "probability": 0.56103515625}, {"start": 1798.0, "end": 1798.48, "word": " square,", "probability": 0.32763671875}, {"start": 1800.0, "end": 1800.62, "word": " times", "probability": 0.916015625}, {"start": 1800.62, "end": 1802.02, "word": " 59.", "probability": 0.93408203125}], "temperature": 1.0}, {"id": 65, "seek": 183114, "start": 1803.9, "end": 1831.14, "text": " 1 minus 59 divided by the error. It's three percent. So it's 0.0312 squared. So the answer in this case is part 2.57 times 59 times 41 divided by 03 squared. The answer is part.", "tokens": [502, 3175, 24624, 6666, 538, 264, 6713, 13, 467, 311, 1045, 3043, 13, 407, 309, 311, 1958, 13, 11592, 4762, 8889, 13, 407, 264, 1867, 294, 341, 1389, 307, 644, 568, 13, 19004, 1413, 24624, 1413, 18173, 6666, 538, 43677, 8889, 13, 440, 1867, 307, 644, 13], "avg_logprob": -0.23567707712451616, "compression_ratio": 1.424, "no_speech_prob": 0.0, "words": [{"start": 1803.9, "end": 1804.12, "word": " 1", "probability": 0.57275390625}, {"start": 1804.12, "end": 1804.48, "word": " minus", "probability": 0.97314453125}, {"start": 1804.48, "end": 1804.88, "word": " 59", "probability": 0.96240234375}, {"start": 1804.88, "end": 1806.9, "word": " divided", "probability": 0.465576171875}, {"start": 1806.9, "end": 1807.26, "word": " by", "probability": 0.9638671875}, {"start": 1807.26, "end": 1807.44, "word": " the", "probability": 0.8935546875}, {"start": 1807.44, "end": 1807.74, "word": " error.", "probability": 0.74951171875}, {"start": 1808.78, "end": 1809.18, "word": " It's", "probability": 0.9375}, {"start": 1809.18, "end": 1809.44, "word": " three", "probability": 0.1202392578125}, {"start": 1809.44, "end": 1809.64, "word": " percent.", "probability": 0.246337890625}, {"start": 1810.4, "end": 1810.92, "word": " So", "probability": 0.921875}, {"start": 1810.92, "end": 1811.16, "word": " it's", "probability": 0.911865234375}, {"start": 1811.16, "end": 1811.44, "word": " 0", "probability": 0.8935546875}, {"start": 1811.44, "end": 1813.34, "word": ".0312", "probability": 0.88134765625}, {"start": 1813.34, "end": 1813.8, "word": " squared.", "probability": 0.56396484375}, {"start": 1816.26, "end": 1816.98, "word": " So", "probability": 0.9365234375}, {"start": 1816.98, "end": 1817.26, "word": " the", "probability": 0.89208984375}, {"start": 1817.26, "end": 1817.58, "word": " answer", "probability": 0.95361328125}, {"start": 1817.58, "end": 1817.8, "word": " in", "probability": 0.86181640625}, {"start": 1817.8, "end": 1817.98, "word": " this", "probability": 0.9423828125}, {"start": 1817.98, "end": 1818.24, "word": " case", "probability": 0.9091796875}, {"start": 1818.24, "end": 1818.46, "word": " is", "probability": 0.92333984375}, {"start": 1818.46, "end": 1818.72, "word": " part", "probability": 0.720703125}, {"start": 1818.72, "end": 1823.42, "word": " 2", "probability": 0.8291015625}, {"start": 1823.42, "end": 1824.06, "word": ".57", "probability": 0.995849609375}, {"start": 1824.06, "end": 1825.3, "word": " times", "probability": 0.912109375}, {"start": 1825.3, "end": 1825.9, "word": " 59", "probability": 0.9794921875}, {"start": 1825.9, "end": 1826.64, "word": " times", "probability": 0.90478515625}, {"start": 1826.64, "end": 1827.14, "word": " 41", "probability": 0.97705078125}, {"start": 1827.14, "end": 1827.76, "word": " divided", "probability": 0.7470703125}, {"start": 1827.76, "end": 1828.02, "word": " by", "probability": 0.97216796875}, {"start": 1828.02, "end": 1828.44, "word": " 03", "probability": 0.58447265625}, {"start": 1828.44, "end": 1829.2, "word": " squared.", "probability": 0.85791015625}, {"start": 1829.98, "end": 1830.3, "word": " The", "probability": 0.8759765625}, {"start": 1830.3, "end": 1830.6, "word": " answer", "probability": 0.95361328125}, {"start": 1830.6, "end": 1830.84, "word": " is", "probability": 0.9453125}, {"start": 1830.84, "end": 1831.14, "word": " part.", "probability": 0.89794921875}], "temperature": 1.0}, {"id": 66, "seek": 186505, "start": 1841.65, "end": 1865.05, "text": " You will get the exact answer if you use 2.576. You will get the exact answer. But anyway, if you use one of these, you will get approximate answer to be 1784. Any question? 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That means the sample proportion is 118 divided by 200, which gives 0.59. So we have to use 59% as the sample proportion. Is it clear?", "tokens": [2602, 295, 1958, 13, 20, 11, 570, 264, 31120, 8209, 257, 4974, 6889, 295, 2744, 2331, 11, 293, 415, 10704, 300, 2975, 23, 295, 552, 366, 10040, 4669, 9418, 13, 663, 1355, 264, 6889, 16068, 307, 2975, 23, 6666, 538, 2331, 11, 597, 2709, 1958, 13, 19600, 13, 407, 321, 362, 281, 764, 24624, 4, 382, 264, 6889, 16068, 13, 1119, 309, 1850, 30], "avg_logprob": -0.13689903846153847, "compression_ratio": 1.4887640449438202, "no_speech_prob": 0.0, "words": [{"start": 1866.68, "end": 1867.22, "word": " instead", "probability": 0.56982421875}, {"start": 1867.22, "end": 1867.88, "word": " of", "probability": 0.9658203125}, {"start": 1867.88, "end": 1868.44, "word": " 0", "probability": 0.5146484375}, {"start": 1868.44, "end": 1868.78, "word": ".5,", "probability": 0.989013671875}, {"start": 1868.9, "end": 1869.22, "word": " because", "probability": 0.8955078125}, {"start": 1869.22, "end": 1869.82, "word": " the", "probability": 0.9013671875}, {"start": 1869.82, "end": 1871.24, "word": " dean", "probability": 0.796875}, {"start": 1871.24, "end": 1871.76, "word": " selected", "probability": 0.876953125}, {"start": 1871.76, "end": 1871.94, "word": " a", "probability": 0.947265625}, {"start": 1871.94, "end": 1872.14, "word": " random", "probability": 0.8525390625}, {"start": 1872.14, "end": 1872.48, "word": " sample", "probability": 0.8515625}, {"start": 1872.48, "end": 1872.66, "word": " of", "probability": 0.943359375}, {"start": 1872.66, "end": 1872.88, "word": " size", "probability": 0.82568359375}, {"start": 1872.88, "end": 1873.3, "word": " 200,", "probability": 0.94287109375}, {"start": 1873.5, "end": 1873.64, "word": " and", "probability": 0.9296875}, {"start": 1873.64, "end": 1873.8, "word": " he", "probability": 0.96337890625}, {"start": 1873.8, "end": 1874.12, "word": " finds", "probability": 0.89306640625}, {"start": 1874.12, "end": 1874.58, "word": " that", "probability": 0.93359375}, {"start": 1874.58, "end": 1876.12, "word": " 118", "probability": 0.826171875}, {"start": 1876.12, "end": 1876.58, "word": " of", "probability": 0.96728515625}, {"start": 1876.58, "end": 1876.82, "word": " them", "probability": 0.89892578125}, {"start": 1876.82, "end": 1877.02, "word": " are", "probability": 0.939453125}, {"start": 1877.02, "end": 1877.38, "word": " receiving", "probability": 0.91845703125}, {"start": 1877.38, "end": 1877.86, "word": " financial", "probability": 0.8701171875}, {"start": 1877.86, "end": 1878.22, "word": " aid.", "probability": 0.95703125}, {"start": 1878.84, "end": 1879.2, "word": " That", "probability": 0.9052734375}, {"start": 1879.2, "end": 1879.56, "word": " means", "probability": 0.92822265625}, {"start": 1879.56, "end": 1880.08, "word": " the", "probability": 0.8798828125}, {"start": 1880.08, "end": 1880.94, "word": " sample", "probability": 0.84228515625}, {"start": 1880.94, "end": 1881.48, "word": " proportion", "probability": 0.7412109375}, {"start": 1881.48, "end": 1882.92, "word": " is", "probability": 0.921875}, {"start": 1882.92, "end": 1884.16, "word": " 118", "probability": 0.952392578125}, {"start": 1884.16, "end": 1884.46, "word": " divided", "probability": 0.77587890625}, {"start": 1884.46, "end": 1884.6, "word": " by", "probability": 0.96630859375}, {"start": 1884.6, "end": 1884.98, "word": " 200,", "probability": 0.9208984375}, {"start": 1885.36, "end": 1885.7, "word": " which", "probability": 0.95068359375}, {"start": 1885.7, "end": 1885.94, "word": " gives", "probability": 0.8505859375}, {"start": 1885.94, "end": 1886.2, "word": " 0", "probability": 0.96337890625}, {"start": 1886.2, "end": 1886.68, "word": ".59.", "probability": 0.99755859375}, {"start": 1887.2, "end": 1887.38, "word": " So", "probability": 0.95263671875}, {"start": 1887.38, "end": 1887.48, "word": " we", "probability": 0.86083984375}, {"start": 1887.48, "end": 1887.6, "word": " have", "probability": 0.9462890625}, {"start": 1887.6, "end": 1887.7, "word": " to", "probability": 0.970703125}, {"start": 1887.7, "end": 1887.94, "word": " use", "probability": 0.88037109375}, {"start": 1887.94, "end": 1888.66, "word": " 59", "probability": 0.98388671875}, {"start": 1888.66, "end": 1889.48, "word": "%", "probability": 0.95263671875}, {"start": 1889.48, "end": 1890.2, "word": " as", "probability": 0.9501953125}, {"start": 1890.2, "end": 1890.42, "word": " the", "probability": 0.8818359375}, {"start": 1890.42, "end": 1890.82, "word": " sample", "probability": 0.8779296875}, {"start": 1890.82, "end": 1891.6, "word": " proportion.", "probability": 0.69189453125}, {"start": 1892.96, "end": 1893.68, "word": " Is", "probability": 0.95703125}, {"start": 1893.68, "end": 1893.82, "word": " it", "probability": 0.86083984375}, {"start": 1893.82, "end": 1894.1, "word": " clear?", "probability": 0.91259765625}], "temperature": 1.0}, {"id": 68, "seek": 192392, "start": 1896.68, "end": 1923.92, "text": " Next, number three. An economist is interested in studying the incomes of consumers in a particular region. The population standard deviation is known to be 1,000. A random sample of 50 individuals resulted in an average income of $15,000.", "tokens": [3087, 11, 1230, 1045, 13, 1107, 36696, 307, 3102, 294, 7601, 264, 42458, 295, 11883, 294, 257, 1729, 4458, 13, 440, 4415, 3832, 25163, 307, 2570, 281, 312, 502, 11, 1360, 13, 316, 4974, 6889, 295, 2625, 5346, 18753, 294, 364, 4274, 5742, 295, 1848, 5211, 11, 1360, 13], "avg_logprob": -0.13820311933755874, "compression_ratio": 1.3953488372093024, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1896.68, "end": 1897.16, "word": " Next,", "probability": 0.89990234375}, {"start": 1898.04, "end": 1898.36, "word": " number", "probability": 0.857421875}, {"start": 1898.36, "end": 1898.76, "word": " three.", "probability": 0.429443359375}, {"start": 1901.7, "end": 1902.04, "word": " An", "probability": 0.9521484375}, {"start": 1902.04, "end": 1902.6, "word": " economist", "probability": 0.88232421875}, {"start": 1902.6, "end": 1903.66, "word": " is", "probability": 0.93994140625}, {"start": 1903.66, "end": 1904.22, "word": " interested", "probability": 0.857421875}, {"start": 1904.22, "end": 1904.68, "word": " in", "probability": 0.93896484375}, {"start": 1904.68, "end": 1905.12, "word": " studying", "probability": 0.951171875}, {"start": 1905.12, "end": 1905.34, "word": " the", "probability": 0.91162109375}, {"start": 1905.34, "end": 1905.86, "word": " incomes", "probability": 0.92138671875}, {"start": 1905.86, "end": 1907.84, "word": " of", "probability": 0.9697265625}, {"start": 1907.84, "end": 1908.98, "word": " consumers", "probability": 0.92724609375}, {"start": 1908.98, "end": 1909.2, "word": " in", "probability": 0.85546875}, {"start": 1909.2, "end": 1909.24, "word": " a", "probability": 0.515625}, {"start": 1909.24, "end": 1909.58, "word": " particular", "probability": 0.90185546875}, {"start": 1909.58, "end": 1910.0, "word": " region.", "probability": 0.93505859375}, {"start": 1911.24, "end": 1911.62, "word": " The", "probability": 0.89599609375}, {"start": 1911.62, "end": 1912.34, "word": " population", "probability": 0.90966796875}, {"start": 1912.34, "end": 1913.34, "word": " standard", "probability": 0.888671875}, {"start": 1913.34, "end": 1913.76, "word": " deviation", "probability": 0.958984375}, {"start": 1913.76, "end": 1914.08, "word": " is", "probability": 0.9501953125}, {"start": 1914.08, "end": 1914.44, "word": " known", "probability": 0.7255859375}, {"start": 1914.44, "end": 1915.6, "word": " to", "probability": 0.96923828125}, {"start": 1915.6, "end": 1915.96, "word": " be", "probability": 0.95458984375}, {"start": 1915.96, "end": 1916.4, "word": " 1", "probability": 0.87158203125}, {"start": 1916.4, "end": 1916.94, "word": ",000.", "probability": 0.994873046875}, {"start": 1917.34, "end": 1917.56, "word": " A", "probability": 0.830078125}, {"start": 1917.56, "end": 1917.78, "word": " random", "probability": 0.85107421875}, {"start": 1917.78, "end": 1918.12, "word": " sample", "probability": 0.69140625}, {"start": 1918.12, "end": 1918.36, "word": " of", "probability": 0.9677734375}, {"start": 1918.36, "end": 1918.66, "word": " 50", "probability": 0.82373046875}, {"start": 1918.66, "end": 1919.32, "word": " individuals", "probability": 0.849609375}, {"start": 1919.32, "end": 1920.56, "word": " resulted", "probability": 0.91015625}, {"start": 1920.56, "end": 1921.08, "word": " in", "probability": 0.94140625}, {"start": 1921.08, "end": 1921.64, "word": " an", "probability": 0.9521484375}, {"start": 1921.64, "end": 1922.06, "word": " average", "probability": 0.78271484375}, {"start": 1922.06, "end": 1922.8, "word": " income", "probability": 0.947265625}, {"start": 1922.8, "end": 1923.08, "word": " of", "probability": 0.96533203125}, {"start": 1923.08, "end": 1923.4, "word": " $15", "probability": 0.9892578125}, {"start": 1923.4, "end": 1923.92, "word": ",000.", "probability": 0.998779296875}], "temperature": 1.0}, {"id": 69, "seek": 195440, "start": 1925.44, "end": 1954.4, "text": " What is the weight of the 90% confidence interval? So here in this example, the population standard deviation sigma is known. So sigma is $1000. Random sample of size 50 is selected. This sample gives an average", "tokens": [708, 307, 264, 3364, 295, 264, 4289, 4, 6687, 15035, 30, 407, 510, 294, 341, 1365, 11, 264, 4415, 3832, 25163, 12771, 307, 2570, 13, 407, 12771, 307, 1848, 21199, 13, 37603, 6889, 295, 2744, 2625, 307, 8209, 13, 639, 6889, 2709, 364, 4274], "avg_logprob": -0.2203125066227383, "compression_ratio": 1.3766233766233766, "no_speech_prob": 0.0, "words": [{"start": 1925.44, "end": 1925.94, "word": " What", "probability": 0.461669921875}, {"start": 1925.94, "end": 1926.26, "word": " is", "probability": 0.9248046875}, {"start": 1926.26, "end": 1926.46, "word": " the", "probability": 0.9140625}, {"start": 1926.46, "end": 1926.7, "word": " weight", "probability": 0.78369140625}, {"start": 1926.7, "end": 1927.3, "word": " of", "probability": 0.96142578125}, {"start": 1927.3, "end": 1927.5, "word": " the", "probability": 0.7197265625}, {"start": 1927.5, "end": 1927.76, "word": " 90", "probability": 0.9482421875}, {"start": 1927.76, "end": 1928.34, "word": "%", "probability": 0.82958984375}, {"start": 1928.34, "end": 1929.16, "word": " confidence", "probability": 0.9658203125}, {"start": 1929.16, "end": 1929.76, "word": " interval?", "probability": 0.984375}, {"start": 1930.56, "end": 1930.78, "word": " So", "probability": 0.7314453125}, {"start": 1930.78, "end": 1931.08, "word": " here", "probability": 0.74609375}, {"start": 1931.08, "end": 1931.52, "word": " in", "probability": 0.6796875}, {"start": 1931.52, "end": 1931.98, "word": " this", "probability": 0.94921875}, {"start": 1931.98, "end": 1933.08, "word": " example,", "probability": 0.962890625}, {"start": 1934.74, "end": 1935.0, "word": " the", "probability": 0.6904296875}, {"start": 1935.0, "end": 1935.86, "word": " population", "probability": 0.876953125}, {"start": 1935.86, "end": 1936.18, "word": " standard", "probability": 0.43505859375}, {"start": 1936.18, "end": 1936.56, "word": " deviation", "probability": 0.9306640625}, {"start": 1936.56, "end": 1936.92, "word": " sigma", "probability": 0.4541015625}, {"start": 1936.92, "end": 1937.18, "word": " is", "probability": 0.92822265625}, {"start": 1937.18, "end": 1937.44, "word": " known.", "probability": 0.68408203125}, {"start": 1938.64, "end": 1939.1, "word": " So", "probability": 0.91455078125}, {"start": 1939.1, "end": 1939.52, "word": " sigma", "probability": 0.8505859375}, {"start": 1939.52, "end": 1940.82, "word": " is", "probability": 0.94091796875}, {"start": 1940.82, "end": 1941.48, "word": " $1000.", "probability": 0.623779296875}, {"start": 1944.6, "end": 1945.52, "word": " Random", "probability": 0.71337890625}, {"start": 1945.52, "end": 1945.9, "word": " sample", "probability": 0.91162109375}, {"start": 1945.9, "end": 1946.1, "word": " of", "probability": 0.9599609375}, {"start": 1946.1, "end": 1946.44, "word": " size", "probability": 0.85791015625}, {"start": 1946.44, "end": 1946.94, "word": " 50", "probability": 0.95556640625}, {"start": 1946.94, "end": 1949.14, "word": " is", "probability": 0.90673828125}, {"start": 1949.14, "end": 1949.56, "word": " selected.", "probability": 0.890625}, {"start": 1951.42, "end": 1951.92, "word": " This", "probability": 0.8623046875}, {"start": 1951.92, "end": 1952.28, "word": " sample", "probability": 0.8857421875}, {"start": 1952.28, "end": 1952.76, "word": " gives", "probability": 0.90966796875}, {"start": 1952.76, "end": 1953.92, "word": " an", "probability": 0.94482421875}, {"start": 1953.92, "end": 1954.4, "word": " average", "probability": 0.779296875}], "temperature": 1.0}, {"id": 70, "seek": 198257, "start": 1956.15, "end": 1982.57, "text": " of $15,000 ask about what is the width of the 90% confidence interval. So again, here we are asking about the width of the confidence interval. If we have a random sample of size 50,", "tokens": [295, 1848, 5211, 11, 1360, 1029, 466, 437, 307, 264, 11402, 295, 264, 4289, 4, 6687, 15035, 13, 407, 797, 11, 510, 321, 366, 3365, 466, 264, 11402, 295, 264, 6687, 15035, 13, 759, 321, 362, 257, 4974, 6889, 295, 2744, 2625, 11], "avg_logprob": -0.14071378179571845, "compression_ratio": 1.4296875, "no_speech_prob": 0.0, "words": [{"start": 1956.15, "end": 1956.55, "word": " of", "probability": 0.497314453125}, {"start": 1956.55, "end": 1957.61, "word": " $15", "probability": 0.912841796875}, {"start": 1957.61, "end": 1958.17, "word": ",000", "probability": 0.95849609375}, {"start": 1958.17, "end": 1961.43, "word": " ask", "probability": 0.1722412109375}, {"start": 1961.43, "end": 1961.95, "word": " about", "probability": 0.90380859375}, {"start": 1961.95, "end": 1962.93, "word": " what", "probability": 0.85791015625}, {"start": 1962.93, "end": 1963.21, "word": " is", "probability": 0.93505859375}, {"start": 1963.21, "end": 1963.43, "word": " the", "probability": 0.92724609375}, {"start": 1963.43, "end": 1963.73, "word": " width", "probability": 0.83447265625}, {"start": 1963.73, "end": 1965.19, "word": " of", "probability": 0.962890625}, {"start": 1965.19, "end": 1965.43, "word": " the", "probability": 0.86962890625}, {"start": 1965.43, "end": 1965.91, "word": " 90", "probability": 0.9765625}, {"start": 1965.91, "end": 1966.61, "word": "%", "probability": 0.939453125}, {"start": 1966.61, "end": 1968.15, "word": " confidence", "probability": 0.83837890625}, {"start": 1968.15, "end": 1968.49, "word": " interval.", "probability": 0.98486328125}, {"start": 1969.95, "end": 1970.75, "word": " So", "probability": 0.9267578125}, {"start": 1970.75, "end": 1971.07, "word": " again,", "probability": 0.8759765625}, {"start": 1972.13, "end": 1975.63, "word": " here", "probability": 0.8447265625}, {"start": 1975.63, "end": 1975.77, "word": " we", "probability": 0.76806640625}, {"start": 1975.77, "end": 1975.93, "word": " are", "probability": 0.935546875}, {"start": 1975.93, "end": 1976.31, "word": " asking", "probability": 0.875}, {"start": 1976.31, "end": 1976.73, "word": " about", "probability": 0.90673828125}, {"start": 1976.73, "end": 1977.73, "word": " the", "probability": 0.92529296875}, {"start": 1977.73, "end": 1977.99, "word": " width", "probability": 0.958984375}, {"start": 1977.99, "end": 1978.15, "word": " of", "probability": 0.96484375}, {"start": 1978.15, "end": 1978.29, "word": " the", "probability": 0.91845703125}, {"start": 1978.29, "end": 1978.71, "word": " confidence", "probability": 0.97119140625}, {"start": 1978.71, "end": 1979.11, "word": " interval.", "probability": 0.95751953125}, {"start": 1979.93, "end": 1980.65, "word": " If", "probability": 0.96923828125}, {"start": 1980.65, "end": 1980.85, "word": " we", "probability": 0.95849609375}, {"start": 1980.85, "end": 1981.01, "word": " have", "probability": 0.94091796875}, {"start": 1981.01, "end": 1981.17, "word": " a", "probability": 0.9853515625}, {"start": 1981.17, "end": 1981.41, "word": " random", "probability": 0.87109375}, {"start": 1981.41, "end": 1981.73, "word": " sample", "probability": 0.91162109375}, {"start": 1981.73, "end": 1981.95, "word": " of", "probability": 0.955078125}, {"start": 1981.95, "end": 1982.17, "word": " size", "probability": 0.8818359375}, {"start": 1982.17, "end": 1982.57, "word": " 50,", "probability": 0.765625}], "temperature": 1.0}, {"id": 71, "seek": 200180, "start": 1983.32, "end": 2001.8, "text": " And that sample gives an average of $15,000. And we know that the population standard deviation is 1,000. Now, what's the width of the 90% confidence interval? Any idea of this?", "tokens": [400, 300, 6889, 2709, 364, 4274, 295, 1848, 5211, 11, 1360, 13, 400, 321, 458, 300, 264, 4415, 3832, 25163, 307, 502, 11, 1360, 13, 823, 11, 437, 311, 264, 11402, 295, 264, 4289, 4, 6687, 15035, 30, 2639, 1558, 295, 341, 30], "avg_logprob": -0.11434659446504983, "compression_ratio": 1.2992700729927007, "no_speech_prob": 0.0, "words": [{"start": 1983.32, "end": 1983.62, "word": " And", "probability": 0.79248046875}, {"start": 1983.62, "end": 1983.84, "word": " that", "probability": 0.92041015625}, {"start": 1983.84, "end": 1984.18, "word": " sample", "probability": 0.744140625}, {"start": 1984.18, "end": 1984.48, "word": " gives", "probability": 0.8876953125}, {"start": 1984.48, "end": 1984.68, "word": " an", "probability": 0.943359375}, {"start": 1984.68, "end": 1984.98, "word": " average", "probability": 0.7705078125}, {"start": 1984.98, "end": 1985.2, "word": " of", "probability": 0.96630859375}, {"start": 1985.2, "end": 1985.52, "word": " $15", "probability": 0.9248046875}, {"start": 1985.52, "end": 1985.88, "word": ",000.", "probability": 0.967041015625}, {"start": 1986.84, "end": 1987.56, "word": " And", "probability": 0.95556640625}, {"start": 1987.56, "end": 1987.74, "word": " we", "probability": 0.96142578125}, {"start": 1987.74, "end": 1987.88, "word": " know", "probability": 0.8837890625}, {"start": 1987.88, "end": 1988.18, "word": " that", "probability": 0.89208984375}, {"start": 1988.18, "end": 1988.7, "word": " the", "probability": 0.90869140625}, {"start": 1988.7, "end": 1989.1, "word": " population", "probability": 0.94677734375}, {"start": 1989.1, "end": 1989.56, "word": " standard", "probability": 0.91552734375}, {"start": 1989.56, "end": 1990.04, "word": " deviation", "probability": 0.931640625}, {"start": 1990.04, "end": 1990.94, "word": " is", "probability": 0.9462890625}, {"start": 1990.94, "end": 1991.26, "word": " 1", "probability": 0.7236328125}, {"start": 1991.26, "end": 1991.68, "word": ",000.", "probability": 0.968994140625}, {"start": 1993.24, "end": 1993.96, "word": " Now,", "probability": 0.96142578125}, {"start": 1994.08, "end": 1994.42, "word": " what's", "probability": 0.964111328125}, {"start": 1994.42, "end": 1994.58, "word": " the", "probability": 0.92529296875}, {"start": 1994.58, "end": 1994.88, "word": " width", "probability": 0.55419921875}, {"start": 1994.88, "end": 1995.98, "word": " of", "probability": 0.9638671875}, {"start": 1995.98, "end": 1996.16, "word": " the", "probability": 0.9091796875}, {"start": 1996.16, "end": 1996.52, "word": " 90", "probability": 0.98388671875}, {"start": 1996.52, "end": 1997.02, "word": "%", "probability": 0.95458984375}, {"start": 1997.02, "end": 1997.58, "word": " confidence", "probability": 0.95556640625}, {"start": 1997.58, "end": 1998.02, "word": " interval?", "probability": 0.953125}, {"start": 1998.88, "end": 1999.44, "word": " Any", "probability": 0.91162109375}, {"start": 1999.44, "end": 2000.02, "word": " idea", "probability": 0.919921875}, {"start": 2000.02, "end": 2001.54, "word": " of", "probability": 0.85888671875}, {"start": 2001.54, "end": 2001.8, "word": " this?", "probability": 0.93798828125}], "temperature": 1.0}, {"id": 72, "seek": 203180, "start": 2013.76, "end": 2031.8, "text": " So idea number one is fine. You may calculate the lower limit and upper limit. And the difference between these two gives the width. So idea number one, the width equals the distance between upper limit", "tokens": [407, 1558, 1230, 472, 307, 2489, 13, 509, 815, 8873, 264, 3126, 4948, 293, 6597, 4948, 13, 400, 264, 2649, 1296, 613, 732, 2709, 264, 11402, 13, 407, 1558, 1230, 472, 11, 264, 11402, 6915, 264, 4560, 1296, 6597, 4948], "avg_logprob": -0.20236279906296148, "compression_ratio": 1.5859375, "no_speech_prob": 0.0, "words": [{"start": 2013.76, "end": 2014.46, "word": " So", "probability": 0.140869140625}, {"start": 2014.46, "end": 2015.16, "word": " idea", "probability": 0.771484375}, {"start": 2015.16, "end": 2015.42, "word": " number", "probability": 0.92431640625}, {"start": 2015.42, "end": 2015.62, "word": " one", "probability": 0.76416015625}, {"start": 2015.62, "end": 2015.78, "word": " is", "probability": 0.94287109375}, {"start": 2015.78, "end": 2016.08, "word": " fine.", "probability": 0.86865234375}, {"start": 2016.42, "end": 2016.86, "word": " You", "probability": 0.93603515625}, {"start": 2016.86, "end": 2017.56, "word": " may", "probability": 0.849609375}, {"start": 2017.56, "end": 2018.2, "word": " calculate", "probability": 0.9169921875}, {"start": 2018.2, "end": 2020.02, "word": " the", "probability": 0.8271484375}, {"start": 2020.02, "end": 2020.64, "word": " lower", "probability": 0.8818359375}, {"start": 2020.64, "end": 2020.96, "word": " limit", "probability": 0.95849609375}, {"start": 2020.96, "end": 2021.18, "word": " and", "probability": 0.92724609375}, {"start": 2021.18, "end": 2021.42, "word": " upper", "probability": 0.82177734375}, {"start": 2021.42, "end": 2021.88, "word": " limit.", "probability": 0.9658203125}, {"start": 2022.52, "end": 2022.94, "word": " And", "probability": 0.95166015625}, {"start": 2022.94, "end": 2023.06, "word": " the", "probability": 0.91455078125}, {"start": 2023.06, "end": 2023.4, "word": " difference", "probability": 0.869140625}, {"start": 2023.4, "end": 2023.76, "word": " between", "probability": 0.8740234375}, {"start": 2023.76, "end": 2024.08, "word": " these", "probability": 0.8642578125}, {"start": 2024.08, "end": 2024.3, "word": " two", "probability": 0.92236328125}, {"start": 2024.3, "end": 2024.7, "word": " gives", "probability": 0.88330078125}, {"start": 2024.7, "end": 2024.98, "word": " the", "probability": 0.892578125}, {"start": 2024.98, "end": 2025.18, "word": " width.", "probability": 0.59814453125}, {"start": 2025.64, "end": 2026.02, "word": " So", "probability": 0.9140625}, {"start": 2026.02, "end": 2026.36, "word": " idea", "probability": 0.88037109375}, {"start": 2026.36, "end": 2026.64, "word": " number", "probability": 0.94091796875}, {"start": 2026.64, "end": 2026.96, "word": " one,", "probability": 0.908203125}, {"start": 2027.5, "end": 2027.68, "word": " the", "probability": 0.8974609375}, {"start": 2027.68, "end": 2028.04, "word": " width", "probability": 0.96630859375}, {"start": 2028.04, "end": 2029.92, "word": " equals", "probability": 0.6220703125}, {"start": 2029.92, "end": 2030.14, "word": " the", "probability": 0.91650390625}, {"start": 2030.14, "end": 2030.64, "word": " distance", "probability": 0.935546875}, {"start": 2030.64, "end": 2031.02, "word": " between", "probability": 0.8740234375}, {"start": 2031.02, "end": 2031.36, "word": " upper", "probability": 0.853515625}, {"start": 2031.36, "end": 2031.8, "word": " limit", "probability": 0.96484375}], "temperature": 1.0}, {"id": 73, "seek": 206359, "start": 2034.11, "end": 2063.59, "text": " our limit minus lower limit. Now this distance gives a width, that's correct. Let's see. So in other words, you have to find the confidence interval by using this equation x bar plus or minus z sigma over root n, x bar is given. Now for 90% we know that z equals", "tokens": [527, 4948, 3175, 3126, 4948, 13, 823, 341, 4560, 2709, 257, 11402, 11, 300, 311, 3006, 13, 961, 311, 536, 13, 407, 294, 661, 2283, 11, 291, 362, 281, 915, 264, 6687, 15035, 538, 1228, 341, 5367, 2031, 2159, 1804, 420, 3175, 710, 12771, 670, 5593, 297, 11, 2031, 2159, 307, 2212, 13, 823, 337, 4289, 4, 321, 458, 300, 710, 6915], "avg_logprob": -0.21093750047305274, "compression_ratio": 1.445054945054945, "no_speech_prob": 0.0, "words": [{"start": 2034.11, "end": 2034.41, "word": " our", "probability": 0.1761474609375}, {"start": 2034.41, "end": 2034.79, "word": " limit", "probability": 0.9248046875}, {"start": 2034.79, "end": 2035.45, "word": " minus", "probability": 0.91943359375}, {"start": 2035.45, "end": 2035.71, "word": " lower", "probability": 0.8349609375}, {"start": 2035.71, "end": 2036.03, "word": " limit.", "probability": 0.916015625}, {"start": 2038.15, "end": 2038.79, "word": " Now", "probability": 0.8623046875}, {"start": 2038.79, "end": 2039.07, "word": " this", "probability": 0.67724609375}, {"start": 2039.07, "end": 2039.53, "word": " distance", "probability": 0.94091796875}, {"start": 2039.53, "end": 2039.95, "word": " gives", "probability": 0.88671875}, {"start": 2039.95, "end": 2040.23, "word": " a", "probability": 0.29931640625}, {"start": 2040.23, "end": 2040.53, "word": " width,", "probability": 0.89697265625}, {"start": 2040.65, "end": 2040.95, "word": " that's", "probability": 0.9111328125}, {"start": 2040.95, "end": 2041.31, "word": " correct.", "probability": 0.85400390625}, {"start": 2042.67, "end": 2043.09, "word": " Let's", "probability": 0.951416015625}, {"start": 2043.09, "end": 2043.27, "word": " see.", "probability": 0.91259765625}, {"start": 2044.71, "end": 2045.31, "word": " So", "probability": 0.9326171875}, {"start": 2045.31, "end": 2045.93, "word": " in", "probability": 0.68896484375}, {"start": 2045.93, "end": 2046.25, "word": " other", "probability": 0.8896484375}, {"start": 2046.25, "end": 2046.61, "word": " words,", "probability": 0.88037109375}, {"start": 2046.71, "end": 2046.81, "word": " you", "probability": 0.953125}, {"start": 2046.81, "end": 2047.01, "word": " have", "probability": 0.94580078125}, {"start": 2047.01, "end": 2047.13, "word": " to", "probability": 0.96826171875}, {"start": 2047.13, "end": 2047.37, "word": " find", "probability": 0.90380859375}, {"start": 2047.37, "end": 2047.53, "word": " the", "probability": 0.8662109375}, {"start": 2047.53, "end": 2047.91, "word": " confidence", "probability": 0.96826171875}, {"start": 2047.91, "end": 2048.49, "word": " interval", "probability": 0.96240234375}, {"start": 2048.49, "end": 2049.87, "word": " by", "probability": 0.787109375}, {"start": 2049.87, "end": 2050.21, "word": " using", "probability": 0.93359375}, {"start": 2050.21, "end": 2050.47, "word": " this", "probability": 0.92578125}, {"start": 2050.47, "end": 2051.07, "word": " equation", "probability": 0.865234375}, {"start": 2051.07, "end": 2051.39, "word": " x", "probability": 0.27587890625}, {"start": 2051.39, "end": 2051.57, "word": " bar", "probability": 0.7978515625}, {"start": 2051.57, "end": 2051.89, "word": " plus", "probability": 0.9658203125}, {"start": 2051.89, "end": 2052.07, "word": " or", "probability": 0.94677734375}, {"start": 2052.07, "end": 2052.33, "word": " minus", "probability": 0.9853515625}, {"start": 2052.33, "end": 2052.69, "word": " z", "probability": 0.92578125}, {"start": 2052.69, "end": 2054.61, "word": " sigma", "probability": 0.6181640625}, {"start": 2054.61, "end": 2055.61, "word": " over", "probability": 0.9130859375}, {"start": 2055.61, "end": 2055.85, "word": " root", "probability": 0.94482421875}, {"start": 2055.85, "end": 2056.11, "word": " n,", "probability": 0.83154296875}, {"start": 2056.37, "end": 2056.55, "word": " x", "probability": 0.994140625}, {"start": 2056.55, "end": 2056.71, "word": " bar", "probability": 0.91943359375}, {"start": 2056.71, "end": 2056.85, "word": " is", "probability": 0.94384765625}, {"start": 2056.85, "end": 2057.07, "word": " given.", "probability": 0.896484375}, {"start": 2060.19, "end": 2060.67, "word": " Now", "probability": 0.9482421875}, {"start": 2060.67, "end": 2060.89, "word": " for", "probability": 0.7880859375}, {"start": 2060.89, "end": 2061.17, "word": " 90", "probability": 0.93212890625}, {"start": 2061.17, "end": 2061.39, "word": "%", "probability": 0.615234375}, {"start": 2061.39, "end": 2061.71, "word": " we", "probability": 0.91064453125}, {"start": 2061.71, "end": 2061.87, "word": " know", "probability": 0.87939453125}, {"start": 2061.87, "end": 2062.29, "word": " that", "probability": 0.94091796875}, {"start": 2062.29, "end": 2062.87, "word": " z", "probability": 0.96435546875}, {"start": 2062.87, "end": 2063.59, "word": " equals", "probability": 0.92333984375}], "temperature": 1.0}, {"id": 74, "seek": 209073, "start": 2064.37, "end": 2090.73, "text": " 1.645 sigma is 1000 divided by root 50 plus or minus. By calculator, 1000 times this number divided by root 50 will give around 232.6.", "tokens": [502, 13, 21, 8465, 12771, 307, 9714, 6666, 538, 5593, 2625, 1804, 420, 3175, 13, 3146, 24993, 11, 9714, 1413, 341, 1230, 6666, 538, 5593, 2625, 486, 976, 926, 6673, 17, 13, 21, 13], "avg_logprob": -0.23058035629136223, "compression_ratio": 1.2616822429906542, "no_speech_prob": 0.0, "words": [{"start": 2064.37, "end": 2064.71, "word": " 1", "probability": 0.459228515625}, {"start": 2064.71, "end": 2067.53, "word": ".645", "probability": 0.92529296875}, {"start": 2067.53, "end": 2068.43, "word": " sigma", "probability": 0.215087890625}, {"start": 2068.43, "end": 2068.69, "word": " is", "probability": 0.84423828125}, {"start": 2068.69, "end": 2069.39, "word": " 1000", "probability": 0.65576171875}, {"start": 2069.39, "end": 2072.67, "word": " divided", "probability": 0.4306640625}, {"start": 2072.67, "end": 2072.87, "word": " by", "probability": 0.9697265625}, {"start": 2072.87, "end": 2073.07, "word": " root", "probability": 0.8251953125}, {"start": 2073.07, "end": 2073.51, "word": " 50", "probability": 0.86669921875}, {"start": 2073.51, "end": 2076.09, "word": " plus", "probability": 0.828125}, {"start": 2076.09, "end": 2076.31, "word": " or", "probability": 0.9365234375}, {"start": 2076.31, "end": 2076.67, "word": " minus.", "probability": 0.98974609375}, {"start": 2078.43, "end": 2079.05, "word": " By", "probability": 0.8271484375}, {"start": 2079.05, "end": 2079.59, "word": " calculator,", "probability": 0.81591796875}, {"start": 2080.43, "end": 2080.85, "word": " 1000", "probability": 0.80078125}, {"start": 2080.85, "end": 2081.47, "word": " times", "probability": 0.8974609375}, {"start": 2081.47, "end": 2081.71, "word": " this", "probability": 0.9267578125}, {"start": 2081.71, "end": 2082.09, "word": " number", "probability": 0.935546875}, {"start": 2082.09, "end": 2082.51, "word": " divided", "probability": 0.7568359375}, {"start": 2082.51, "end": 2082.77, "word": " by", "probability": 0.97021484375}, {"start": 2082.77, "end": 2083.17, "word": " root", "probability": 0.865234375}, {"start": 2083.17, "end": 2083.67, "word": " 50", "probability": 0.96240234375}, {"start": 2083.67, "end": 2084.63, "word": " will", "probability": 0.81787109375}, {"start": 2084.63, "end": 2085.01, "word": " give", "probability": 0.86572265625}, {"start": 2085.01, "end": 2089.19, "word": " around", "probability": 0.80322265625}, {"start": 2089.19, "end": 2090.13, "word": " 232", "probability": 0.9326171875}, {"start": 2090.13, "end": 2090.73, "word": ".6.", "probability": 0.9892578125}], "temperature": 1.0}, {"id": 75, "seek": 212027, "start": 2098.29, "end": 2120.27, "text": " So the upper limit is this value and lower limit 147671. So now the upper limit and lower limit are computed. Now the difference between these two values will give the weight.", "tokens": [407, 264, 6597, 4948, 307, 341, 2158, 293, 3126, 4948, 3499, 25026, 29985, 13, 407, 586, 264, 6597, 4948, 293, 3126, 4948, 366, 40610, 13, 823, 264, 2649, 1296, 613, 732, 4190, 486, 976, 264, 3364, 13], "avg_logprob": -0.2754934273268047, "compression_ratio": 1.4789915966386555, "no_speech_prob": 0.0, "words": [{"start": 2098.29, "end": 2099.09, "word": " So", "probability": 0.361572265625}, {"start": 2099.09, "end": 2099.39, "word": " the", "probability": 0.70849609375}, {"start": 2099.39, "end": 2099.81, "word": " upper", "probability": 0.8125}, {"start": 2099.81, "end": 2100.23, "word": " limit", "probability": 0.95458984375}, {"start": 2100.23, "end": 2103.21, "word": " is", "probability": 0.8369140625}, {"start": 2103.21, "end": 2103.45, "word": " this", "probability": 0.90771484375}, {"start": 2103.45, "end": 2103.83, "word": " value", "probability": 0.97216796875}, {"start": 2103.83, "end": 2104.95, "word": " and", "probability": 0.496826171875}, {"start": 2104.95, "end": 2105.21, "word": " lower", "probability": 0.67822265625}, {"start": 2105.21, "end": 2105.79, "word": " limit", "probability": 0.94384765625}, {"start": 2105.79, "end": 2109.65, "word": " 147671.", "probability": 0.6207682291666666}, {"start": 2111.35, "end": 2111.59, "word": " So", "probability": 0.74853515625}, {"start": 2111.59, "end": 2111.81, "word": " now", "probability": 0.80712890625}, {"start": 2111.81, "end": 2112.07, "word": " the", "probability": 0.5869140625}, {"start": 2112.07, "end": 2112.35, "word": " upper", "probability": 0.8134765625}, {"start": 2112.35, "end": 2112.75, "word": " limit", "probability": 0.79150390625}, {"start": 2112.75, "end": 2113.51, "word": " and", "probability": 0.62353515625}, {"start": 2113.51, "end": 2113.71, "word": " lower", "probability": 0.76220703125}, {"start": 2113.71, "end": 2113.99, "word": " limit", "probability": 0.91259765625}, {"start": 2113.99, "end": 2114.25, "word": " are", "probability": 0.92724609375}, {"start": 2114.25, "end": 2114.73, "word": " computed.", "probability": 0.87451171875}, {"start": 2116.07, "end": 2116.87, "word": " Now", "probability": 0.8896484375}, {"start": 2116.87, "end": 2117.07, "word": " the", "probability": 0.79541015625}, {"start": 2117.07, "end": 2117.47, "word": " difference", "probability": 0.8720703125}, {"start": 2117.47, "end": 2117.81, "word": " between", "probability": 0.88134765625}, {"start": 2117.81, "end": 2118.11, "word": " these", "probability": 0.86083984375}, {"start": 2118.11, "end": 2118.59, "word": " two", "probability": 0.84130859375}, {"start": 2118.59, "end": 2119.05, "word": " values", "probability": 0.9638671875}, {"start": 2119.05, "end": 2119.31, "word": " will", "probability": 0.8603515625}, {"start": 2119.31, "end": 2119.69, "word": " give", "probability": 0.89599609375}, {"start": 2119.69, "end": 2120.15, "word": " the", "probability": 0.383544921875}, {"start": 2120.15, "end": 2120.27, "word": " weight.", "probability": 0.71875}], "temperature": 1.0}, {"id": 76, "seek": 215027, "start": 2122.77, "end": 2150.27, "text": " If you subtract these two values, what equals 15,000? And the answer is 465.13, around. Maybe I took two minutes to figure the answer, the right answer. But there is another one, another idea, maybe shorter.", "tokens": [759, 291, 16390, 613, 732, 4190, 11, 437, 6915, 2119, 11, 1360, 30, 400, 264, 1867, 307, 1017, 16824, 13, 7668, 11, 926, 13, 2704, 286, 1890, 732, 2077, 281, 2573, 264, 1867, 11, 264, 558, 1867, 13, 583, 456, 307, 1071, 472, 11, 1071, 1558, 11, 1310, 11639, 13], "avg_logprob": -0.24800858661240222, "compression_ratio": 1.3774834437086092, "no_speech_prob": 0.0, "words": [{"start": 2122.77, "end": 2123.07, "word": " If", "probability": 0.71826171875}, {"start": 2123.07, "end": 2123.27, "word": " you", "probability": 0.9462890625}, {"start": 2123.27, "end": 2123.75, "word": " subtract", "probability": 0.76611328125}, {"start": 2123.75, "end": 2124.01, "word": " these", "probability": 0.85400390625}, {"start": 2124.01, "end": 2124.19, "word": " two", "probability": 0.84619140625}, {"start": 2124.19, "end": 2124.55, "word": " values,", "probability": 0.943359375}, {"start": 2124.65, "end": 2124.81, "word": " what", "probability": 0.44580078125}, {"start": 2124.81, "end": 2125.17, "word": " equals", "probability": 0.7099609375}, {"start": 2125.17, "end": 2125.59, "word": " 15", "probability": 0.45947265625}, {"start": 2125.59, "end": 2126.03, "word": ",000?", "probability": 0.6790771484375}, {"start": 2130.67, "end": 2131.35, "word": " And", "probability": 0.84375}, {"start": 2131.35, "end": 2131.47, "word": " the", "probability": 0.90771484375}, {"start": 2131.47, "end": 2131.75, "word": " answer", "probability": 0.95849609375}, {"start": 2131.75, "end": 2132.03, "word": " is", "probability": 0.94482421875}, {"start": 2132.03, "end": 2134.73, "word": " 465", "probability": 0.740478515625}, {"start": 2134.73, "end": 2135.81, "word": ".13,", "probability": 0.84521484375}, {"start": 2136.47, "end": 2137.19, "word": " around.", "probability": 0.9052734375}, {"start": 2140.05, "end": 2140.73, "word": " Maybe", "probability": 0.939453125}, {"start": 2140.73, "end": 2140.97, "word": " I", "probability": 0.73095703125}, {"start": 2140.97, "end": 2141.23, "word": " took", "probability": 0.63427734375}, {"start": 2141.23, "end": 2141.45, "word": " two", "probability": 0.7109375}, {"start": 2141.45, "end": 2141.83, "word": " minutes", "probability": 0.92041015625}, {"start": 2141.83, "end": 2143.39, "word": " to", "probability": 0.85400390625}, {"start": 2143.39, "end": 2143.65, "word": " figure", "probability": 0.96875}, {"start": 2143.65, "end": 2144.89, "word": " the", "probability": 0.472412109375}, {"start": 2144.89, "end": 2145.27, "word": " answer,", "probability": 0.814453125}, {"start": 2145.43, "end": 2145.55, "word": " the", "probability": 0.87548828125}, {"start": 2145.55, "end": 2145.79, "word": " right", "probability": 0.9248046875}, {"start": 2145.79, "end": 2146.19, "word": " answer.", "probability": 0.9462890625}, {"start": 2146.87, "end": 2147.41, "word": " But", "probability": 0.94287109375}, {"start": 2147.41, "end": 2147.59, "word": " there", "probability": 0.89404296875}, {"start": 2147.59, "end": 2147.75, "word": " is", "probability": 0.90771484375}, {"start": 2147.75, "end": 2148.07, "word": " another", "probability": 0.91796875}, {"start": 2148.07, "end": 2148.41, "word": " one,", "probability": 0.916015625}, {"start": 2149.03, "end": 2149.35, "word": " another", "probability": 0.69482421875}, {"start": 2149.35, "end": 2149.59, "word": " idea,", "probability": 0.89453125}, {"start": 2149.71, "end": 2149.83, "word": " maybe", "probability": 0.92138671875}, {"start": 2149.83, "end": 2150.27, "word": " shorter.", "probability": 0.90625}], "temperature": 1.0}, {"id": 77, "seek": 217944, "start": 2151.39, "end": 2179.45, "text": " It'll take shorter time. It's correct, but straightforward. Just compute the lower and upper limits. And the width is the difference between these two values. If you look carefully at this equation, difference between these two values gives the width.", "tokens": [467, 603, 747, 11639, 565, 13, 467, 311, 3006, 11, 457, 15325, 13, 1449, 14722, 264, 3126, 293, 6597, 10406, 13, 400, 264, 11402, 307, 264, 2649, 1296, 613, 732, 4190, 13, 759, 291, 574, 7500, 412, 341, 5367, 11, 2649, 1296, 613, 732, 4190, 2709, 264, 11402, 13], "avg_logprob": -0.17968749463558198, "compression_ratio": 1.575, "no_speech_prob": 0.0, "words": [{"start": 2151.39, "end": 2151.67, "word": " It'll", "probability": 0.3525390625}, {"start": 2151.67, "end": 2151.93, "word": " take", "probability": 0.88037109375}, {"start": 2151.93, "end": 2152.31, "word": " shorter", "probability": 0.794921875}, {"start": 2152.31, "end": 2152.79, "word": " time.", "probability": 0.88525390625}, {"start": 2156.89, "end": 2157.53, "word": " It's", "probability": 0.90185546875}, {"start": 2157.53, "end": 2157.91, "word": " correct,", "probability": 0.90087890625}, {"start": 2158.01, "end": 2158.15, "word": " but", "probability": 0.88525390625}, {"start": 2158.15, "end": 2158.93, "word": " straightforward.", "probability": 0.7890625}, {"start": 2159.45, "end": 2159.77, "word": " Just", "probability": 0.8603515625}, {"start": 2159.77, "end": 2160.23, "word": " compute", "probability": 0.89892578125}, {"start": 2160.23, "end": 2160.65, "word": " the", "probability": 0.9091796875}, {"start": 2160.65, "end": 2162.01, "word": " lower", "probability": 0.8701171875}, {"start": 2162.01, "end": 2162.19, "word": " and", "probability": 0.939453125}, {"start": 2162.19, "end": 2162.39, "word": " upper", "probability": 0.8115234375}, {"start": 2162.39, "end": 2162.87, "word": " limits.", "probability": 0.97265625}, {"start": 2164.73, "end": 2165.09, "word": " And", "probability": 0.95654296875}, {"start": 2165.09, "end": 2165.25, "word": " the", "probability": 0.90869140625}, {"start": 2165.25, "end": 2165.43, "word": " width", "probability": 0.68017578125}, {"start": 2165.43, "end": 2165.63, "word": " is", "probability": 0.94140625}, {"start": 2165.63, "end": 2165.79, "word": " the", "probability": 0.9189453125}, {"start": 2165.79, "end": 2166.13, "word": " difference", "probability": 0.86083984375}, {"start": 2166.13, "end": 2166.45, "word": " between", "probability": 0.86669921875}, {"start": 2166.45, "end": 2166.69, "word": " these", "probability": 0.86279296875}, {"start": 2166.69, "end": 2166.85, "word": " two", "probability": 0.9140625}, {"start": 2166.85, "end": 2167.19, "word": " values.", "probability": 0.8017578125}, {"start": 2171.37, "end": 2172.01, "word": " If", "probability": 0.9306640625}, {"start": 2172.01, "end": 2172.09, "word": " you", "probability": 0.939453125}, {"start": 2172.09, "end": 2172.23, "word": " look", "probability": 0.81298828125}, {"start": 2172.23, "end": 2172.55, "word": " carefully", "probability": 0.8203125}, {"start": 2172.55, "end": 2172.75, "word": " at", "probability": 0.96142578125}, {"start": 2172.75, "end": 2172.93, "word": " this", "probability": 0.9482421875}, {"start": 2172.93, "end": 2173.47, "word": " equation,", "probability": 0.9765625}, {"start": 2173.79, "end": 2176.05, "word": " difference", "probability": 0.475830078125}, {"start": 2176.05, "end": 2176.49, "word": " between", "probability": 0.88427734375}, {"start": 2176.49, "end": 2176.71, "word": " these", "probability": 0.873046875}, {"start": 2176.71, "end": 2176.91, "word": " two", "probability": 0.9287109375}, {"start": 2176.91, "end": 2177.41, "word": " values", "probability": 0.96875}, {"start": 2177.41, "end": 2178.99, "word": " gives", "probability": 0.865234375}, {"start": 2178.99, "end": 2179.21, "word": " the", "probability": 0.916015625}, {"start": 2179.21, "end": 2179.45, "word": " width.", "probability": 0.9765625}], "temperature": 1.0}, {"id": 78, "seek": 221021, "start": 2181.24, "end": 2210.22, "text": " Now let's imagine that the lower limit equals x bar minus the error term. And upper limit is also x bar plus the error term. Now if we add this, or if we subtract 2 from 1, you will get upper limit", "tokens": [823, 718, 311, 3811, 300, 264, 3126, 4948, 6915, 2031, 2159, 3175, 264, 6713, 1433, 13, 400, 6597, 4948, 307, 611, 2031, 2159, 1804, 264, 6713, 1433, 13, 823, 498, 321, 909, 341, 11, 420, 498, 321, 16390, 568, 490, 502, 11, 291, 486, 483, 6597, 4948], "avg_logprob": -0.24788411147892475, "compression_ratio": 1.4887218045112782, "no_speech_prob": 0.0, "words": [{"start": 2181.24, "end": 2181.56, "word": " Now", "probability": 0.62548828125}, {"start": 2181.56, "end": 2182.42, "word": " let's", "probability": 0.689697265625}, {"start": 2182.42, "end": 2182.9, "word": " imagine", "probability": 0.87060546875}, {"start": 2182.9, "end": 2183.24, "word": " that", "probability": 0.900390625}, {"start": 2183.24, "end": 2183.44, "word": " the", "probability": 0.806640625}, {"start": 2183.44, "end": 2183.6, "word": " lower", "probability": 0.82763671875}, {"start": 2183.6, "end": 2184.0, "word": " limit", "probability": 0.96435546875}, {"start": 2184.0, "end": 2185.1, "word": " equals", "probability": 0.76806640625}, {"start": 2185.1, "end": 2185.5, "word": " x", "probability": 0.53857421875}, {"start": 2185.5, "end": 2185.88, "word": " bar", "probability": 0.5703125}, {"start": 2185.88, "end": 2188.92, "word": " minus", "probability": 0.912109375}, {"start": 2188.92, "end": 2190.58, "word": " the", "probability": 0.8095703125}, {"start": 2190.58, "end": 2190.8, "word": " error", "probability": 0.48583984375}, {"start": 2190.8, "end": 2191.06, "word": " term.", "probability": 0.53369140625}, {"start": 2192.88, "end": 2193.36, "word": " And", "probability": 0.79345703125}, {"start": 2193.36, "end": 2193.68, "word": " upper", "probability": 0.59228515625}, {"start": 2193.68, "end": 2194.02, "word": " limit", "probability": 0.97216796875}, {"start": 2194.02, "end": 2194.68, "word": " is", "probability": 0.93505859375}, {"start": 2194.68, "end": 2195.0, "word": " also", "probability": 0.8701171875}, {"start": 2195.0, "end": 2195.28, "word": " x", "probability": 0.9892578125}, {"start": 2195.28, "end": 2195.7, "word": " bar", "probability": 0.93212890625}, {"start": 2195.7, "end": 2196.34, "word": " plus", "probability": 0.953125}, {"start": 2196.34, "end": 2197.38, "word": " the", "probability": 0.8759765625}, {"start": 2197.38, "end": 2197.66, "word": " error", "probability": 0.88232421875}, {"start": 2197.66, "end": 2197.96, "word": " term.", "probability": 0.912109375}, {"start": 2201.46, "end": 2202.18, "word": " Now", "probability": 0.92822265625}, {"start": 2202.18, "end": 2202.42, "word": " if", "probability": 0.7548828125}, {"start": 2202.42, "end": 2202.62, "word": " we", "probability": 0.95556640625}, {"start": 2202.62, "end": 2202.92, "word": " add", "probability": 0.89599609375}, {"start": 2202.92, "end": 2203.32, "word": " this,", "probability": 0.56689453125}, {"start": 2204.04, "end": 2204.32, "word": " or", "probability": 0.916015625}, {"start": 2204.32, "end": 2204.56, "word": " if", "probability": 0.87744140625}, {"start": 2204.56, "end": 2204.7, "word": " we", "probability": 0.92431640625}, {"start": 2204.7, "end": 2205.18, "word": " subtract", "probability": 0.86181640625}, {"start": 2205.18, "end": 2206.06, "word": " 2", "probability": 0.436279296875}, {"start": 2206.06, "end": 2206.26, "word": " from", "probability": 0.8974609375}, {"start": 2206.26, "end": 2206.58, "word": " 1,", "probability": 0.97412109375}, {"start": 2207.9, "end": 2208.22, "word": " you", "probability": 0.75732421875}, {"start": 2208.22, "end": 2208.38, "word": " will", "probability": 0.8896484375}, {"start": 2208.38, "end": 2208.66, "word": " get", "probability": 0.93701171875}, {"start": 2208.66, "end": 2209.82, "word": " upper", "probability": 0.76220703125}, {"start": 2209.82, "end": 2210.22, "word": " limit", "probability": 0.962890625}], "temperature": 1.0}, {"id": 79, "seek": 223978, "start": 2210.86, "end": 2239.78, "text": " minus lower limit equals x bar cancels with 2x bar. If you subtract, w minus equals 2e. Upper limit minus lower limit is the width. So w, the width is", "tokens": [3175, 3126, 4948, 6915, 2031, 2159, 393, 66, 1625, 365, 568, 87, 2159, 13, 759, 291, 16390, 11, 261, 3175, 6915, 568, 68, 13, 36926, 4948, 3175, 3126, 4948, 307, 264, 11402, 13, 407, 261, 11, 264, 11402, 307], "avg_logprob": -0.3433593772351742, "compression_ratio": 1.3981481481481481, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2210.86, "end": 2211.3, "word": " minus", "probability": 0.2259521484375}, {"start": 2211.3, "end": 2211.62, "word": " lower", "probability": 0.7646484375}, {"start": 2211.62, "end": 2211.96, "word": " limit", "probability": 0.9296875}, {"start": 2211.96, "end": 2212.56, "word": " equals", "probability": 0.83837890625}, {"start": 2212.56, "end": 2215.74, "word": " x", "probability": 0.343994140625}, {"start": 2215.74, "end": 2217.26, "word": " bar", "probability": 0.7373046875}, {"start": 2217.26, "end": 2218.36, "word": " cancels", "probability": 0.7701822916666666}, {"start": 2218.36, "end": 2221.2, "word": " with", "probability": 0.1710205078125}, {"start": 2221.2, "end": 2223.6, "word": " 2x", "probability": 0.64990234375}, {"start": 2223.6, "end": 2223.94, "word": " bar.", "probability": 0.92333984375}, {"start": 2225.26, "end": 2225.54, "word": " If", "probability": 0.43994140625}, {"start": 2225.54, "end": 2225.68, "word": " you", "probability": 0.64794921875}, {"start": 2225.68, "end": 2226.12, "word": " subtract,", "probability": 0.88330078125}, {"start": 2226.68, "end": 2226.96, "word": " w", "probability": 0.59814453125}, {"start": 2226.96, "end": 2227.28, "word": " minus", "probability": 0.83984375}, {"start": 2227.28, "end": 2229.02, "word": " equals", "probability": 0.82421875}, {"start": 2229.02, "end": 2230.96, "word": " 2e.", "probability": 0.76416015625}, {"start": 2232.52, "end": 2233.16, "word": " Upper", "probability": 0.89453125}, {"start": 2233.16, "end": 2233.44, "word": " limit", "probability": 0.95849609375}, {"start": 2233.44, "end": 2233.84, "word": " minus", "probability": 0.97607421875}, {"start": 2233.84, "end": 2234.7, "word": " lower", "probability": 0.81640625}, {"start": 2234.7, "end": 2235.06, "word": " limit", "probability": 0.95703125}, {"start": 2235.06, "end": 2235.92, "word": " is", "probability": 0.88525390625}, {"start": 2235.92, "end": 2236.1, "word": " the", "probability": 0.88037109375}, {"start": 2236.1, "end": 2236.3, "word": " width.", "probability": 0.974609375}, {"start": 2237.46, "end": 2237.68, "word": " So", "probability": 0.88623046875}, {"start": 2237.68, "end": 2238.06, "word": " w,", "probability": 0.59130859375}, {"start": 2238.76, "end": 2239.02, "word": " the", "probability": 0.916015625}, {"start": 2239.02, "end": 2239.3, "word": " width", "probability": 0.96826171875}, {"start": 2239.3, "end": 2239.78, "word": " is", "probability": 0.69677734375}], "temperature": 1.0}, {"id": 80, "seek": 226621, "start": 2241.34, "end": 2266.22, "text": " twice the sampling error. So we have this new information, W equals twice of the margin of error. If we add 1 and 2, that will give lower limit plus upper limit equals to x bar. That means x bar equals lower limit plus upper limit divided by 2.", "tokens": [6091, 264, 21179, 6713, 13, 407, 321, 362, 341, 777, 1589, 11, 343, 6915, 6091, 295, 264, 10270, 295, 6713, 13, 759, 321, 909, 502, 293, 568, 11, 300, 486, 976, 3126, 4948, 1804, 6597, 4948, 6915, 281, 2031, 2159, 13, 663, 1355, 2031, 2159, 6915, 3126, 4948, 1804, 6597, 4948, 6666, 538, 568, 13], "avg_logprob": -0.15527344308793545, "compression_ratio": 1.6225165562913908, "no_speech_prob": 0.0, "words": [{"start": 2241.34, "end": 2241.94, "word": " twice", "probability": 0.377197265625}, {"start": 2241.94, "end": 2242.54, "word": " the", "probability": 0.806640625}, {"start": 2242.54, "end": 2242.88, "word": " sampling", "probability": 0.78173828125}, {"start": 2242.88, "end": 2243.2, "word": " error.", "probability": 0.95068359375}, {"start": 2243.98, "end": 2244.48, "word": " So", "probability": 0.95263671875}, {"start": 2244.48, "end": 2244.62, "word": " we", "probability": 0.8203125}, {"start": 2244.62, "end": 2244.8, "word": " have", "probability": 0.93798828125}, {"start": 2244.8, "end": 2245.26, "word": " this", "probability": 0.896484375}, {"start": 2245.26, "end": 2245.46, "word": " new", "probability": 0.833984375}, {"start": 2245.46, "end": 2245.92, "word": " information,", "probability": 0.744140625}, {"start": 2246.12, "end": 2246.46, "word": " W", "probability": 0.60693359375}, {"start": 2246.46, "end": 2247.24, "word": " equals", "probability": 0.86083984375}, {"start": 2247.24, "end": 2249.34, "word": " twice", "probability": 0.93310546875}, {"start": 2249.34, "end": 2249.62, "word": " of", "probability": 0.9375}, {"start": 2249.62, "end": 2249.74, "word": " the", "probability": 0.91650390625}, {"start": 2249.74, "end": 2249.98, "word": " margin", "probability": 0.9052734375}, {"start": 2249.98, "end": 2250.16, "word": " of", "probability": 0.88916015625}, {"start": 2250.16, "end": 2250.3, "word": " error.", "probability": 0.8681640625}, {"start": 2251.32, "end": 2251.92, "word": " If", "probability": 0.9560546875}, {"start": 2251.92, "end": 2252.12, "word": " we", "probability": 0.95947265625}, {"start": 2252.12, "end": 2252.38, "word": " add", "probability": 0.88525390625}, {"start": 2252.38, "end": 2252.6, "word": " 1", "probability": 0.46728515625}, {"start": 2252.6, "end": 2252.78, "word": " and", "probability": 0.93701171875}, {"start": 2252.78, "end": 2253.04, "word": " 2,", "probability": 0.99658203125}, {"start": 2253.32, "end": 2253.6, "word": " that", "probability": 0.92529296875}, {"start": 2253.6, "end": 2253.78, "word": " will", "probability": 0.86279296875}, {"start": 2253.78, "end": 2254.12, "word": " give", "probability": 0.8564453125}, {"start": 2254.12, "end": 2256.4, "word": " lower", "probability": 0.7490234375}, {"start": 2256.4, "end": 2256.8, "word": " limit", "probability": 0.9638671875}, {"start": 2256.8, "end": 2257.34, "word": " plus", "probability": 0.89453125}, {"start": 2257.34, "end": 2257.64, "word": " upper", "probability": 0.84619140625}, {"start": 2257.64, "end": 2257.96, "word": " limit", "probability": 0.9677734375}, {"start": 2257.96, "end": 2258.38, "word": " equals", "probability": 0.92041015625}, {"start": 2258.38, "end": 2258.6, "word": " to", "probability": 0.86865234375}, {"start": 2258.6, "end": 2258.82, "word": " x", "probability": 0.646484375}, {"start": 2258.82, "end": 2259.08, "word": " bar.", "probability": 0.82421875}, {"start": 2260.24, "end": 2260.84, "word": " That", "probability": 0.91845703125}, {"start": 2260.84, "end": 2261.12, "word": " means", "probability": 0.9208984375}, {"start": 2261.12, "end": 2261.4, "word": " x", "probability": 0.9658203125}, {"start": 2261.4, "end": 2261.62, "word": " bar", "probability": 0.93115234375}, {"start": 2261.62, "end": 2262.2, "word": " equals", "probability": 0.94287109375}, {"start": 2262.2, "end": 2263.46, "word": " lower", "probability": 0.85302734375}, {"start": 2263.46, "end": 2263.88, "word": " limit", "probability": 0.97021484375}, {"start": 2263.88, "end": 2264.9, "word": " plus", "probability": 0.89697265625}, {"start": 2264.9, "end": 2265.22, "word": " upper", "probability": 0.86962890625}, {"start": 2265.22, "end": 2265.52, "word": " limit", "probability": 0.96826171875}, {"start": 2265.52, "end": 2265.8, "word": " divided", "probability": 0.6982421875}, {"start": 2265.8, "end": 2266.02, "word": " by", "probability": 0.97412109375}, {"start": 2266.02, "end": 2266.22, "word": " 2.", "probability": 0.8251953125}], "temperature": 1.0}, {"id": 81, "seek": 230281, "start": 2273.97, "end": 2302.81, "text": " the error, and X bar is the average of lower and upper limits. So by using this idea now, if we compute the error term, E equals Z sigma over root N, this quantity. And again, Z is 1645. 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This gives 232.6. This is the error tier, or the margin of error. As we know, that's called margin of error or sampling error. So the error is this amount.", "tokens": [9886, 482, 538, 5593, 2625, 13, 639, 2709, 6673, 17, 13, 21, 13, 639, 307, 264, 6713, 12362, 11, 420, 264, 10270, 295, 6713, 13, 1018, 321, 458, 11, 300, 311, 1219, 10270, 295, 6713, 420, 21179, 6713, 13, 407, 264, 6713, 307, 341, 2372, 13], "avg_logprob": -0.19980052620806593, "compression_ratio": 1.3671875, "no_speech_prob": 0.0, "words": [{"start": 2304.58, "end": 2305.08, "word": " Divide", "probability": 0.682861328125}, {"start": 2305.08, "end": 2305.26, "word": " by", "probability": 0.939453125}, {"start": 2305.26, "end": 2305.52, "word": " root", "probability": 0.67626953125}, {"start": 2305.52, "end": 2305.94, "word": " 50.", "probability": 0.88037109375}, {"start": 2308.32, "end": 2309.0, "word": " This", "probability": 0.8427734375}, {"start": 2309.0, "end": 2309.38, "word": " gives", "probability": 0.8994140625}, {"start": 2309.38, "end": 2311.18, "word": " 232", "probability": 0.82568359375}, {"start": 2311.18, "end": 2311.84, "word": ".6.", "probability": 0.969482421875}, {"start": 2313.6, "end": 2314.28, "word": " This", "probability": 0.8232421875}, {"start": 2314.28, "end": 2314.38, "word": " is", "probability": 0.89697265625}, {"start": 2314.38, "end": 2314.48, "word": " the", "probability": 0.86328125}, {"start": 2314.48, "end": 2314.7, "word": " error", "probability": 0.88720703125}, {"start": 2314.7, "end": 2314.96, "word": " tier,", "probability": 0.55810546875}, {"start": 2316.3, "end": 2316.64, "word": " or", "probability": 0.9462890625}, {"start": 2316.64, "end": 2316.78, "word": " the", "probability": 0.912109375}, {"start": 2316.78, "end": 2317.04, "word": " margin", "probability": 0.935546875}, {"start": 2317.04, "end": 2317.2, "word": " of", "probability": 0.9609375}, {"start": 2317.2, "end": 2317.42, "word": " error.", "probability": 0.89697265625}, {"start": 2318.42, "end": 2319.1, "word": " As", "probability": 0.95849609375}, {"start": 2319.1, "end": 2319.22, "word": " we", "probability": 0.55517578125}, {"start": 2319.22, "end": 2319.32, "word": " know,", "probability": 0.8798828125}, {"start": 2319.42, "end": 2319.74, "word": " that's", "probability": 0.923828125}, {"start": 2319.74, "end": 2320.04, "word": " called", "probability": 0.84716796875}, {"start": 2320.04, "end": 2320.62, "word": " margin", "probability": 0.93994140625}, {"start": 2320.62, "end": 2323.36, "word": " of", "probability": 0.9462890625}, {"start": 2323.36, "end": 2323.72, "word": " error", "probability": 0.90869140625}, {"start": 2323.72, "end": 2325.62, "word": " or", "probability": 0.53173828125}, {"start": 2325.62, "end": 2326.1, "word": " sampling", "probability": 0.96875}, {"start": 2326.1, "end": 2326.4, "word": " error.", "probability": 0.92529296875}, {"start": 2330.58, "end": 2331.26, "word": " So", "probability": 0.943359375}, {"start": 2331.26, "end": 2331.4, "word": " the", "probability": 0.8564453125}, {"start": 2331.4, "end": 2331.58, "word": " error", "probability": 0.78662109375}, {"start": 2331.58, "end": 2331.76, "word": " is", "probability": 0.63037109375}, {"start": 2331.76, "end": 2332.02, "word": " this", "probability": 0.9208984375}, {"start": 2332.02, "end": 2332.36, "word": " amount.", "probability": 0.9013671875}], "temperature": 1.0}, {"id": 83, "seek": 236337, "start": 2334.17, "end": 2363.37, "text": " The width is twice this value. So W equals 2 times the error. And the answer should be the same as the one we just... So we end with the same result. Now which one is shorter? Forget about my explanation up to this point. We started from this one. 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Then we found the error to be this 232 multiply this by 2 will give the sampling error or the, I'm sorry, will give the weight of the interval. Now imagine for this problem, the income, the average income is not given. Suppose x bar is not given.", "tokens": [286, 914, 341, 2372, 13, 1396, 321, 1352, 264, 6713, 281, 312, 341, 6673, 17, 12972, 341, 538, 568, 486, 976, 264, 21179, 6713, 420, 264, 11, 286, 478, 2597, 11, 486, 976, 264, 3364, 295, 264, 15035, 13, 823, 3811, 337, 341, 1154, 11, 264, 5742, 11, 264, 4274, 5742, 307, 406, 2212, 13, 21360, 2031, 2159, 307, 406, 2212, 13], "avg_logprob": -0.2901785733207824, "compression_ratio": 1.5892857142857142, "no_speech_prob": 0.0, "words": [{"start": 2364.05, "end": 2364.35, "word": " I", "probability": 0.63916015625}, {"start": 2364.35, "end": 2364.49, "word": " mean", "probability": 0.951171875}, {"start": 2364.49, "end": 2364.75, "word": " this", "probability": 0.7421875}, {"start": 2364.75, "end": 2365.15, "word": " amount.", "probability": 0.8896484375}, {"start": 2366.43, "end": 2366.79, "word": " Then", "probability": 0.5888671875}, {"start": 2366.79, "end": 2366.99, "word": " we", "probability": 0.86962890625}, {"start": 2366.99, "end": 2367.39, "word": " found", "probability": 0.88330078125}, {"start": 2367.39, "end": 2369.05, "word": " the", "probability": 0.755859375}, {"start": 2369.05, "end": 2369.33, "word": " error", "probability": 0.884765625}, {"start": 2369.33, "end": 2369.53, "word": " to", "probability": 0.95361328125}, {"start": 2369.53, "end": 2369.75, "word": " be", "probability": 0.9541015625}, {"start": 2369.75, "end": 2370.13, "word": " this", "probability": 0.814453125}, {"start": 2370.13, "end": 2371.15, "word": " 232", "probability": 0.90087890625}, {"start": 2371.15, "end": 2371.65, "word": " multiply", "probability": 0.2393798828125}, {"start": 2371.65, "end": 2371.99, "word": " this", "probability": 0.890625}, {"start": 2371.99, "end": 2372.15, "word": " by", "probability": 0.9677734375}, {"start": 2372.15, "end": 2372.39, "word": " 2", "probability": 0.81201171875}, {"start": 2372.39, "end": 2372.95, "word": " will", "probability": 0.283203125}, {"start": 2372.95, "end": 2373.13, "word": " give", "probability": 0.859375}, {"start": 2373.13, "end": 2373.39, "word": " the", "probability": 0.861328125}, {"start": 2373.39, "end": 2373.75, "word": " sampling", "probability": 0.2442626953125}, {"start": 2373.75, "end": 2374.09, "word": " error", "probability": 0.9169921875}, {"start": 2374.09, "end": 2374.33, "word": " or", "probability": 0.365478515625}, {"start": 2374.33, "end": 2374.59, "word": " the,", "probability": 0.63232421875}, {"start": 2375.01, "end": 2375.15, "word": " I'm", "probability": 0.94287109375}, {"start": 2375.15, "end": 2375.33, "word": " sorry,", "probability": 0.8798828125}, {"start": 2375.45, "end": 2375.55, "word": " will", "probability": 0.75732421875}, {"start": 2375.55, "end": 2375.77, "word": " give", "probability": 0.87890625}, {"start": 2375.77, "end": 2376.49, "word": " the", "probability": 0.90771484375}, {"start": 2376.49, "end": 2377.37, "word": " weight", "probability": 0.3505859375}, {"start": 2377.37, "end": 2377.53, "word": " of", "probability": 0.85693359375}, {"start": 2377.53, "end": 2377.67, "word": " the", "probability": 0.876953125}, {"start": 2377.67, "end": 2377.97, "word": " interval.", "probability": 0.41845703125}, {"start": 2378.51, "end": 2378.75, "word": " Now", "probability": 0.955078125}, {"start": 2378.75, "end": 2379.17, "word": " imagine", "probability": 0.82568359375}, {"start": 2379.17, "end": 2379.63, "word": " for", "probability": 0.87744140625}, {"start": 2379.63, "end": 2379.91, "word": " this", "probability": 0.94580078125}, {"start": 2379.91, "end": 2380.43, "word": " problem,", "probability": 0.87158203125}, {"start": 2381.39, "end": 2381.63, "word": " the", "probability": 0.90087890625}, {"start": 2381.63, "end": 2382.13, "word": " income,", "probability": 0.88916015625}, {"start": 2382.45, "end": 2382.49, "word": " the", "probability": 0.916015625}, {"start": 2382.49, "end": 2382.83, "word": " average", "probability": 0.78955078125}, {"start": 2382.83, "end": 2383.17, "word": " income", "probability": 0.9384765625}, {"start": 2383.17, "end": 2383.37, "word": " is", "probability": 0.904296875}, {"start": 2383.37, "end": 2383.57, "word": " not", "probability": 0.94677734375}, {"start": 2383.57, "end": 2383.83, "word": " given.", "probability": 0.8896484375}, {"start": 2387.59, "end": 2388.21, "word": " Suppose", "probability": 0.6494140625}, {"start": 2388.21, "end": 2388.69, "word": " x", "probability": 0.7294921875}, {"start": 2388.69, "end": 2389.07, "word": " bar", "probability": 0.794921875}, {"start": 2389.07, "end": 2391.59, "word": " is", "probability": 0.92529296875}, {"start": 2391.59, "end": 2391.91, "word": " not", "probability": 0.947265625}, {"start": 2391.91, "end": 2392.21, "word": " given.", "probability": 0.89501953125}], "temperature": 1.0}, {"id": 85, "seek": 242269, "start": 2394.49, "end": 2422.69, "text": " Now the question is, can you find the answer by using this idea? But here, without using x bar, we computed the sampling error to multiply this value by 2 and get the answer. So that's for number 12. Again, for this particular example, there are two ways to solve this problem.", "tokens": [823, 264, 1168, 307, 11, 393, 291, 915, 264, 1867, 538, 1228, 341, 1558, 30, 583, 510, 11, 1553, 1228, 2031, 2159, 11, 321, 40610, 264, 21179, 6713, 281, 12972, 341, 2158, 538, 568, 293, 483, 264, 1867, 13, 407, 300, 311, 337, 1230, 2272, 13, 3764, 11, 337, 341, 1729, 1365, 11, 456, 366, 732, 2098, 281, 5039, 341, 1154, 13], "avg_logprob": -0.13789682586987814, "compression_ratio": 1.4631578947368422, "no_speech_prob": 0.0, "words": [{"start": 2394.49, "end": 2394.75, "word": " Now", "probability": 0.8818359375}, {"start": 2394.75, "end": 2394.91, "word": " the", "probability": 0.677734375}, {"start": 2394.91, "end": 2395.19, "word": " question", "probability": 0.91748046875}, {"start": 2395.19, "end": 2395.45, "word": " is,", "probability": 0.9482421875}, {"start": 2395.55, "end": 2395.71, "word": " can", "probability": 0.8876953125}, {"start": 2395.71, "end": 2395.99, "word": " you", 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then subtract upper limit from the lower limit, you will get the width of the interval. The other way, just compute the error and multiply the answer by 2, you will get the same result. Number 13.", "tokens": [440, 700, 472, 11, 291, 362, 281, 7690, 264, 6687, 15035, 11, 550, 16390, 6597, 4948, 490, 264, 3126, 4948, 11, 291, 486, 483, 264, 11402, 295, 264, 15035, 13, 440, 661, 636, 11, 445, 14722, 264, 6713, 293, 12972, 264, 1867, 538, 568, 11, 291, 486, 483, 264, 912, 1874, 13, 5118, 3705, 13], "avg_logprob": -0.18526785607848847, "compression_ratio": 1.5602409638554218, "no_speech_prob": 0.0, "words": [{"start": 2424.65, "end": 2424.93, "word": " The", "probability": 0.5712890625}, {"start": 2424.93, "end": 2425.23, "word": " first", "probability": 0.880859375}, {"start": 2425.23, "end": 2425.47, "word": " one,", "probability": 0.9130859375}, {"start": 2425.57, "end": 2425.61, "word": " you", "probability": 0.93701171875}, {"start": 2425.61, "end": 2425.79, "word": " have", "probability": 0.91748046875}, {"start": 2425.79, "end": 2425.91, "word": " to", "probability": 0.96923828125}, {"start": 2425.91, "end": 2426.35, "word": " construct", "probability": 0.95263671875}, {"start": 2426.35, "end": 2426.55, "word": " the", "probability": 0.74072265625}, {"start": 2426.55, "end": 2426.91, "word": " confidence", "probability": 0.97509765625}, {"start": 2426.91, "end": 2427.43, "word": " interval,", "probability": 0.96142578125}, {"start": 2428.07, "end": 2428.39, "word": " then", "probability": 0.64111328125}, {"start": 2428.39, "end": 2428.89, "word": " subtract", "probability": 0.79833984375}, {"start": 2428.89, "end": 2429.37, "word": " upper", "probability": 0.63720703125}, {"start": 2429.37, "end": 2429.73, "word": " limit", "probability": 0.93798828125}, {"start": 2429.73, "end": 2430.91, "word": " from", "probability": 0.87841796875}, {"start": 2430.91, "end": 2431.27, "word": " the", "probability": 0.880859375}, {"start": 2431.27, "end": 2431.81, "word": " lower", "probability": 0.8642578125}, {"start": 2431.81, "end": 2432.17, "word": " limit,", "probability": 0.96044921875}, {"start": 2432.69, "end": 2432.91, "word": " you", "probability": 0.9345703125}, {"start": 2432.91, "end": 2433.07, "word": " will", "probability": 0.8798828125}, {"start": 2433.07, "end": 2433.35, "word": " get", "probability": 0.93798828125}, {"start": 2433.35, "end": 2433.57, "word": " the", "probability": 0.91357421875}, {"start": 2433.57, "end": 2433.91, "word": " width", "probability": 0.94580078125}, {"start": 2433.91, "end": 2434.69, "word": " of", "probability": 0.95654296875}, {"start": 2434.69, "end": 2434.83, "word": " the", "probability": 0.91845703125}, {"start": 2434.83, "end": 2435.17, "word": " interval.", "probability": 0.96142578125}, {"start": 2436.95, "end": 2437.15, "word": " The", "probability": 0.8681640625}, {"start": 2437.15, "end": 2437.51, "word": " other", "probability": 0.8857421875}, {"start": 2437.51, "end": 2438.03, "word": " way,", "probability": 0.71630859375}, {"start": 2438.61, "end": 2439.07, "word": " just", "probability": 0.861328125}, {"start": 2439.07, "end": 2439.55, "word": " compute", "probability": 0.8974609375}, {"start": 2439.55, "end": 2439.81, "word": " the", "probability": 0.916015625}, {"start": 2439.81, "end": 2440.15, "word": " error", "probability": 0.890625}, {"start": 2440.15, "end": 2440.95, "word": " and", "probability": 0.5615234375}, {"start": 2440.95, "end": 2441.39, "word": " multiply", "probability": 0.9052734375}, {"start": 2441.39, "end": 2441.65, "word": " the", "probability": 0.91357421875}, {"start": 2441.65, "end": 2441.91, "word": " answer", "probability": 0.9482421875}, {"start": 2441.91, "end": 2442.15, "word": " by", "probability": 0.96826171875}, {"start": 2442.15, "end": 2442.45, "word": " 2,", "probability": 0.50048828125}, {"start": 2443.35, "end": 2443.55, "word": " you", "probability": 0.93896484375}, {"start": 2443.55, "end": 2443.73, "word": " will", "probability": 0.8857421875}, {"start": 2443.73, "end": 2443.91, "word": " get", "probability": 0.85888671875}, {"start": 2443.91, "end": 2444.09, "word": " the", "probability": 0.9111328125}, {"start": 2444.09, "end": 2444.29, "word": " same", "probability": 0.89990234375}, {"start": 2444.29, "end": 2444.71, "word": " result.", "probability": 0.9130859375}, {"start": 2446.75, "end": 2447.43, "word": " Number", "probability": 0.80712890625}, {"start": 2447.43, "end": 2448.21, "word": " 13.", "probability": 0.8681640625}], "temperature": 1.0}, {"id": 87, "seek": 248360, "start": 2456.02, "end": 2483.6, "text": " 13th says that the head librarian at the Library of Congress has asked her assistant for an interval estimate of a mean number of books checked out each day. The assistant provides the following interval estimate. From 740 to 920 books per day.", "tokens": [3705, 392, 1619, 300, 264, 1378, 42558, 412, 264, 12806, 295, 6426, 575, 2351, 720, 10994, 337, 364, 15035, 12539, 295, 257, 914, 1230, 295, 3642, 10033, 484, 1184, 786, 13, 440, 10994, 6417, 264, 3480, 15035, 12539, 13, 3358, 1614, 5254, 281, 1722, 2009, 3642, 680, 786, 13], "avg_logprob": -0.11539062291383743, "compression_ratio": 1.4759036144578312, "no_speech_prob": 0.0, "words": [{"start": 2456.02, "end": 2456.94, "word": " 13th", "probability": 0.698974609375}, {"start": 2456.94, "end": 2457.16, "word": " says", "probability": 0.8896484375}, {"start": 2457.16, "end": 2457.4, "word": " that", "probability": 0.91748046875}, {"start": 2457.4, "end": 2457.62, "word": " the", "probability": 0.83740234375}, {"start": 2457.62, "end": 2457.94, "word": " head", "probability": 0.89111328125}, {"start": 2457.94, "end": 2459.8, "word": " librarian", "probability": 0.93603515625}, {"start": 2459.8, "end": 2460.26, "word": " at", "probability": 0.9404296875}, {"start": 2460.26, "end": 2460.52, "word": " the", "probability": 0.90478515625}, {"start": 2460.52, "end": 2460.98, "word": " Library", "probability": 0.72412109375}, {"start": 2460.98, "end": 2461.18, "word": " of", "probability": 0.97314453125}, {"start": 2461.18, "end": 2461.72, "word": " Congress", "probability": 0.95947265625}, {"start": 2461.72, "end": 2462.82, "word": " has", "probability": 0.90771484375}, {"start": 2462.82, "end": 2463.3, "word": " asked", "probability": 0.8271484375}, {"start": 2463.3, "end": 2463.76, "word": " her", "probability": 0.8583984375}, {"start": 2463.76, "end": 2464.22, "word": " assistant", "probability": 0.9482421875}, {"start": 2464.22, "end": 2464.6, "word": " for", "probability": 0.95068359375}, {"start": 2464.6, "end": 2464.78, "word": " an", "probability": 0.95361328125}, {"start": 2464.78, "end": 2465.12, "word": " interval", "probability": 0.98486328125}, {"start": 2465.12, "end": 2465.92, "word": " estimate", "probability": 0.90283203125}, {"start": 2465.92, "end": 2466.82, "word": " of", "probability": 0.9638671875}, {"start": 2466.82, "end": 2466.96, "word": " a", "probability": 0.74365234375}, {"start": 2466.96, "end": 2467.06, "word": " mean", "probability": 0.96142578125}, {"start": 2467.06, "end": 2467.44, "word": " number", "probability": 0.9365234375}, {"start": 2467.44, "end": 2467.66, "word": " of", "probability": 0.96142578125}, {"start": 2467.66, "end": 2467.98, "word": " books", "probability": 0.912109375}, {"start": 2467.98, "end": 2468.42, "word": " checked", "probability": 0.8486328125}, {"start": 2468.42, "end": 2468.96, "word": " out", "probability": 0.87353515625}, {"start": 2468.96, "end": 2469.56, "word": " each", "probability": 0.9482421875}, {"start": 2469.56, "end": 2469.84, "word": " day.", "probability": 0.94775390625}, {"start": 2471.1, "end": 2471.32, "word": " The", "probability": 0.89453125}, {"start": 2471.32, "end": 2471.94, "word": " assistant", "probability": 0.951171875}, {"start": 2471.94, "end": 2472.52, "word": " provides", "probability": 0.83837890625}, {"start": 2472.52, "end": 2472.72, "word": " the", "probability": 0.91796875}, {"start": 2472.72, "end": 2473.1, "word": " following", "probability": 0.8759765625}, {"start": 2473.1, "end": 2473.98, "word": " interval", "probability": 0.98291015625}, {"start": 2473.98, "end": 2474.6, "word": " estimate.", "probability": 0.890625}, {"start": 2476.22, "end": 2477.14, "word": " From", "probability": 0.7548828125}, {"start": 2477.14, "end": 2478.52, "word": " 740", "probability": 0.907958984375}, {"start": 2478.52, "end": 2480.34, "word": " to", "probability": 0.92578125}, {"start": 2480.34, "end": 2482.02, "word": " 920", "probability": 0.938232421875}, {"start": 2482.02, "end": 2483.0, "word": " books", "probability": 0.91748046875}, {"start": 2483.0, "end": 2483.3, "word": " per", "probability": 0.94580078125}, {"start": 2483.3, "end": 2483.6, "word": " day.", "probability": 0.9580078125}], "temperature": 1.0}, {"id": 88, "seek": 251169, "start": 2484.66, "end": 2511.7, "text": " If the head librarian knows that the population standard deviation is 150 books shipped outwardly, approximately how large a sample did her assistant use to determine the interval estimate? So the information we have is the following. We have information about the confidence interval.", "tokens": [759, 264, 1378, 42558, 3255, 300, 264, 4415, 3832, 25163, 307, 8451, 3642, 25312, 26914, 356, 11, 10447, 577, 2416, 257, 6889, 630, 720, 10994, 764, 281, 6997, 264, 15035, 12539, 30, 407, 264, 1589, 321, 362, 307, 264, 3480, 13, 492, 362, 1589, 466, 264, 6687, 15035, 13], "avg_logprob": -0.256718755364418, "compression_ratio": 1.5212765957446808, "no_speech_prob": 0.0, "words": [{"start": 2484.66, "end": 2484.98, "word": " If", "probability": 0.55224609375}, {"start": 2484.98, "end": 2485.14, "word": " the", "probability": 0.8466796875}, {"start": 2485.14, "end": 2485.42, "word": " head", "probability": 0.81787109375}, {"start": 2485.42, "end": 2486.32, "word": " librarian", "probability": 0.496337890625}, {"start": 2486.32, "end": 2487.02, "word": " knows", "probability": 0.82275390625}, {"start": 2487.02, "end": 2487.4, "word": " that", "probability": 0.80615234375}, {"start": 2487.4, "end": 2488.36, "word": " the", "probability": 0.7451171875}, {"start": 2488.36, "end": 2488.8, "word": " population", "probability": 0.89697265625}, {"start": 2488.8, "end": 2489.12, "word": " standard", "probability": 0.3955078125}, {"start": 2489.12, "end": 2489.44, "word": " deviation", "probability": 0.97998046875}, {"start": 2489.44, "end": 2489.66, "word": " is", "probability": 0.919921875}, {"start": 2489.66, "end": 2490.54, "word": " 150", "probability": 0.853515625}, {"start": 2490.54, "end": 2493.52, "word": " books", "probability": 0.583984375}, {"start": 2493.52, "end": 2493.88, "word": " shipped", "probability": 0.9287109375}, {"start": 2493.88, "end": 2494.78, "word": " outwardly,", "probability": 0.535400390625}, {"start": 2494.9, "end": 2495.56, "word": " approximately", "probability": 0.8544921875}, {"start": 2495.56, "end": 2495.8, "word": " how", "probability": 0.88818359375}, {"start": 2495.8, "end": 2496.12, "word": " large", "probability": 0.96484375}, {"start": 2496.12, "end": 2496.32, "word": " a", "probability": 0.767578125}, {"start": 2496.32, "end": 2496.68, "word": " sample", "probability": 0.89111328125}, {"start": 2496.68, "end": 2497.42, "word": " did", "probability": 0.947265625}, {"start": 2497.42, "end": 2497.58, "word": " her", "probability": 0.912109375}, {"start": 2497.58, "end": 2498.04, "word": " assistant", "probability": 0.9599609375}, {"start": 2498.04, "end": 2498.56, "word": " use", "probability": 0.85888671875}, {"start": 2498.56, "end": 2499.2, "word": " to", "probability": 0.9140625}, {"start": 2499.2, "end": 2499.64, "word": " determine", "probability": 0.92041015625}, {"start": 2499.64, "end": 2499.88, "word": " the", "probability": 0.88916015625}, {"start": 2499.88, "end": 2500.2, "word": " interval", "probability": 0.3818359375}, {"start": 2500.2, "end": 2500.84, "word": " estimate?", "probability": 0.8701171875}, {"start": 2502.4, "end": 2503.04, "word": " So", "probability": 0.70361328125}, {"start": 2503.04, "end": 2503.18, "word": " the", "probability": 0.7099609375}, {"start": 2503.18, "end": 2503.62, "word": " information", "probability": 0.83203125}, {"start": 2503.62, "end": 2503.86, "word": " we", "probability": 0.92919921875}, {"start": 2503.86, "end": 2504.2, "word": " have", "probability": 0.9453125}, {"start": 2504.2, "end": 2506.38, "word": " is", "probability": 0.88916015625}, {"start": 2506.38, "end": 2506.54, "word": " the", "probability": 0.892578125}, {"start": 2506.54, "end": 2506.8, "word": " following.", "probability": 0.8916015625}, {"start": 2507.44, "end": 2508.18, "word": " We", "probability": 0.912109375}, {"start": 2508.18, "end": 2508.36, "word": " have", "probability": 0.94677734375}, {"start": 2508.36, "end": 2508.78, "word": " information", "probability": 0.8203125}, {"start": 2508.78, "end": 2509.18, "word": " about", "probability": 0.90234375}, {"start": 2509.18, "end": 2510.86, "word": " the", "probability": 0.84716796875}, {"start": 2510.86, "end": 2511.22, "word": " confidence", "probability": 0.90771484375}, {"start": 2511.22, "end": 2511.7, "word": " interval.", "probability": 0.927734375}], "temperature": 1.0}, {"id": 89, "seek": 254888, "start": 2521.44, "end": 2548.88, "text": " 920 books. And sigma is known to be 150. That's all we have. He asked about how large a sample did Herelsen's conclusion determine the interval estimate. Look at the answers. A is 2.", "tokens": [1722, 2009, 3642, 13, 400, 12771, 307, 444, 648, 281, 312, 8451, 13, 663, 311, 439, 321, 362, 13, 634, 2351, 466, 577, 2416, 257, 6889, 630, 634, 4419, 6748, 311, 10063, 6997, 264, 15035, 12539, 13, 2053, 412, 264, 6338, 13, 316, 307, 568, 13], "avg_logprob": -0.37001329533597255, "compression_ratio": 1.2797202797202798, "no_speech_prob": 0.0, "words": [{"start": 2521.4400000000005, "end": 2522.1200000000003, "word": " 920", "probability": 0.681396484375}, {"start": 2522.1200000000003, "end": 2522.8, "word": " books.", "probability": 0.2607421875}, {"start": 2525.94, "end": 2526.62, "word": " And", "probability": 0.93408203125}, {"start": 2526.62, "end": 2526.9, "word": " sigma", "probability": 0.63623046875}, {"start": 2526.9, "end": 2527.16, "word": " is", "probability": 0.9541015625}, {"start": 2527.16, "end": 2527.48, "word": " known", "probability": 0.61669921875}, {"start": 2527.48, "end": 2528.14, "word": " to", "probability": 0.96044921875}, {"start": 2528.14, "end": 2528.26, "word": " be", "probability": 0.94775390625}, {"start": 2528.26, "end": 2528.7, "word": " 150.", "probability": 0.8271484375}, {"start": 2532.98, "end": 2533.66, "word": " That's", "probability": 0.88037109375}, {"start": 2533.66, "end": 2534.62, "word": " all", "probability": 0.95556640625}, {"start": 2534.62, "end": 2535.18, "word": " we", "probability": 0.95654296875}, {"start": 2535.18, "end": 2535.56, "word": " have.", "probability": 0.94091796875}, {"start": 2536.34, "end": 2536.58, "word": " He", "probability": 0.65234375}, {"start": 2536.58, "end": 2536.78, "word": " asked", "probability": 0.434326171875}, {"start": 2536.78, "end": 2537.08, "word": " about", "probability": 0.88720703125}, {"start": 2537.08, "end": 2537.34, "word": " how", "probability": 0.91162109375}, {"start": 2537.34, "end": 2537.7, "word": " large", "probability": 0.87158203125}, {"start": 2537.7, "end": 2537.98, "word": " a", "probability": 0.8125}, {"start": 2537.98, "end": 2538.28, "word": " sample", "probability": 0.94921875}, {"start": 2538.28, "end": 2538.58, "word": " did", "probability": 0.88671875}, {"start": 2538.58, "end": 2539.14, "word": " Herelsen's", "probability": 0.340240478515625}, {"start": 2539.14, "end": 2539.46, "word": " conclusion", "probability": 0.1898193359375}, {"start": 2539.46, "end": 2540.16, "word": " determine", "probability": 0.9384765625}, {"start": 2540.16, "end": 2540.88, "word": " the", "probability": 0.91455078125}, {"start": 2540.88, "end": 2541.26, "word": " interval", "probability": 0.80615234375}, {"start": 2541.26, "end": 2541.82, "word": " estimate.", "probability": 0.8759765625}, {"start": 2546.74, "end": 2547.42, "word": " Look", "probability": 0.82373046875}, {"start": 2547.42, "end": 2547.56, "word": " at", "probability": 0.93701171875}, {"start": 2547.56, "end": 2547.7, "word": " the", "probability": 0.9208984375}, {"start": 2547.7, "end": 2547.98, "word": " answers.", "probability": 0.80419921875}, {"start": 2548.16, "end": 2548.36, "word": " A", "probability": 0.751953125}, {"start": 2548.36, "end": 2548.58, "word": " is", "probability": 0.94189453125}, {"start": 2548.58, "end": 2548.88, "word": " 2.", "probability": 0.72900390625}], "temperature": 1.0}, {"id": 90, "seek": 257655, "start": 2549.83, "end": 2576.55, "text": " B is 3, C is 12, it cannot be determined from the information given. Now, in order to find the number, the sample, we need Sigma or E squared. Confidence is not given. Sigma is okay. We can find the error.", "tokens": [363, 307, 805, 11, 383, 307, 2272, 11, 309, 2644, 312, 9540, 490, 264, 1589, 2212, 13, 823, 11, 294, 1668, 281, 915, 264, 1230, 11, 264, 6889, 11, 321, 643, 36595, 420, 462, 8889, 13, 11701, 2778, 307, 406, 2212, 13, 36595, 307, 1392, 13, 492, 393, 915, 264, 6713, 13], "avg_logprob": -0.3010023517428704, "compression_ratio": 1.3642384105960266, "no_speech_prob": 0.0, "words": [{"start": 2549.83, "end": 2550.15, "word": " B", "probability": 0.654296875}, {"start": 2550.15, "end": 2550.31, "word": " is", "probability": 0.837890625}, {"start": 2550.31, "end": 2550.61, "word": " 3,", "probability": 0.703125}, {"start": 2550.95, "end": 2551.11, "word": " C", "probability": 0.849609375}, {"start": 2551.11, "end": 2551.25, "word": " is", "probability": 0.94482421875}, {"start": 2551.25, "end": 2551.57, "word": " 12,", "probability": 0.955078125}, {"start": 2551.73, "end": 2551.85, "word": " it", "probability": 0.469970703125}, {"start": 2551.85, "end": 2552.05, "word": " cannot", "probability": 0.7900390625}, {"start": 2552.05, "end": 2552.27, "word": " be", "probability": 0.9248046875}, {"start": 2552.27, "end": 2552.65, "word": " determined", "probability": 0.927734375}, {"start": 2552.65, "end": 2553.07, "word": " from", "probability": 0.85009765625}, {"start": 2553.07, "end": 2553.23, "word": " the", "probability": 0.86572265625}, {"start": 2553.23, "end": 2553.63, "word": " information", "probability": 0.76025390625}, {"start": 2553.63, "end": 2553.95, "word": " given.", "probability": 0.86572265625}, {"start": 2557.19, "end": 2557.43, "word": " Now,", "probability": 0.90673828125}, {"start": 2557.51, "end": 2557.61, "word": " in", "probability": 0.93896484375}, {"start": 2557.61, "end": 2557.77, "word": " order", "probability": 0.923828125}, {"start": 2557.77, "end": 2558.03, "word": " to", "probability": 0.96923828125}, {"start": 2558.03, "end": 2558.31, "word": " find", "probability": 0.88818359375}, {"start": 2558.31, "end": 2558.99, "word": " the", "probability": 0.90966796875}, {"start": 2558.99, "end": 2559.53, "word": " number,", "probability": 0.6650390625}, {"start": 2560.03, "end": 2560.61, "word": " the", "probability": 0.90673828125}, {"start": 2560.61, "end": 2561.09, "word": " sample,", "probability": 0.59375}, {"start": 2562.99, "end": 2563.19, "word": " we", "probability": 0.9140625}, {"start": 2563.19, "end": 2563.57, "word": " need", "probability": 0.923828125}, {"start": 2563.57, "end": 2564.21, "word": " Sigma", "probability": 0.3271484375}, {"start": 2564.21, "end": 2564.71, "word": " or", "probability": 0.306884765625}, {"start": 2564.71, "end": 2565.03, "word": " E", "probability": 0.427734375}, {"start": 2565.03, "end": 2565.45, "word": " squared.", "probability": 0.54052734375}, {"start": 2567.03, "end": 2567.63, "word": " Confidence", "probability": 0.962646484375}, {"start": 2567.63, "end": 2567.87, "word": " is", "probability": 0.9462890625}, {"start": 2567.87, "end": 2568.03, "word": " not", "probability": 0.9501953125}, {"start": 2568.03, "end": 2568.35, "word": " given.", "probability": 0.89501953125}, {"start": 2570.55, "end": 2571.17, "word": " Sigma", "probability": 0.92919921875}, {"start": 2571.17, "end": 2571.39, "word": " is", "probability": 0.95361328125}, {"start": 2571.39, "end": 2571.75, "word": " okay.", "probability": 0.67822265625}, {"start": 2574.25, "end": 2574.89, "word": " We", "probability": 0.370361328125}, {"start": 2574.89, "end": 2575.83, "word": " can", "probability": 0.50048828125}, {"start": 2575.83, "end": 2576.17, "word": " find", "probability": 0.8525390625}, {"start": 2576.17, "end": 2576.35, "word": " the", "probability": 0.826171875}, {"start": 2576.35, "end": 2576.55, "word": " error.", "probability": 0.919921875}], "temperature": 1.0}, {"id": 91, "seek": 260819, "start": 2579.26, "end": 2608.2, "text": " The error is just W divided by 2. So the error is fine. I mean, E is fine. E is B minus A or upper limit minus lower limit divided by 2. So width divided by 2. So this is fine. But you don't have information about Z. We are looking for N. 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So the information is determined from the information given. Make sense? So we cannot compute this score. Z is fine. Z is 150. 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Now for number 14, we have the same information. But here, she asked her assistant to use 25 days. So now, n is 25. We have the same information about the interval.", "tokens": [9886, 482, 538, 732, 2709, 264, 912, 1874, 13, 823, 337, 1230, 3499, 11, 321, 362, 264, 912, 1589, 13, 583, 510, 11, 750, 2351, 720, 10994, 281, 764, 3552, 1708, 13, 407, 586, 11, 297, 307, 3552, 13, 492, 362, 264, 912, 1589, 466, 264, 15035, 13], "avg_logprob": -0.2342155563588045, "compression_ratio": 1.4428571428571428, "no_speech_prob": 0.0, "words": [{"start": 2637.93, "end": 2638.45, "word": " Divide", "probability": 0.72705078125}, {"start": 2638.45, "end": 2638.69, "word": " by", "probability": 0.93505859375}, {"start": 2638.69, "end": 2639.09, "word": " two", "probability": 0.5654296875}, {"start": 2639.09, "end": 2639.53, "word": " gives", "probability": 0.693359375}, {"start": 2639.53, "end": 2640.05, "word": " the", "probability": 0.89453125}, {"start": 2640.05, "end": 2640.59, "word": " same", "probability": 0.5615234375}, {"start": 2640.59, "end": 2640.77, "word": " result.", "probability": 0.61572265625}, {"start": 2641.75, "end": 2642.59, "word": " Now", "probability": 0.8818359375}, {"start": 2642.59, "end": 2642.85, "word": " for", "probability": 0.6845703125}, {"start": 2642.85, "end": 2643.03, "word": " number", "probability": 0.8330078125}, {"start": 2643.03, "end": 2643.59, "word": " 14,", "probability": 0.734375}, {"start": 2645.03, "end": 2645.51, "word": " we", "probability": 0.919921875}, {"start": 2645.51, "end": 2645.79, "word": " have", "probability": 0.94921875}, {"start": 2645.79, "end": 2647.71, "word": " the", "probability": 0.83349609375}, {"start": 2647.71, "end": 2647.91, "word": " same", "probability": 0.89892578125}, {"start": 2647.91, "end": 2648.41, "word": " information.", "probability": 0.84326171875}, {"start": 2650.37, "end": 2650.93, "word": " But", "probability": 0.88671875}, {"start": 2650.93, "end": 2651.33, "word": " here,", "probability": 0.8583984375}, {"start": 2654.45, "end": 2656.09, "word": " she", "probability": 0.8544921875}, {"start": 2656.09, "end": 2656.43, "word": " asked", "probability": 0.62158203125}, {"start": 2656.43, "end": 2656.67, "word": " her", "probability": 0.9228515625}, {"start": 2656.67, "end": 2657.15, "word": " assistant", "probability": 0.93310546875}, {"start": 2657.15, "end": 2657.57, "word": " to", "probability": 0.72802734375}, {"start": 2657.57, "end": 2657.79, "word": " use", "probability": 0.8720703125}, {"start": 2657.79, "end": 2658.47, "word": " 25", "probability": 0.83154296875}, {"start": 2658.47, "end": 2659.01, "word": " days.", "probability": 0.951171875}, {"start": 2659.99, "end": 2660.09, "word": " So", "probability": 0.8662109375}, {"start": 2660.09, "end": 2660.41, "word": " now,", "probability": 0.88232421875}, {"start": 2661.21, "end": 2662.03, "word": " n", "probability": 0.5625}, {"start": 2662.03, "end": 2662.17, "word": " is", "probability": 0.912109375}, {"start": 2662.17, "end": 2662.51, "word": " 25.", "probability": 0.947265625}, {"start": 2663.21, "end": 2663.49, "word": " We", "probability": 0.94677734375}, {"start": 2663.49, "end": 2663.63, "word": " have", "probability": 0.9296875}, {"start": 2663.63, "end": 2663.77, "word": " the", "probability": 0.90380859375}, {"start": 2663.77, "end": 2663.93, "word": " same", "probability": 0.90673828125}, {"start": 2663.93, "end": 2664.35, "word": " information", "probability": 0.859375}, {"start": 2664.35, "end": 2664.73, "word": " about", "probability": 0.90283203125}, {"start": 2664.73, "end": 2664.99, "word": " the", "probability": 0.8896484375}, {"start": 2664.99, "end": 2665.31, "word": " interval.", "probability": 0.86083984375}], "temperature": 1.0}, {"id": 94, "seek": 269624, "start": 2672.02, "end": 2696.24, "text": " And sigma is 150. So she asked her assistant to use 25 days of data to construct the interval estimate. So n is 25. What confidence level can she attach to the interval estimate? Now in this case, we are asking about confidence, not z.", "tokens": [400, 12771, 307, 8451, 13, 407, 750, 2351, 720, 10994, 281, 764, 3552, 1708, 295, 1412, 281, 7690, 264, 15035, 12539, 13, 407, 297, 307, 3552, 13, 708, 6687, 1496, 393, 750, 5085, 281, 264, 15035, 12539, 30, 823, 294, 341, 1389, 11, 321, 366, 3365, 466, 6687, 11, 406, 710, 13], "avg_logprob": -0.2175707513431333, "compression_ratio": 1.475, "no_speech_prob": 0.0, "words": [{"start": 2672.02, "end": 2672.36, "word": " And", "probability": 0.46533203125}, {"start": 2672.36, "end": 2672.66, "word": " sigma", "probability": 0.509765625}, {"start": 2672.66, "end": 2672.88, "word": " is", "probability": 0.89697265625}, {"start": 2672.88, "end": 2673.3, "word": " 150.", "probability": 0.83984375}, {"start": 2676.3, "end": 2677.02, "word": " So", "probability": 0.87939453125}, {"start": 2677.02, "end": 2677.64, "word": " she", "probability": 0.61962890625}, {"start": 2677.64, "end": 2678.1, "word": " asked", "probability": 0.7958984375}, {"start": 2678.1, "end": 2678.36, "word": " her", "probability": 0.8037109375}, {"start": 2678.36, "end": 2678.8, "word": " assistant", "probability": 0.94384765625}, {"start": 2678.8, "end": 2679.1, "word": " to", "probability": 0.53662109375}, {"start": 2679.1, "end": 2679.22, "word": " use", "probability": 0.8759765625}, {"start": 2679.22, "end": 2679.64, "word": " 25", "probability": 0.919921875}, {"start": 2679.64, "end": 2680.16, "word": " days", "probability": 0.931640625}, {"start": 2680.16, "end": 2680.5, "word": " of", "probability": 0.958984375}, {"start": 2680.5, "end": 2680.8, "word": " data", "probability": 0.95068359375}, {"start": 2680.8, "end": 2681.06, "word": " to", "probability": 0.94970703125}, {"start": 2681.06, "end": 2681.56, "word": " construct", "probability": 0.9638671875}, {"start": 2681.56, "end": 2681.74, "word": " the", "probability": 0.630859375}, {"start": 2681.74, "end": 2682.04, "word": " interval", "probability": 0.9775390625}, {"start": 2682.04, "end": 2682.5, "word": " estimate.", "probability": 0.865234375}, {"start": 2683.02, "end": 2683.18, "word": " So", "probability": 0.92529296875}, {"start": 2683.18, "end": 2683.34, "word": " n", "probability": 0.4873046875}, {"start": 2683.34, "end": 2683.46, "word": " is", "probability": 0.91796875}, {"start": 2683.46, "end": 2683.86, "word": " 25.", "probability": 0.93896484375}, {"start": 2684.98, "end": 2685.32, "word": " What", "probability": 0.88037109375}, {"start": 2685.32, "end": 2685.74, "word": " confidence", "probability": 0.98388671875}, {"start": 2685.74, "end": 2686.2, "word": " level", "probability": 0.9501953125}, {"start": 2686.2, "end": 2686.5, "word": " can", "probability": 0.9443359375}, {"start": 2686.5, "end": 2686.88, "word": " she", "probability": 0.9267578125}, {"start": 2686.88, "end": 2687.72, "word": " attach", "probability": 0.8798828125}, {"start": 2687.72, "end": 2688.12, "word": " to", "probability": 0.9658203125}, {"start": 2688.12, "end": 2688.3, "word": " the", "probability": 0.91845703125}, {"start": 2688.3, "end": 2688.72, "word": " interval", "probability": 0.9833984375}, {"start": 2688.72, "end": 2689.26, "word": " estimate?", "probability": 0.8818359375}, {"start": 2691.12, "end": 2691.3, "word": " Now", "probability": 0.53076171875}, {"start": 2691.3, "end": 2691.46, "word": " in", "probability": 0.623046875}, {"start": 2691.46, "end": 2691.62, "word": " this", "probability": 0.951171875}, {"start": 2691.62, "end": 2691.92, "word": " case,", "probability": 0.923828125}, {"start": 2692.7, "end": 2693.0, "word": " we", "probability": 0.96044921875}, {"start": 2693.0, "end": 2693.18, "word": " are", "probability": 0.931640625}, {"start": 2693.18, "end": 2693.5, "word": " asking", "probability": 0.86865234375}, {"start": 2693.5, "end": 2694.08, "word": " about", "probability": 0.904296875}, {"start": 2694.08, "end": 2695.18, "word": " confidence,", "probability": 0.27490234375}, {"start": 2695.66, "end": 2696.04, "word": " not", "probability": 0.935546875}, {"start": 2696.04, "end": 2696.24, "word": " z.", "probability": 0.53173828125}], "temperature": 1.0}, {"id": 95, "seek": 272855, "start": 2700.93, "end": 2728.55, "text": " You have to distinguish between confidence level and z. We use z, I'm sorry, we use z level to compute the z score. Now, which one is correct? 99.7, 99, 98, 95.4. Let's see. Now, what's the average? I'm sorry, the formula is x bar plus or minus z sigma over root n. 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We are looking about this one. Now, also there are two ways to solve this problem. Either focus on the aortia, or just find a continuous interval by itself. So let's focus on this one. Z sigma over root of.", "tokens": [682, 341, 1389, 11, 341, 307, 264, 8513, 321, 362, 13, 492, 366, 1237, 466, 341, 472, 13, 823, 11, 611, 456, 366, 732, 2098, 281, 5039, 341, 1154, 13, 13746, 1879, 322, 264, 257, 477, 654, 11, 420, 445, 915, 257, 10957, 15035, 538, 2564, 13, 407, 718, 311, 1879, 322, 341, 472, 13, 1176, 12771, 670, 5593, 295, 13], "avg_logprob": -0.31779233005739027, "compression_ratio": 1.4705882352941178, "no_speech_prob": 0.0, "words": [{"start": 2729.07, "end": 2729.27, "word": " In", "probability": 0.36962890625}, {"start": 2729.27, "end": 2729.49, "word": " this", "probability": 0.9462890625}, {"start": 2729.49, "end": 2729.83, "word": " case,", "probability": 0.912109375}, {"start": 2731.13, "end": 2731.43, "word": " this", "probability": 0.8125}, {"start": 2731.43, "end": 2731.53, "word": " is", "probability": 0.9462890625}, {"start": 2731.53, "end": 2731.63, "word": " the", "probability": 0.6611328125}, {"start": 2731.63, "end": 2731.89, "word": " formula", "probability": 0.433349609375}, {"start": 2731.89, "end": 2732.15, "word": " we", "probability": 0.8447265625}, {"start": 2732.15, "end": 2732.33, "word": " have.", "probability": 0.9267578125}, {"start": 2733.91, "end": 2734.49, "word": " We", "probability": 0.83544921875}, {"start": 2734.49, "end": 2734.71, "word": " are", "probability": 0.91650390625}, {"start": 2734.71, "end": 2735.03, "word": " looking", "probability": 0.442138671875}, {"start": 2735.03, "end": 2735.61, "word": " about", "probability": 0.72119140625}, {"start": 2735.61, "end": 2736.03, "word": " this", "probability": 0.6064453125}, {"start": 2736.03, "end": 2736.39, "word": " one.", "probability": 0.399169921875}, {"start": 2737.41, "end": 2737.85, "word": " Now,", "probability": 0.943359375}, {"start": 2738.01, "end": 2738.29, "word": " also", "probability": 0.5361328125}, {"start": 2738.29, "end": 2738.47, "word": " there", "probability": 0.69580078125}, {"start": 2738.47, "end": 2738.59, "word": " are", "probability": 0.93798828125}, {"start": 2738.59, "end": 2738.77, "word": " two", "probability": 0.912109375}, {"start": 2738.77, "end": 2739.05, "word": " ways", "probability": 0.90283203125}, {"start": 2739.05, "end": 2739.21, "word": " to", "probability": 0.951171875}, {"start": 2739.21, "end": 2739.41, "word": " solve", "probability": 0.93115234375}, {"start": 2739.41, "end": 2739.59, "word": " this", "probability": 0.9443359375}, {"start": 2739.59, "end": 2739.95, "word": " problem.", "probability": 0.8671875}, {"start": 2740.11, "end": 2740.37, "word": " Either", "probability": 0.81298828125}, {"start": 2740.37, "end": 2742.43, "word": " focus", "probability": 0.78125}, {"start": 2742.43, "end": 2743.11, "word": " on", "probability": 0.94775390625}, {"start": 2743.11, "end": 2743.25, "word": " the", "probability": 0.89794921875}, {"start": 2743.25, "end": 2743.73, "word": " aortia,", "probability": 0.5616658528645834}, {"start": 2745.57, "end": 2746.09, "word": " or", "probability": 0.94091796875}, {"start": 2746.09, "end": 2746.41, "word": " just", "probability": 0.8974609375}, {"start": 2746.41, "end": 2746.69, "word": " find", "probability": 0.8896484375}, {"start": 2746.69, "end": 2746.85, "word": " a", "probability": 0.6552734375}, {"start": 2746.85, "end": 2747.19, "word": " continuous", "probability": 0.3466796875}, {"start": 2747.19, "end": 2747.69, "word": " interval", "probability": 0.88623046875}, {"start": 2747.69, "end": 2747.95, "word": " by", "probability": 0.96337890625}, {"start": 2747.95, "end": 2748.37, "word": " itself.", "probability": 0.8173828125}, {"start": 2748.95, "end": 2749.19, "word": " So", "probability": 0.95556640625}, {"start": 2749.19, "end": 2749.41, "word": " let's", "probability": 0.8857421875}, {"start": 2749.41, "end": 2749.91, "word": " focus", "probability": 0.9423828125}, {"start": 2749.91, "end": 2750.83, "word": " on", "probability": 0.95068359375}, {"start": 2750.83, "end": 2751.07, "word": " this", "probability": 0.95263671875}, {"start": 2751.07, "end": 2751.39, "word": " one.", "probability": 0.92431640625}, {"start": 2753.03, "end": 2753.53, "word": " Z", "probability": 0.6748046875}, {"start": 2753.53, "end": 2754.83, "word": " sigma", "probability": 0.69970703125}, {"start": 2754.83, "end": 2755.83, "word": " over", "probability": 0.796875}, {"start": 2755.83, "end": 2756.07, "word": " root", "probability": 0.89794921875}, {"start": 2756.07, "end": 2756.23, "word": " of.", "probability": 0.55908203125}], "temperature": 1.0}, {"id": 97, "seek": 278792, "start": 2759.62, "end": 2787.92, "text": " And we have x bar. What's the value of x bar? x bar 740 plus x bar 830. 1660 divided by 2, 830.", "tokens": [400, 321, 362, 2031, 2159, 13, 708, 311, 264, 2158, 295, 2031, 2159, 30, 2031, 2159, 1614, 5254, 1804, 2031, 2159, 1649, 3446, 13, 3165, 4550, 6666, 538, 568, 11, 1649, 3446, 13], "avg_logprob": -0.19404871980933583, "compression_ratio": 1.103448275862069, "no_speech_prob": 0.0, "words": [{"start": 2759.62, "end": 2759.88, "word": " And", "probability": 0.7421875}, {"start": 2759.88, "end": 2760.0, "word": " we", "probability": 0.89501953125}, {"start": 2760.0, "end": 2760.14, "word": " have", "probability": 0.94873046875}, {"start": 2760.14, "end": 2760.38, "word": " x", "probability": 0.666015625}, {"start": 2760.38, "end": 2760.68, "word": " bar.", "probability": 0.7880859375}, {"start": 2761.22, "end": 2761.82, "word": " What's", "probability": 0.797607421875}, {"start": 2761.82, "end": 2761.88, "word": " the", "probability": 0.91796875}, {"start": 2761.88, "end": 2762.0, "word": " value", "probability": 0.97021484375}, {"start": 2762.0, "end": 2762.14, "word": " of", "probability": 0.9423828125}, {"start": 2762.14, "end": 2762.24, "word": " x", "probability": 0.994140625}, {"start": 2762.24, "end": 2762.52, "word": " bar?", "probability": 0.94287109375}, {"start": 2764.74, "end": 2765.38, "word": " x", "probability": 0.7470703125}, {"start": 2765.38, "end": 2765.78, "word": " bar", "probability": 0.9345703125}, {"start": 2765.78, "end": 2767.9, "word": " 740", "probability": 0.746337890625}, {"start": 2767.9, "end": 2769.1, "word": " plus", "probability": 0.87255859375}, {"start": 2769.1, "end": 2775.24, "word": " x", "probability": 0.7255859375}, {"start": 2775.24, "end": 2775.48, "word": " bar", "probability": 0.94921875}, {"start": 2775.48, "end": 2776.4, "word": " 830.", "probability": 0.94189453125}, {"start": 2785.38, "end": 2786.02, "word": " 1660", "probability": 0.63916015625}, {"start": 2786.02, "end": 2786.32, "word": " divided", "probability": 0.708984375}, {"start": 2786.32, "end": 2786.5, "word": " by", "probability": 0.96875}, {"start": 2786.5, "end": 2786.88, "word": " 2,", "probability": 0.76220703125}, {"start": 2787.22, "end": 2787.92, "word": " 830.", "probability": 0.940185546875}], "temperature": 1.0}, {"id": 98, "seek": 281490, "start": 2789.74, "end": 2814.9, "text": " Now, z equals, I don't know, sigma, sigma is 150, n is 5. So here we have 30 sigma. Now, what's the value of sigma? 36, so we have x bar, now the value of x bar.", "tokens": [823, 11, 710, 6915, 11, 286, 500, 380, 458, 11, 12771, 11, 12771, 307, 8451, 11, 297, 307, 1025, 13, 407, 510, 321, 362, 2217, 12771, 13, 823, 11, 437, 311, 264, 2158, 295, 12771, 30, 8652, 11, 370, 321, 362, 2031, 2159, 11, 586, 264, 2158, 295, 2031, 2159, 13], "avg_logprob": -0.30183294530098254, "compression_ratio": 1.35, "no_speech_prob": 0.0, "words": [{"start": 2789.74, "end": 2790.06, "word": " Now,", "probability": 0.68017578125}, {"start": 2790.18, "end": 2790.3, "word": " z", "probability": 0.611328125}, {"start": 2790.3, "end": 2790.84, "word": " equals,", "probability": 0.501953125}, {"start": 2791.28, "end": 2791.54, "word": " I", "probability": 0.87939453125}, {"start": 2791.54, "end": 2791.74, "word": " don't", "probability": 0.970458984375}, {"start": 2791.74, "end": 2791.98, "word": " know,", "probability": 0.8486328125}, {"start": 2792.44, "end": 2792.96, "word": " sigma,", "probability": 0.82568359375}, {"start": 2793.72, "end": 2794.86, "word": " sigma", "probability": 0.87255859375}, {"start": 2794.86, "end": 2795.08, "word": " is", "probability": 0.92578125}, {"start": 2795.08, "end": 2795.64, "word": " 150,", "probability": 0.35791015625}, {"start": 2797.12, "end": 2797.72, "word": " n", "probability": 0.418701171875}, {"start": 2797.72, "end": 2797.9, "word": " is", "probability": 0.92431640625}, {"start": 2797.9, "end": 2798.18, "word": " 5.", "probability": 0.783203125}, {"start": 2799.26, "end": 2799.54, "word": " So", "probability": 0.8935546875}, {"start": 2799.54, "end": 2799.74, "word": " here", "probability": 0.72705078125}, {"start": 2799.74, "end": 2799.9, "word": " we", "probability": 0.77197265625}, {"start": 2799.9, "end": 2800.66, "word": " have", "probability": 0.9501953125}, {"start": 2800.66, "end": 2801.22, "word": " 30", "probability": 0.5673828125}, {"start": 2801.22, "end": 2801.6, "word": " sigma.", "probability": 0.88671875}, {"start": 2804.98, "end": 2805.54, "word": " Now,", "probability": 0.9267578125}, {"start": 2805.94, "end": 2806.76, "word": " what's", "probability": 0.643798828125}, {"start": 2806.76, "end": 2806.92, "word": " the", "probability": 0.9189453125}, {"start": 2806.92, "end": 2807.12, "word": " value", "probability": 0.98486328125}, {"start": 2807.12, "end": 2807.3, "word": " of", "probability": 0.95166015625}, {"start": 2807.3, "end": 2807.54, "word": " sigma?", "probability": 0.9404296875}, {"start": 2810.08, "end": 2810.64, "word": " 36,", "probability": 0.327392578125}, {"start": 2810.92, "end": 2811.04, "word": " so", "probability": 0.9130859375}, {"start": 2811.04, "end": 2811.16, "word": " we", "probability": 0.91162109375}, {"start": 2811.16, "end": 2811.28, "word": " have", "probability": 0.94873046875}, {"start": 2811.28, "end": 2811.56, "word": " x", "probability": 0.96728515625}, {"start": 2811.56, "end": 2811.88, "word": " bar,", "probability": 0.79833984375}, {"start": 2813.74, "end": 2813.98, "word": " now", "probability": 0.7607421875}, {"start": 2813.98, "end": 2814.16, "word": " the", "probability": 0.8447265625}, {"start": 2814.16, "end": 2814.32, "word": " value", "probability": 0.982421875}, {"start": 2814.32, "end": 2814.48, "word": " of", "probability": 0.74462890625}, {"start": 2814.48, "end": 2814.62, "word": " x", "probability": 0.9951171875}, {"start": 2814.62, "end": 2814.9, "word": " bar.", "probability": 0.94384765625}], "temperature": 1.0}, {"id": 99, "seek": 284963, "start": 2822.33, "end": 2849.63, "text": " So we have x bar 830 plus or minus 30 there. Now, if you look carefully at this equation, what's the value of z in order to have this confidence interval, which is 740 and 920?", "tokens": [407, 321, 362, 2031, 2159, 1649, 3446, 1804, 420, 3175, 2217, 456, 13, 823, 11, 498, 291, 574, 7500, 412, 341, 5367, 11, 437, 311, 264, 2158, 295, 710, 294, 1668, 281, 362, 341, 6687, 15035, 11, 597, 307, 1614, 5254, 293, 1722, 2009, 30], "avg_logprob": -0.20686141984618228, "compression_ratio": 1.2464788732394365, "no_speech_prob": 0.0, "words": [{"start": 2822.33, "end": 2822.57, "word": " So", "probability": 0.8349609375}, {"start": 2822.57, "end": 2822.69, "word": " we", "probability": 0.6640625}, {"start": 2822.69, "end": 2822.87, "word": " have", "probability": 0.9423828125}, {"start": 2822.87, "end": 2823.41, "word": " x", "probability": 0.7421875}, {"start": 2823.41, "end": 2823.77, "word": " bar", "probability": 0.3154296875}, {"start": 2823.77, "end": 2825.33, "word": " 830", "probability": 0.76806640625}, {"start": 2825.33, "end": 2826.73, "word": " plus", "probability": 0.7373046875}, {"start": 2826.73, "end": 2828.15, "word": " or", "probability": 0.94287109375}, {"start": 2828.15, "end": 2828.83, "word": " minus", "probability": 0.98779296875}, {"start": 2828.83, "end": 2830.21, "word": " 30", "probability": 0.412841796875}, {"start": 2830.21, "end": 2830.53, "word": " there.", "probability": 0.468505859375}, {"start": 2835.29, "end": 2836.05, "word": " Now,", "probability": 0.92041015625}, {"start": 2836.43, "end": 2836.63, "word": " if", "probability": 0.94482421875}, {"start": 2836.63, "end": 2836.71, "word": " you", "probability": 0.94970703125}, {"start": 2836.71, "end": 2836.89, "word": " look", "probability": 0.96337890625}, {"start": 2836.89, "end": 2837.23, "word": " carefully", "probability": 0.79296875}, {"start": 2837.23, "end": 2837.41, "word": " at", "probability": 0.95361328125}, {"start": 2837.41, "end": 2837.57, "word": " this", "probability": 0.93798828125}, {"start": 2837.57, "end": 2838.03, "word": " equation,", "probability": 0.984375}, {"start": 2839.55, "end": 2840.01, "word": " what's", "probability": 0.938720703125}, {"start": 2840.01, "end": 2840.15, "word": " the", "probability": 0.91748046875}, {"start": 2840.15, "end": 2840.41, "word": " value", "probability": 0.9794921875}, {"start": 2840.41, "end": 2840.59, "word": " of", "probability": 0.8388671875}, {"start": 2840.59, "end": 2840.79, "word": " z", "probability": 0.61328125}, {"start": 2840.79, "end": 2842.51, "word": " in", "probability": 0.81494140625}, {"start": 2842.51, "end": 2842.79, "word": " order", "probability": 0.91845703125}, {"start": 2842.79, "end": 2843.35, "word": " to", "probability": 0.96923828125}, {"start": 2843.35, "end": 2844.27, "word": " have", "probability": 0.87255859375}, {"start": 2844.27, "end": 2844.57, "word": " this", "probability": 0.9375}, {"start": 2844.57, "end": 2844.99, "word": " confidence", "probability": 0.483154296875}, {"start": 2844.99, "end": 2845.43, "word": " interval,", "probability": 0.95556640625}, {"start": 2845.97, "end": 2846.31, "word": " which", "probability": 0.95361328125}, {"start": 2846.31, "end": 2846.49, "word": " is", "probability": 0.9423828125}, {"start": 2846.49, "end": 2847.21, "word": " 740", "probability": 0.9111328125}, {"start": 2847.21, "end": 2849.05, "word": " and", "probability": 0.90380859375}, {"start": 2849.05, "end": 2849.63, "word": " 920?", "probability": 0.889892578125}], "temperature": 1.0}, {"id": 100, "seek": 288189, "start": 2856.17, "end": 2881.89, "text": " So, Z should be... What's the value of Z? Now, 830 minus 3Z equals this value. So, Z equals... 3. So, Z is 3. That's why. Now, Z is 3.", "tokens": [407, 11, 1176, 820, 312, 485, 708, 311, 264, 2158, 295, 1176, 30, 823, 11, 1649, 3446, 3175, 805, 57, 6915, 341, 2158, 13, 407, 11, 1176, 6915, 485, 805, 13, 407, 11, 1176, 307, 805, 13, 663, 311, 983, 13, 823, 11, 1176, 307, 805, 13], "avg_logprob": -0.3227539124588172, "compression_ratio": 1.3106796116504855, "no_speech_prob": 0.0, "words": [{"start": 2856.17, "end": 2856.85, "word": " So,", "probability": 0.5244140625}, {"start": 2857.05, "end": 2857.29, "word": " Z", "probability": 0.3876953125}, {"start": 2857.29, "end": 2857.71, "word": " should", "probability": 0.869140625}, {"start": 2857.71, "end": 2860.73, "word": " be...", "probability": 0.42303466796875}, {"start": 2860.73, "end": 2861.45, "word": " What's", "probability": 0.719482421875}, {"start": 2861.45, "end": 2861.53, "word": " the", "probability": 0.92431640625}, {"start": 2861.53, "end": 2861.67, "word": " value", "probability": 0.98388671875}, {"start": 2861.67, "end": 2861.81, "word": " of", "probability": 0.9658203125}, {"start": 2861.81, "end": 2861.93, "word": " Z?", "probability": 0.97216796875}, {"start": 2862.59, "end": 2863.07, "word": " Now,", "probability": 0.89990234375}, {"start": 2863.45, "end": 2864.01, "word": " 830", "probability": 0.2108154296875}, {"start": 2864.01, "end": 2864.39, "word": " minus", "probability": 0.9248046875}, {"start": 2864.39, "end": 2865.81, "word": " 3Z", "probability": 0.50726318359375}, {"start": 2865.81, "end": 2866.29, "word": " equals", "probability": 0.7685546875}, {"start": 2866.29, "end": 2866.61, "word": " this", "probability": 0.921875}, {"start": 2866.61, "end": 2866.87, "word": " value.", "probability": 0.97021484375}, {"start": 2869.83, "end": 2870.15, "word": " So,", "probability": 0.91943359375}, {"start": 2870.23, "end": 2870.31, "word": " Z", "probability": 0.9755859375}, {"start": 2870.31, "end": 2873.39, "word": " equals...", "probability": 0.6571044921875}, {"start": 2873.39, "end": 2876.45, "word": " 3.", "probability": 0.459228515625}, {"start": 2876.83, "end": 2877.41, "word": " So,", "probability": 0.94775390625}, {"start": 2877.53, "end": 2877.75, "word": " Z", "probability": 0.986328125}, {"start": 2877.75, "end": 2877.99, "word": " is", "probability": 0.92626953125}, {"start": 2877.99, "end": 2878.31, "word": " 3.", "probability": 0.87353515625}, {"start": 2879.53, "end": 2879.93, "word": " That's", "probability": 0.928955078125}, {"start": 2879.93, "end": 2880.13, "word": " why.", "probability": 0.77783203125}, {"start": 2880.53, "end": 2880.85, "word": " Now,", "probability": 0.95166015625}, {"start": 2881.19, "end": 2881.41, "word": " Z", "probability": 0.98583984375}, {"start": 2881.41, "end": 2881.61, "word": " is", "probability": 0.93994140625}, {"start": 2881.61, "end": 2881.89, "word": " 3.", "probability": 0.90478515625}], "temperature": 1.0}, {"id": 101, "seek": 291064, "start": 2883.06, "end": 2910.64, "text": " What do you think the corresponding C level? 99.7% If you remember for the 68 empirical rule 68, 95, 99.7% In chapter 6 we said that", "tokens": [708, 360, 291, 519, 264, 11760, 383, 1496, 30, 11803, 13, 22, 4, 759, 291, 1604, 337, 264, 23317, 31886, 4978, 23317, 11, 13420, 11, 11803, 13, 22, 4, 682, 7187, 1386, 321, 848, 300], "avg_logprob": -0.3454861086275842, "compression_ratio": 1.146551724137931, "no_speech_prob": 0.0, "words": [{"start": 2883.06, "end": 2883.38, "word": " What", "probability": 0.41552734375}, {"start": 2883.38, "end": 2883.54, "word": " do", "probability": 0.6474609375}, {"start": 2883.54, "end": 2883.54, "word": " you", "probability": 0.95556640625}, {"start": 2883.54, "end": 2883.86, "word": " think", "probability": 0.916015625}, {"start": 2883.86, "end": 2884.1, "word": " the", "probability": 0.3994140625}, {"start": 2884.1, "end": 2884.64, "word": " corresponding", "probability": 0.70849609375}, {"start": 2884.64, "end": 2884.92, "word": " C", "probability": 0.398681640625}, {"start": 2884.92, "end": 2885.18, "word": " level?", "probability": 0.58349609375}, {"start": 2891.46, "end": 2892.3, "word": " 99", "probability": 0.5810546875}, {"start": 2892.3, "end": 2892.96, "word": ".7", "probability": 0.964599609375}, {"start": 2892.96, "end": 2893.06, "word": "%", "probability": 0.68701171875}, {"start": 2893.06, "end": 2896.56, "word": " If", "probability": 0.55908203125}, {"start": 2896.56, "end": 2896.72, "word": " you", "probability": 0.9521484375}, {"start": 2896.72, "end": 2897.06, "word": " remember", "probability": 0.8798828125}, {"start": 2897.06, "end": 2898.24, "word": " for", "probability": 0.54736328125}, {"start": 2898.24, "end": 2898.66, "word": " the", "probability": 0.857421875}, {"start": 2898.66, "end": 2900.16, "word": " 68", "probability": 0.6533203125}, {"start": 2900.16, "end": 2901.36, "word": " empirical", "probability": 0.6240234375}, {"start": 2901.36, "end": 2901.78, "word": " rule", "probability": 0.81494140625}, {"start": 2901.78, "end": 2902.62, "word": " 68,", "probability": 0.52587890625}, {"start": 2904.24, "end": 2905.7, "word": " 95,", "probability": 0.572265625}, {"start": 2906.76, "end": 2907.08, "word": " 99", "probability": 0.9521484375}, {"start": 2907.08, "end": 2907.66, "word": ".7", "probability": 0.973876953125}, {"start": 2907.66, "end": 2908.08, "word": "%", "probability": 0.80712890625}, {"start": 2908.08, "end": 2909.18, "word": " In", "probability": 0.638671875}, {"start": 2909.18, "end": 2909.44, "word": " chapter", "probability": 0.6201171875}, {"start": 2909.44, "end": 2909.82, "word": " 6", "probability": 0.77587890625}, {"start": 2909.82, "end": 2910.04, "word": " we", "probability": 0.69677734375}, {"start": 2910.04, "end": 2910.28, "word": " said", "probability": 0.91064453125}, {"start": 2910.28, "end": 2910.64, "word": " that", "probability": 0.94091796875}], "temperature": 1.0}, {"id": 102, "seek": 293728, "start": 2911.56, "end": 2937.28, "text": " 99.7% of the data falls within three standard deviations of the mean. So if these three, I am sure that we are using 99.7% for the confidence level. So for this particular example here, we have new information about the sample size. So N is 25.", "tokens": [11803, 13, 22, 4, 295, 264, 1412, 8804, 1951, 1045, 3832, 31219, 763, 295, 264, 914, 13, 407, 498, 613, 1045, 11, 286, 669, 988, 300, 321, 366, 1228, 11803, 13, 22, 4, 337, 264, 6687, 1496, 13, 407, 337, 341, 1729, 1365, 510, 11, 321, 362, 777, 1589, 466, 264, 6889, 2744, 13, 407, 426, 307, 3552, 13], "avg_logprob": -0.14570313195387521, "compression_ratio": 1.467065868263473, "no_speech_prob": 0.0, "words": [{"start": 2911.56, "end": 2912.02, "word": " 99", "probability": 0.5009765625}, {"start": 2912.02, "end": 2912.66, "word": ".7", "probability": 0.9814453125}, {"start": 2912.66, "end": 2912.96, "word": "%", "probability": 0.771484375}, {"start": 2912.96, "end": 2913.26, "word": " of", "probability": 0.92919921875}, {"start": 2913.26, "end": 2913.4, "word": " the", "probability": 0.91259765625}, {"start": 2913.4, "end": 2913.76, "word": " data", "probability": 0.94921875}, {"start": 2913.76, "end": 2914.42, "word": " falls", "probability": 0.80029296875}, {"start": 2914.42, "end": 2914.88, "word": " within", "probability": 0.9111328125}, {"start": 2914.88, "end": 2916.0, "word": " three", "probability": 0.63671875}, {"start": 2916.0, "end": 2916.38, "word": " standard", "probability": 0.908203125}, {"start": 2916.38, "end": 2916.9, "word": " deviations", "probability": 0.90771484375}, {"start": 2916.9, "end": 2917.1, "word": " of", "probability": 0.96240234375}, {"start": 2917.1, "end": 2917.22, "word": " the", "probability": 0.9267578125}, {"start": 2917.22, "end": 2917.42, "word": " mean.", "probability": 0.97509765625}, {"start": 2918.48, "end": 2918.84, "word": " So", "probability": 0.9384765625}, {"start": 2918.84, "end": 2919.12, "word": " if", "probability": 0.7314453125}, {"start": 2919.12, "end": 2919.36, "word": " these", "probability": 0.452880859375}, {"start": 2919.36, "end": 2919.78, "word": " three,", "probability": 0.900390625}, {"start": 2919.96, "end": 2920.06, "word": " I", "probability": 0.99658203125}, {"start": 2920.06, "end": 2920.2, "word": " am", "probability": 0.88427734375}, {"start": 2920.2, "end": 2920.46, "word": " sure", "probability": 0.91064453125}, {"start": 2920.46, "end": 2920.84, "word": " that", "probability": 0.9296875}, {"start": 2920.84, "end": 2921.84, "word": " we", "probability": 0.92431640625}, {"start": 2921.84, "end": 2921.98, "word": " are", "probability": 0.9404296875}, {"start": 2921.98, "end": 2922.5, "word": " using", "probability": 0.93017578125}, {"start": 2922.5, "end": 2923.2, "word": " 99", "probability": 0.96630859375}, {"start": 2923.2, "end": 2924.02, "word": ".7", "probability": 0.997314453125}, {"start": 2924.02, "end": 2925.0, "word": "%", "probability": 0.974609375}, {"start": 2925.0, "end": 2925.66, "word": " for", "probability": 0.93701171875}, {"start": 2925.66, "end": 2925.84, "word": " the", "probability": 0.91015625}, {"start": 2925.84, "end": 2926.26, "word": " confidence", "probability": 0.9716796875}, {"start": 2926.26, "end": 2926.54, "word": " level.", "probability": 0.947265625}, {"start": 2928.6, "end": 2929.36, "word": " So", "probability": 0.8876953125}, {"start": 2929.36, "end": 2930.1, "word": " for", "probability": 0.70263671875}, {"start": 2930.1, "end": 2930.34, "word": " this", "probability": 0.9443359375}, {"start": 2930.34, "end": 2930.72, "word": " particular", "probability": 0.8916015625}, {"start": 2930.72, "end": 2931.22, "word": " example", "probability": 0.9765625}, {"start": 2931.22, "end": 2931.52, "word": " here,", "probability": 0.8037109375}, {"start": 2931.58, "end": 2931.7, "word": " we", "probability": 0.95654296875}, {"start": 2931.7, "end": 2932.06, "word": " have", "probability": 0.94482421875}, {"start": 2932.06, "end": 2932.68, "word": " new", "probability": 0.56396484375}, {"start": 2932.68, "end": 2933.28, "word": " information", "probability": 0.84130859375}, {"start": 2933.28, "end": 2933.78, "word": " about", "probability": 0.9013671875}, {"start": 2933.78, "end": 2934.66, "word": " the", "probability": 0.86181640625}, {"start": 2934.66, "end": 2934.9, "word": " sample", "probability": 0.8818359375}, {"start": 2934.9, "end": 2935.42, "word": " size.", "probability": 0.849609375}, {"start": 2936.06, "end": 2936.64, "word": " So", "probability": 0.94482421875}, {"start": 2936.64, "end": 2936.8, "word": " N", "probability": 0.4189453125}, {"start": 2936.8, "end": 2936.9, "word": " is", "probability": 0.94384765625}, {"start": 2936.9, "end": 2937.28, "word": " 25.", "probability": 0.93896484375}], "temperature": 1.0}, {"id": 103, "seek": 296585, "start": 2941.63, "end": 2965.85, "text": " So just simple calculation x bar as I mentioned here. The average is lower limit plus upper limit divided by 2. So x bar equals 830. So now your confidence interval is x bar plus or minus z sigma over root n.", "tokens": [407, 445, 2199, 17108, 2031, 2159, 382, 286, 2835, 510, 13, 440, 4274, 307, 3126, 4948, 1804, 6597, 4948, 6666, 538, 568, 13, 407, 2031, 2159, 6915, 1649, 3446, 13, 407, 586, 428, 6687, 15035, 307, 2031, 2159, 1804, 420, 3175, 710, 12771, 670, 5593, 297, 13], "avg_logprob": -0.20491535930583873, "compression_ratio": 1.375, "no_speech_prob": 0.0, "words": [{"start": 2941.63, "end": 2941.97, "word": " So", "probability": 0.72802734375}, {"start": 2941.97, "end": 2942.25, "word": " just", "probability": 0.60400390625}, {"start": 2942.25, "end": 2942.57, "word": " simple", "probability": 0.79052734375}, {"start": 2942.57, "end": 2943.17, "word": " calculation", "probability": 0.86669921875}, {"start": 2943.17, "end": 2943.61, "word": " x", "probability": 0.3623046875}, {"start": 2943.61, "end": 2943.95, "word": " bar", "probability": 0.83447265625}, {"start": 2943.95, "end": 2945.63, "word": " as", "probability": 0.646484375}, {"start": 2945.63, "end": 2945.81, "word": " I", "probability": 0.91650390625}, {"start": 2945.81, "end": 2946.19, "word": " mentioned", "probability": 0.78857421875}, {"start": 2946.19, "end": 2946.55, "word": " here.", "probability": 0.8447265625}, {"start": 2948.23, "end": 2948.67, "word": " The", "probability": 0.8544921875}, {"start": 2948.67, "end": 2949.15, "word": " average", "probability": 0.77978515625}, {"start": 2949.15, "end": 2949.67, "word": " is", "probability": 0.93701171875}, {"start": 2949.67, "end": 2950.29, "word": " lower", "probability": 0.83203125}, {"start": 2950.29, "end": 2950.63, "word": " limit", "probability": 0.97021484375}, {"start": 2950.63, "end": 2950.97, "word": " plus", "probability": 0.90771484375}, {"start": 2950.97, "end": 2951.23, "word": " upper", "probability": 0.88330078125}, {"start": 2951.23, "end": 2951.51, "word": " limit", "probability": 0.970703125}, {"start": 2951.51, "end": 2951.73, "word": " divided", "probability": 0.708984375}, {"start": 2951.73, "end": 2951.91, "word": " by", "probability": 0.970703125}, {"start": 2951.91, "end": 2952.17, "word": " 2.", "probability": 0.57666015625}, {"start": 2952.83, "end": 2953.11, "word": " So", "probability": 0.93701171875}, {"start": 2953.11, "end": 2953.37, "word": " x", "probability": 0.92138671875}, {"start": 2953.37, "end": 2953.73, "word": " bar", "probability": 0.9072265625}, {"start": 2953.73, "end": 2955.57, "word": " equals", "probability": 0.9208984375}, {"start": 2955.57, "end": 2956.99, "word": " 830.", "probability": 0.8583984375}, {"start": 2957.69, "end": 2957.89, "word": " So", "probability": 0.93359375}, {"start": 2957.89, "end": 2958.07, "word": " now", "probability": 0.86865234375}, {"start": 2958.07, "end": 2958.27, "word": " your", "probability": 0.82861328125}, {"start": 2958.27, "end": 2958.67, "word": " confidence", "probability": 0.97900390625}, {"start": 2958.67, "end": 2959.17, "word": " interval", "probability": 0.96533203125}, {"start": 2959.17, "end": 2959.63, "word": " is", "probability": 0.93994140625}, {"start": 2959.63, "end": 2960.33, "word": " x", "probability": 0.97412109375}, {"start": 2960.33, "end": 2960.65, "word": " bar", "probability": 0.94775390625}, {"start": 2960.65, "end": 2962.45, "word": " plus", "probability": 0.9208984375}, {"start": 2962.45, "end": 2962.69, "word": " or", "probability": 0.95947265625}, {"start": 2962.69, "end": 2963.23, "word": " minus", "probability": 0.98583984375}, {"start": 2963.23, "end": 2964.63, "word": " z", "probability": 0.76123046875}, {"start": 2964.63, "end": 2965.13, "word": " sigma", "probability": 0.84326171875}, {"start": 2965.13, "end": 2965.29, "word": " over", "probability": 0.892578125}, {"start": 2965.29, "end": 2965.59, "word": " root", "probability": 0.94677734375}, {"start": 2965.59, "end": 2965.85, "word": " n.", "probability": 0.85498046875}], "temperature": 1.0}, {"id": 104, "seek": 299387, "start": 2967.59, "end": 2993.87, "text": " z sigma over root n, z is unknown, sigma is 150, n is 25, which is 5, square root of it, so we'll have 3z. So now x bar 830 minus 3z, this is the lower limit, upper limit 830 plus 3z.", "tokens": [710, 12771, 670, 5593, 297, 11, 710, 307, 9841, 11, 12771, 307, 8451, 11, 297, 307, 3552, 11, 597, 307, 1025, 11, 3732, 5593, 295, 309, 11, 370, 321, 603, 362, 805, 89, 13, 407, 586, 2031, 2159, 1649, 3446, 3175, 805, 89, 11, 341, 307, 264, 3126, 4948, 11, 6597, 4948, 1649, 3446, 1804, 805, 89, 13], "avg_logprob": -0.2154396135928267, "compression_ratio": 1.3333333333333333, "no_speech_prob": 0.0, "words": [{"start": 2967.59, "end": 2967.97, "word": " z", "probability": 0.1458740234375}, {"start": 2967.97, "end": 2968.29, "word": " sigma", "probability": 0.7060546875}, {"start": 2968.29, "end": 2968.45, "word": " over", "probability": 0.705078125}, {"start": 2968.45, "end": 2968.71, "word": " root", "probability": 0.9306640625}, {"start": 2968.71, "end": 2968.95, "word": " n,", "probability": 0.8583984375}, {"start": 2969.79, "end": 2970.27, "word": " z", "probability": 0.95068359375}, {"start": 2970.27, "end": 2970.69, "word": " is", "probability": 0.95166015625}, {"start": 2970.69, "end": 2971.07, "word": " unknown,", "probability": 0.8935546875}, {"start": 2972.19, "end": 2972.47, "word": " sigma", "probability": 0.896484375}, {"start": 2972.47, "end": 2972.71, "word": " is", "probability": 0.955078125}, {"start": 2972.71, "end": 2973.25, "word": " 150,", "probability": 0.76513671875}, {"start": 2974.19, "end": 2974.41, "word": " n", "probability": 0.9482421875}, {"start": 2974.41, "end": 2974.55, "word": " is", "probability": 0.9521484375}, {"start": 2974.55, "end": 2974.97, "word": " 25,", "probability": 0.91162109375}, {"start": 2975.69, "end": 2975.91, "word": " which", "probability": 0.94482421875}, {"start": 2975.91, "end": 2976.07, "word": " is", "probability": 0.9453125}, {"start": 2976.07, "end": 2976.41, "word": " 5,", "probability": 0.87109375}, {"start": 2976.51, "end": 2976.73, "word": " square", "probability": 0.560546875}, {"start": 2976.73, "end": 2976.93, "word": " root", "probability": 0.95751953125}, {"start": 2976.93, "end": 2977.03, "word": " of", "probability": 0.9736328125}, {"start": 2977.03, "end": 2977.21, "word": " it,", "probability": 0.880859375}, {"start": 2977.55, "end": 2977.81, "word": " so", "probability": 0.86181640625}, {"start": 2977.81, "end": 2977.97, "word": " we'll", "probability": 0.7421875}, {"start": 2977.97, "end": 2979.33, "word": " have", "probability": 0.57177734375}, {"start": 2979.33, "end": 2980.37, "word": " 3z.", "probability": 0.911865234375}, {"start": 2980.93, "end": 2981.41, "word": " So", "probability": 0.94287109375}, {"start": 2981.41, "end": 2981.67, "word": " now", "probability": 0.80517578125}, {"start": 2981.67, "end": 2982.09, "word": " x", "probability": 0.57177734375}, {"start": 2982.09, "end": 2982.45, "word": " bar", "probability": 0.85791015625}, {"start": 2982.45, "end": 2985.11, "word": " 830", "probability": 0.7054443359375}, {"start": 2985.11, "end": 2986.17, "word": " minus", "probability": 0.96728515625}, {"start": 2986.17, "end": 2988.39, "word": " 3z,", "probability": 0.974853515625}, {"start": 2989.61, "end": 2989.75, "word": " this", "probability": 0.4892578125}, {"start": 2989.75, "end": 2989.83, "word": " is", "probability": 0.94970703125}, {"start": 2989.83, "end": 2989.95, "word": " the", "probability": 0.8994140625}, {"start": 2989.95, "end": 2990.13, "word": " lower", "probability": 0.88427734375}, {"start": 2990.13, "end": 2990.45, "word": " limit,", "probability": 0.96630859375}, {"start": 2990.69, "end": 2990.93, "word": " upper", "probability": 0.81689453125}, {"start": 2990.93, "end": 2991.35, "word": " limit", "probability": 0.96826171875}, {"start": 2991.35, "end": 2993.11, "word": " 830", "probability": 0.814697265625}, {"start": 2993.11, "end": 2993.37, "word": " plus", "probability": 0.9365234375}, {"start": 2993.37, "end": 2993.87, "word": " 3z.", "probability": 0.9951171875}], "temperature": 1.0}, {"id": 105, "seek": 302234, "start": 2995.48, "end": 3022.34, "text": " Now, the confidence interval is given by 740 and 920. Just use the lower limit. 830 minus 3z equals 740. Simple calculation here. 830 minus 740 is 90, equals 3z. That means z equals 3.", "tokens": [823, 11, 264, 6687, 15035, 307, 2212, 538, 1614, 5254, 293, 1722, 2009, 13, 1449, 764, 264, 3126, 4948, 13, 1649, 3446, 3175, 805, 89, 6915, 1614, 5254, 13, 21532, 17108, 510, 13, 1649, 3446, 3175, 1614, 5254, 307, 4289, 11, 6915, 805, 89, 13, 663, 1355, 710, 6915, 805, 13], "avg_logprob": -0.24894831845393547, "compression_ratio": 1.3214285714285714, "no_speech_prob": 0.0, "words": [{"start": 2995.48, "end": 2995.78, "word": " Now,", "probability": 0.68505859375}, {"start": 2996.04, "end": 2996.24, "word": " the", "probability": 0.79736328125}, {"start": 2996.24, "end": 2996.62, "word": " confidence", "probability": 0.9599609375}, {"start": 2996.62, "end": 2997.12, "word": " interval", "probability": 0.9892578125}, {"start": 2997.12, "end": 2997.38, "word": " is", "probability": 0.9140625}, {"start": 2997.38, "end": 2997.62, "word": " given", "probability": 0.861328125}, {"start": 2997.62, "end": 2998.02, "word": " by", "probability": 0.95654296875}, {"start": 2998.02, "end": 2998.82, "word": " 740", "probability": 0.3377685546875}, {"start": 2998.82, "end": 2999.0, "word": " and", "probability": 0.71337890625}, {"start": 2999.0, "end": 2999.6, "word": " 920.", "probability": 0.890380859375}, {"start": 3001.06, "end": 3001.54, "word": " Just", "probability": 0.74267578125}, {"start": 3001.54, "end": 3003.38, "word": " use", "probability": 0.81884765625}, {"start": 3003.38, "end": 3003.54, "word": " the", "probability": 0.89404296875}, {"start": 3003.54, "end": 3003.74, "word": " lower", "probability": 0.81591796875}, {"start": 3003.74, "end": 3004.14, "word": " limit.", "probability": 0.9404296875}, {"start": 3005.36, "end": 3006.0, "word": " 830", "probability": 0.835693359375}, {"start": 3006.0, "end": 3008.04, "word": " minus", "probability": 0.86572265625}, {"start": 3008.04, "end": 3008.52, "word": " 3z", "probability": 0.73046875}, {"start": 3008.52, "end": 3009.02, "word": " equals", "probability": 0.71240234375}, {"start": 3009.02, "end": 3010.82, "word": " 740.", "probability": 0.906494140625}, {"start": 3012.3, "end": 3012.9, "word": " Simple", "probability": 0.362060546875}, {"start": 3012.9, "end": 3013.54, "word": " calculation", "probability": 0.93603515625}, {"start": 3013.54, "end": 3013.96, "word": " here.", "probability": 0.798828125}, {"start": 3016.0, "end": 3016.62, "word": " 830", "probability": 0.901123046875}, {"start": 3016.62, "end": 3017.08, "word": " minus", "probability": 0.982421875}, {"start": 3017.08, "end": 3017.72, "word": " 740", "probability": 0.91748046875}, {"start": 3017.72, "end": 3017.92, "word": " is", "probability": 0.8359375}, {"start": 3017.92, "end": 3018.28, "word": " 90,", "probability": 0.892578125}, {"start": 3018.66, "end": 3019.18, "word": " equals", "probability": 0.501953125}, {"start": 3019.18, "end": 3019.78, "word": " 3z.", "probability": 0.972412109375}, {"start": 3020.64, "end": 3021.24, "word": " That", "probability": 0.849609375}, {"start": 3021.24, "end": 3021.6, "word": " means", "probability": 0.9091796875}, {"start": 3021.6, "end": 3021.84, "word": " z", "probability": 0.8310546875}, {"start": 3021.84, "end": 3022.14, "word": " equals", "probability": 0.78466796875}, {"start": 3022.14, "end": 3022.34, "word": " 3.", "probability": 0.82470703125}], "temperature": 1.0}, {"id": 106, "seek": 304939, "start": 3026.07, "end": 3049.39, "text": " Now the z value is 3, it means the confidence is 9917, so the correct answer is A. The other way, you can use that one, by using the", "tokens": [823, 264, 710, 2158, 307, 805, 11, 309, 1355, 264, 6687, 307, 11803, 7773, 11, 370, 264, 3006, 1867, 307, 316, 13, 440, 661, 636, 11, 291, 393, 764, 300, 472, 11, 538, 1228, 264], "avg_logprob": -0.2916666782564587, "compression_ratio": 1.1981981981981982, "no_speech_prob": 0.0, "words": [{"start": 3026.07, "end": 3026.45, "word": " Now", "probability": 0.7255859375}, {"start": 3026.45, "end": 3026.77, "word": " the", "probability": 0.5078125}, {"start": 3026.77, "end": 3026.91, "word": " z", "probability": 0.5166015625}, {"start": 3026.91, "end": 3027.23, "word": " value", "probability": 0.78271484375}, {"start": 3027.23, "end": 3027.47, "word": " is", "probability": 0.931640625}, {"start": 3027.47, "end": 3027.77, "word": " 3,", "probability": 0.595703125}, {"start": 3028.05, "end": 3028.29, "word": " it", "probability": 0.65771484375}, {"start": 3028.29, "end": 3028.57, "word": " means", "probability": 0.93505859375}, {"start": 3028.57, "end": 3028.77, "word": " the", "probability": 0.78662109375}, {"start": 3028.77, "end": 3029.13, "word": " confidence", "probability": 0.97412109375}, {"start": 3029.13, "end": 3029.75, "word": " is", "probability": 0.92431640625}, {"start": 3029.75, "end": 3031.37, "word": " 9917,", "probability": 0.77490234375}, {"start": 3031.77, "end": 3031.95, "word": " so", "probability": 0.92041015625}, {"start": 3031.95, "end": 3032.15, "word": " the", "probability": 0.9150390625}, {"start": 3032.15, "end": 3032.43, "word": " correct", "probability": 0.91357421875}, {"start": 3032.43, "end": 3032.81, "word": " answer", "probability": 0.951171875}, {"start": 3032.81, "end": 3033.03, "word": " is", "probability": 0.953125}, {"start": 3033.03, "end": 3033.53, "word": " A.", "probability": 0.794921875}, {"start": 3044.69, "end": 3045.25, "word": " The", "probability": 0.2044677734375}, {"start": 3045.25, "end": 3045.51, "word": " other", "probability": 0.8623046875}, {"start": 3045.51, "end": 3045.73, "word": " way,", "probability": 0.95654296875}, {"start": 3046.21, "end": 3046.41, "word": " you", "probability": 0.95068359375}, {"start": 3046.41, "end": 3046.61, "word": " can", "probability": 0.9423828125}, {"start": 3046.61, "end": 3046.79, "word": " use", "probability": 0.8759765625}, {"start": 3046.79, "end": 3046.97, "word": " that", "probability": 0.923828125}, {"start": 3046.97, "end": 3047.25, "word": " one,", "probability": 0.8857421875}, {"start": 3048.37, "end": 3048.59, "word": " by", "probability": 0.95947265625}, {"start": 3048.59, "end": 3048.93, "word": " using", "probability": 0.9296875}, {"start": 3048.93, "end": 3049.39, "word": " the", "probability": 0.91357421875}], "temperature": 1.0}, {"id": 107, "seek": 308087, "start": 3053.01, "end": 3080.87, "text": " Margin of error, which is the difference between these two divided by two, you will get the same result. So there are two methods, one of these straightforward one. The other one, as you mentioned, is the error term. It's B minus upper limit minus lower limit divided by two. 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What's the value for this one? 90. So the margin of error is 90. So E equals E. Sigma or N equals? All squared. So by using this equation you can get your result.", "tokens": [2829, 301, 28868, 6666, 538, 568, 13, 708, 311, 264, 2158, 337, 341, 472, 30, 4289, 13, 407, 264, 10270, 295, 6713, 307, 4289, 13, 407, 462, 6915, 462, 13, 36595, 420, 426, 6915, 30, 1057, 8889, 13, 407, 538, 1228, 341, 5367, 291, 393, 483, 428, 1874, 13], "avg_logprob": -0.30500000059604643, "compression_ratio": 1.3191489361702127, "no_speech_prob": 0.0, "words": [{"start": 3082.89, "end": 3083.39, "word": " Minus", "probability": 0.61041259765625}, {"start": 3083.39, "end": 3083.89, "word": " 74", "probability": 0.2685546875}, {"start": 3083.89, "end": 3084.25, "word": " divided", "probability": 0.39501953125}, {"start": 3084.25, "end": 3084.49, "word": " by", "probability": 0.970703125}, {"start": 3084.49, "end": 3084.75, "word": " 2.", "probability": 0.85498046875}, {"start": 3086.69, "end": 3087.33, "word": " What's", "probability": 0.788818359375}, {"start": 3087.33, "end": 3087.45, "word": " the", "probability": 0.919921875}, {"start": 3087.45, "end": 3087.63, "word": " value", "probability": 0.97021484375}, {"start": 3087.63, "end": 3087.89, "word": " for", "probability": 0.89208984375}, {"start": 3087.89, "end": 3088.11, "word": " this", "probability": 0.9443359375}, {"start": 3088.11, "end": 3088.37, "word": " one?", "probability": 0.91650390625}, {"start": 3094.57, "end": 3095.21, "word": " 90.", "probability": 0.80712890625}, {"start": 3095.67, "end": 3095.99, "word": " So", "probability": 0.857421875}, {"start": 3095.99, "end": 3096.59, "word": " the", "probability": 0.67724609375}, {"start": 3096.59, "end": 3096.97, "word": " margin", "probability": 0.939453125}, {"start": 3096.97, "end": 3097.29, "word": " of", "probability": 0.96337890625}, {"start": 3097.29, "end": 3097.53, "word": " error", "probability": 0.68359375}, {"start": 3097.53, "end": 3098.41, "word": " is", "probability": 0.9404296875}, {"start": 3098.41, "end": 3098.89, "word": " 90.", "probability": 0.966796875}, {"start": 3099.51, "end": 3099.75, "word": " So", "probability": 0.89697265625}, {"start": 3099.75, "end": 3099.95, "word": " E", "probability": 0.76416015625}, {"start": 3099.95, "end": 3100.33, "word": " equals", "probability": 0.79345703125}, {"start": 3100.33, "end": 3100.61, "word": " E.", "probability": 0.51171875}, {"start": 3101.07, "end": 3101.71, "word": " Sigma", "probability": 0.88916015625}, {"start": 3101.71, "end": 3103.09, "word": " or", "probability": 0.55322265625}, {"start": 3103.09, "end": 3103.37, "word": " N", "probability": 0.89404296875}, {"start": 3103.37, "end": 3103.79, "word": " equals?", "probability": 0.84130859375}, {"start": 3107.11, "end": 3107.75, "word": " All", "probability": 0.472900390625}, {"start": 3107.75, "end": 3107.99, "word": " squared.", "probability": 0.49755859375}, {"start": 3109.23, "end": 3109.41, "word": " So", "probability": 0.3828125}, {"start": 3109.41, "end": 3109.55, "word": " by", "probability": 0.86572265625}, {"start": 3109.55, "end": 3109.75, "word": " using", "probability": 0.923828125}, {"start": 3109.75, "end": 3109.95, "word": " this", "probability": 0.93603515625}, {"start": 3109.95, "end": 3110.33, "word": " equation", "probability": 0.96044921875}, {"start": 3110.33, "end": 3110.49, "word": " you", "probability": 0.517578125}, {"start": 3110.49, "end": 3110.61, "word": " can", "probability": 0.927734375}, {"start": 3110.61, "end": 3110.81, "word": " get", "probability": 0.9443359375}, {"start": 3110.81, "end": 3110.99, "word": " your", "probability": 0.861328125}, {"start": 3110.99, "end": 3111.23, "word": " result.", "probability": 0.92724609375}], "temperature": 1.0}, {"id": 109, "seek": 313002, "start": 3112.1, "end": 3130.02, "text": " So, N is 25, Z is unknown, Sigma is 150, R is 90. This one squared. You will get the same Z-score. Make sense?", "tokens": [407, 11, 426, 307, 3552, 11, 1176, 307, 9841, 11, 36595, 307, 8451, 11, 497, 307, 4289, 13, 639, 472, 8889, 13, 509, 486, 483, 264, 912, 1176, 12, 4417, 418, 13, 4387, 2020, 30], "avg_logprob": -0.28927949981557, "compression_ratio": 1.088235294117647, "no_speech_prob": 0.0, "words": [{"start": 3112.1, "end": 3112.42, "word": " So,", "probability": 0.69775390625}, {"start": 3112.6, "end": 3112.64, "word": " N", "probability": 0.468505859375}, {"start": 3112.64, "end": 3112.78, "word": " is", "probability": 0.66650390625}, {"start": 3112.78, "end": 3113.44, "word": " 25,", "probability": 0.82177734375}, {"start": 3115.02, "end": 3115.24, "word": " Z", "probability": 0.8447265625}, {"start": 3115.24, "end": 3115.44, "word": " is", "probability": 0.95068359375}, {"start": 3115.44, "end": 3115.82, "word": " unknown,", "probability": 0.83203125}, {"start": 3116.16, "end": 3116.46, "word": " Sigma", "probability": 0.495849609375}, {"start": 3116.46, "end": 3116.86, "word": " is", "probability": 0.943359375}, {"start": 3116.86, "end": 3118.68, "word": " 150,", "probability": 0.8798828125}, {"start": 3119.32, "end": 3119.68, "word": " R", "probability": 0.41064453125}, {"start": 3119.68, "end": 3119.86, "word": " is", "probability": 0.83544921875}, {"start": 3119.86, "end": 3120.28, "word": " 90.", "probability": 0.97607421875}, {"start": 3121.32, "end": 3121.66, "word": " This", "probability": 0.81640625}, {"start": 3121.66, "end": 3121.92, "word": " one", "probability": 0.8798828125}, {"start": 3121.92, "end": 3122.4, "word": " squared.", "probability": 0.4619140625}, {"start": 3122.92, "end": 3123.06, "word": " You", "probability": 0.560546875}, {"start": 3123.06, "end": 3123.22, "word": " will", "probability": 0.87353515625}, {"start": 3123.22, "end": 3123.66, "word": " get", "probability": 0.9345703125}, {"start": 3123.66, "end": 3125.52, "word": " the", "probability": 0.751953125}, {"start": 3125.52, "end": 3125.9, "word": " same", "probability": 0.904296875}, {"start": 3125.9, "end": 3126.78, "word": " Z", "probability": 0.81103515625}, {"start": 3126.78, "end": 3127.16, "word": "-score.", "probability": 0.648193359375}, {"start": 3128.9, "end": 3129.66, "word": " Make", "probability": 0.72998046875}, {"start": 3129.66, "end": 3130.02, "word": " sense?", "probability": 0.82568359375}], "temperature": 1.0}, {"id": 110, "seek": 316637, "start": 3137.77, "end": 3166.37, "text": " Because if you take z to be three times one-fifth divided by nine squared, you will get the same result for z value. So both will give the same result. So that's for the multiple choice problems. Any question? Let's move to the section number two, true or false problems.", "tokens": [1436, 498, 291, 747, 710, 281, 312, 1045, 1413, 472, 12, 69, 351, 392, 6666, 538, 4949, 8889, 11, 291, 486, 483, 264, 912, 1874, 337, 710, 2158, 13, 407, 1293, 486, 976, 264, 912, 1874, 13, 407, 300, 311, 337, 264, 3866, 3922, 2740, 13, 2639, 1168, 30, 961, 311, 1286, 281, 264, 3541, 1230, 732, 11, 2074, 420, 7908, 2740, 13], "avg_logprob": -0.177734371740371, "compression_ratio": 1.5195530726256983, "no_speech_prob": 0.0, "words": [{"start": 3137.77, "end": 3138.09, "word": " Because", "probability": 0.70556640625}, {"start": 3138.09, "end": 3138.27, "word": " if", "probability": 0.92578125}, {"start": 3138.27, "end": 3138.41, "word": " you", "probability": 0.9541015625}, {"start": 3138.41, "end": 3138.85, "word": " take", "probability": 0.87109375}, {"start": 3138.85, "end": 3139.39, "word": " z", "probability": 0.61767578125}, {"start": 3139.39, "end": 3139.55, "word": " to", "probability": 0.94189453125}, {"start": 3139.55, "end": 3139.67, "word": " be", "probability": 0.9443359375}, {"start": 3139.67, "end": 3140.05, "word": " three", "probability": 0.56591796875}, {"start": 3140.05, "end": 3141.31, "word": " times", "probability": 0.8291015625}, {"start": 3141.31, "end": 3141.55, "word": " one", "probability": 0.71533203125}, {"start": 3141.55, "end": 3141.81, "word": "-fifth", "probability": 0.849365234375}, {"start": 3141.81, "end": 3142.11, "word": " divided", "probability": 0.5849609375}, {"start": 3142.11, "end": 3142.29, "word": " by", "probability": 0.9677734375}, {"start": 3142.29, "end": 3142.55, "word": " nine", "probability": 0.75927734375}, {"start": 3142.55, "end": 3142.93, "word": " squared,", "probability": 0.8642578125}, {"start": 3143.55, "end": 3143.77, "word": " you", "probability": 0.94970703125}, {"start": 3143.77, "end": 3143.93, "word": " will", "probability": 0.89306640625}, {"start": 3143.93, "end": 3144.23, "word": " get", "probability": 0.94287109375}, {"start": 3144.23, "end": 3144.91, "word": " the", "probability": 0.9169921875}, {"start": 3144.91, "end": 3145.15, "word": " same", "probability": 0.89453125}, {"start": 3145.15, "end": 3145.53, "word": " result", "probability": 0.93896484375}, {"start": 3145.53, "end": 3146.87, "word": " for", "probability": 0.7783203125}, {"start": 3146.87, "end": 3147.83, "word": " z", "probability": 0.8466796875}, {"start": 3147.83, "end": 3148.03, "word": " value.", "probability": 0.4443359375}, {"start": 3148.31, "end": 3148.51, "word": " So", "probability": 0.9541015625}, {"start": 3148.51, "end": 3148.83, "word": " both", "probability": 0.81396484375}, {"start": 3148.83, "end": 3149.13, "word": " will", "probability": 0.364501953125}, {"start": 3149.13, "end": 3149.67, "word": " give", "probability": 0.82421875}, {"start": 3149.67, "end": 3150.57, "word": " the", "probability": 0.896484375}, {"start": 3150.57, "end": 3150.79, "word": " same", "probability": 0.90234375}, {"start": 3150.79, "end": 3151.11, "word": " result.", "probability": 0.935546875}, {"start": 3152.19, "end": 3152.49, "word": " So", "probability": 0.9423828125}, {"start": 3152.49, "end": 3152.77, "word": " that's", "probability": 0.936279296875}, {"start": 3152.77, "end": 3153.05, "word": " for", "probability": 0.93359375}, {"start": 3153.05, "end": 3154.81, "word": " the", "probability": 0.896484375}, {"start": 3154.81, "end": 3155.13, "word": " multiple", "probability": 0.9619140625}, {"start": 3155.13, "end": 3155.79, "word": " choice", "probability": 0.77197265625}, {"start": 3155.79, "end": 3157.05, "word": " problems.", "probability": 0.822265625}, {"start": 3158.39, "end": 3158.95, "word": " Any", "probability": 0.8251953125}, {"start": 3158.95, "end": 3159.31, "word": " question?", "probability": 0.5595703125}, {"start": 3160.53, "end": 3161.11, "word": " Let's", "probability": 0.97705078125}, {"start": 3161.11, "end": 3161.49, "word": " move", "probability": 0.94677734375}, {"start": 3161.49, "end": 3161.87, "word": " to", "probability": 0.90771484375}, {"start": 3161.87, "end": 3162.07, "word": " the", "probability": 0.75830078125}, {"start": 3162.07, "end": 3162.43, "word": " section", "probability": 0.88232421875}, {"start": 3162.43, "end": 3162.71, "word": " number", "probability": 0.92333984375}, {"start": 3162.71, "end": 3163.03, "word": " two,", "probability": 0.8916015625}, {"start": 3163.17, "end": 3163.43, "word": " true", "probability": 0.78955078125}, {"start": 3163.43, "end": 3163.77, "word": " or", "probability": 0.9609375}, {"start": 3163.77, "end": 3164.27, "word": " false", "probability": 0.912109375}, {"start": 3164.27, "end": 3166.37, "word": " problems.", "probability": 0.79833984375}], "temperature": 1.0}, {"id": 111, "seek": 319479, "start": 3167.81, "end": 3194.79, "text": " Number one, a race car driver tested his car for time from 0 to 60 mileage per hour. And in 20 tests, obtained an average of 4.85 seconds, with some deviation of 1.47 seconds.", "tokens": [5118, 472, 11, 257, 4569, 1032, 6787, 8246, 702, 1032, 337, 565, 490, 1958, 281, 4060, 43121, 680, 1773, 13, 400, 294, 945, 6921, 11, 14879, 364, 4274, 295, 1017, 13, 19287, 3949, 11, 365, 512, 25163, 295, 502, 13, 14060, 3949, 13], "avg_logprob": -0.27539062161337247, "compression_ratio": 1.3134328358208955, "no_speech_prob": 0.0, "words": [{"start": 3167.81, "end": 3168.47, "word": " Number", "probability": 0.72216796875}, {"start": 3168.47, "end": 3168.79, "word": " one,", "probability": 0.77734375}, {"start": 3171.85, "end": 3172.01, "word": " a", "probability": 0.79541015625}, {"start": 3172.01, "end": 3172.23, "word": " race", "probability": 0.947265625}, {"start": 3172.23, "end": 3172.55, "word": " car", "probability": 0.8681640625}, {"start": 3172.55, "end": 3177.95, "word": " driver", "probability": 0.580078125}, {"start": 3177.95, "end": 3178.43, "word": " tested", "probability": 0.84375}, {"start": 3178.43, "end": 3178.65, "word": " his", "probability": 0.8095703125}, {"start": 3178.65, "end": 3178.93, "word": " car", "probability": 0.9423828125}, {"start": 3178.93, "end": 3179.47, "word": " for", "probability": 0.90966796875}, {"start": 3179.47, "end": 3180.61, "word": " time", "probability": 0.779296875}, {"start": 3180.61, "end": 3180.93, "word": " from", "probability": 0.890625}, {"start": 3180.93, "end": 3181.35, "word": " 0", "probability": 0.30419921875}, {"start": 3181.35, "end": 3181.65, "word": " to", "probability": 0.92431640625}, {"start": 3181.65, "end": 3182.05, "word": " 60", "probability": 0.947265625}, {"start": 3182.05, "end": 3183.45, "word": " mileage", "probability": 0.279052734375}, {"start": 3183.45, "end": 3183.67, "word": " per", "probability": 0.7431640625}, {"start": 3183.67, "end": 3183.97, "word": " hour.", "probability": 0.94970703125}, {"start": 3185.47, "end": 3185.93, "word": " And", "probability": 0.91552734375}, {"start": 3185.93, "end": 3186.21, "word": " in", "probability": 0.88671875}, {"start": 3186.21, "end": 3186.51, "word": " 20", "probability": 0.422119140625}, {"start": 3186.51, "end": 3186.89, "word": " tests,", "probability": 0.8193359375}, {"start": 3186.95, "end": 3187.45, "word": " obtained", "probability": 0.8515625}, {"start": 3187.45, "end": 3187.75, "word": " an", "probability": 0.9541015625}, {"start": 3187.75, "end": 3188.15, "word": " average", "probability": 0.787109375}, {"start": 3188.15, "end": 3188.47, "word": " of", "probability": 0.96533203125}, {"start": 3188.47, "end": 3188.81, "word": " 4", "probability": 0.9970703125}, {"start": 3188.81, "end": 3189.39, "word": ".85", "probability": 0.994873046875}, {"start": 3189.39, "end": 3190.19, "word": " seconds,", "probability": 0.8056640625}, {"start": 3191.25, "end": 3191.49, "word": " with", "probability": 0.90380859375}, {"start": 3191.49, "end": 3191.73, "word": " some", "probability": 0.414794921875}, {"start": 3191.73, "end": 3192.15, "word": " deviation", "probability": 0.8720703125}, {"start": 3192.15, "end": 3192.49, "word": " of", "probability": 0.96240234375}, {"start": 3192.49, "end": 3192.83, "word": " 1", "probability": 0.98828125}, {"start": 3192.83, "end": 3193.57, "word": ".47", "probability": 0.771240234375}, {"start": 3193.57, "end": 3194.79, "word": " seconds.", "probability": 0.7607421875}], "temperature": 1.0}, {"id": 112, "seek": 322362, "start": 3196.12, "end": 3223.62, "text": " 95 confidence interval for the 0 to 60 time is 4.62 seconds up to 5.18. I think straightforward. Just simple calculation, it will give the right answer. x bar n, so we have to use this equation.", "tokens": [13420, 6687, 15035, 337, 264, 1958, 281, 4060, 565, 307, 1017, 13, 28052, 3949, 493, 281, 1025, 13, 6494, 13, 286, 519, 15325, 13, 1449, 2199, 17108, 11, 309, 486, 976, 264, 558, 1867, 13, 2031, 2159, 297, 11, 370, 321, 362, 281, 764, 341, 5367, 13], "avg_logprob": -0.28759765935440856, "compression_ratio": 1.3175675675675675, "no_speech_prob": 0.0, "words": [{"start": 3196.12, "end": 3196.66, "word": " 95", "probability": 0.63818359375}, {"start": 3196.66, "end": 3197.28, "word": " confidence", "probability": 0.5654296875}, {"start": 3197.28, "end": 3197.92, "word": " interval", "probability": 0.66357421875}, {"start": 3197.92, "end": 3198.46, "word": " for", "probability": 0.80322265625}, {"start": 3198.46, "end": 3199.58, "word": " the", "probability": 0.6962890625}, {"start": 3199.58, "end": 3199.84, "word": " 0", "probability": 0.82373046875}, {"start": 3199.84, "end": 3199.98, "word": " to", "probability": 0.857421875}, {"start": 3199.98, "end": 3200.28, "word": " 60", "probability": 0.85107421875}, {"start": 3200.28, "end": 3200.84, "word": " time", "probability": 0.78466796875}, {"start": 3200.84, "end": 3202.36, "word": " is", "probability": 0.865234375}, {"start": 3202.36, "end": 3202.86, "word": " 4", "probability": 0.9697265625}, {"start": 3202.86, "end": 3203.44, "word": ".62", "probability": 0.92578125}, {"start": 3203.44, "end": 3204.06, "word": " seconds", "probability": 0.74951171875}, {"start": 3204.06, "end": 3204.34, "word": " up", "probability": 0.486083984375}, {"start": 3204.34, "end": 3204.68, "word": " to", "probability": 0.94482421875}, {"start": 3204.68, "end": 3205.56, "word": " 5", "probability": 0.986328125}, {"start": 3205.56, "end": 3206.16, "word": ".18.", "probability": 0.987548828125}, {"start": 3206.5, "end": 3207.1, "word": " I", "probability": 0.92529296875}, {"start": 3207.1, "end": 3207.26, "word": " think", "probability": 0.91650390625}, {"start": 3207.26, "end": 3207.84, "word": " straightforward.", "probability": 0.67529296875}, {"start": 3209.12, "end": 3209.54, "word": " Just", "probability": 0.83447265625}, {"start": 3209.54, "end": 3209.82, "word": " simple", "probability": 0.78173828125}, {"start": 3209.82, "end": 3210.38, "word": " calculation,", "probability": 0.88916015625}, {"start": 3210.62, "end": 3210.68, "word": " it", "probability": 0.58984375}, {"start": 3210.68, "end": 3210.8, "word": " will", "probability": 0.8798828125}, {"start": 3210.8, "end": 3211.12, "word": " give", "probability": 0.8740234375}, {"start": 3211.12, "end": 3212.48, "word": " the", "probability": 0.8916015625}, {"start": 3212.48, "end": 3212.86, "word": " right", "probability": 0.92236328125}, {"start": 3212.86, "end": 3213.44, "word": " answer.", "probability": 0.95361328125}, {"start": 3216.66, "end": 3217.66, "word": " x", "probability": 0.2418212890625}, {"start": 3217.66, "end": 3218.0, "word": " bar", "probability": 0.2568359375}, {"start": 3218.0, "end": 3220.64, "word": " n,", "probability": 0.52587890625}, {"start": 3221.36, "end": 3221.6, "word": " so", "probability": 0.67578125}, {"start": 3221.6, "end": 3221.96, "word": " we", "probability": 0.8896484375}, {"start": 3221.96, "end": 3222.16, "word": " have", "probability": 0.8984375}, {"start": 3222.16, "end": 3222.32, "word": " to", "probability": 0.94775390625}, {"start": 3222.32, "end": 3222.54, "word": " use", "probability": 0.841796875}, {"start": 3222.54, "end": 3222.88, "word": " this", "probability": 0.94775390625}, {"start": 3222.88, "end": 3223.62, "word": " equation.", "probability": 0.9228515625}], "temperature": 1.0}, {"id": 113, "seek": 325518, "start": 3228.22, "end": 3255.18, "text": " You can do it. So it says the answer is false. You have to check this result. So it's 4.5 plus or minus T. We have to find T. S is given to be 147 divided by root 20. Now, to find T, we have to use 0 to 5 and 19.", "tokens": [509, 393, 360, 309, 13, 407, 309, 1619, 264, 1867, 307, 7908, 13, 509, 362, 281, 1520, 341, 1874, 13, 407, 309, 311, 1017, 13, 20, 1804, 420, 3175, 314, 13, 492, 362, 281, 915, 314, 13, 318, 307, 2212, 281, 312, 3499, 22, 6666, 538, 5593, 945, 13, 823, 11, 281, 915, 314, 11, 321, 362, 281, 764, 1958, 281, 1025, 293, 1294, 13], "avg_logprob": -0.19625946992274487, "compression_ratio": 1.4013157894736843, "no_speech_prob": 0.0, "words": [{"start": 3228.22, "end": 3228.42, "word": " You", "probability": 0.6181640625}, {"start": 3228.42, "end": 3228.62, "word": " can", "probability": 0.9384765625}, {"start": 3228.62, "end": 3228.8, "word": " do", "probability": 0.9501953125}, {"start": 3228.8, "end": 3229.18, "word": " it.", "probability": 0.951171875}, {"start": 3230.46, "end": 3231.02, "word": " So", "probability": 0.81005859375}, {"start": 3231.02, "end": 3231.62, "word": " it", "probability": 0.25146484375}, {"start": 3231.62, "end": 3231.88, "word": " says", "probability": 0.71337890625}, {"start": 3231.88, "end": 3232.04, "word": " the", "probability": 0.408447265625}, {"start": 3232.04, "end": 3232.24, "word": " answer", "probability": 0.96240234375}, {"start": 3232.24, "end": 3232.5, "word": " is", "probability": 0.9326171875}, {"start": 3232.5, "end": 3232.84, "word": " false.", "probability": 0.448974609375}, {"start": 3233.84, "end": 3234.02, "word": " You", "probability": 0.75537109375}, {"start": 3234.02, "end": 3234.2, "word": " have", "probability": 0.9248046875}, {"start": 3234.2, "end": 3234.32, "word": " to", "probability": 0.966796875}, {"start": 3234.32, "end": 3234.66, "word": " check", "probability": 0.94091796875}, {"start": 3234.66, "end": 3235.08, "word": " this", "probability": 0.76904296875}, {"start": 3235.08, "end": 3235.42, "word": " result.", "probability": 0.88916015625}, {"start": 3235.56, "end": 3235.72, "word": " So", "probability": 0.94580078125}, {"start": 3235.72, "end": 3235.92, "word": " it's", "probability": 0.900390625}, {"start": 3235.92, "end": 3236.24, "word": " 4", "probability": 0.705078125}, {"start": 3236.24, "end": 3237.66, "word": ".5", "probability": 0.42803955078125}, {"start": 3237.66, "end": 3238.16, "word": " plus", "probability": 0.90576171875}, {"start": 3238.16, "end": 3238.34, "word": " or", "probability": 0.9501953125}, {"start": 3238.34, "end": 3238.62, "word": " minus", "probability": 0.98828125}, {"start": 3238.62, "end": 3238.92, "word": " T.", "probability": 0.59130859375}, {"start": 3239.0, "end": 3239.08, "word": " We", "probability": 0.8291015625}, {"start": 3239.08, "end": 3239.26, "word": " have", "probability": 0.94482421875}, {"start": 3239.26, "end": 3239.38, "word": " to", "probability": 0.95751953125}, {"start": 3239.38, "end": 3239.56, "word": " find", "probability": 0.90185546875}, {"start": 3239.56, "end": 3239.84, "word": " T.", "probability": 0.9443359375}, {"start": 3240.72, "end": 3241.02, "word": " S", "probability": 0.93701171875}, {"start": 3241.02, "end": 3241.2, "word": " is", "probability": 0.9482421875}, {"start": 3241.2, "end": 3241.5, "word": " given", "probability": 0.8984375}, {"start": 3241.5, "end": 3242.36, "word": " to", "probability": 0.96533203125}, {"start": 3242.36, "end": 3242.54, "word": " be", "probability": 0.9541015625}, {"start": 3242.54, "end": 3243.46, "word": " 147", "probability": 0.86474609375}, {"start": 3243.46, "end": 3244.84, "word": " divided", "probability": 0.60986328125}, {"start": 3244.84, "end": 3245.08, "word": " by", "probability": 0.970703125}, {"start": 3245.08, "end": 3245.3, "word": " root", "probability": 0.8759765625}, {"start": 3245.3, "end": 3245.62, "word": " 20.", "probability": 0.9384765625}, {"start": 3246.58, "end": 3246.96, "word": " Now,", "probability": 0.95458984375}, {"start": 3247.24, "end": 3247.38, "word": " to", "probability": 0.96044921875}, {"start": 3247.38, "end": 3247.62, "word": " find", "probability": 0.89453125}, {"start": 3247.62, "end": 3248.02, "word": " T,", "probability": 0.99658203125}, {"start": 3249.18, "end": 3249.4, "word": " we", "probability": 0.9482421875}, {"start": 3249.4, "end": 3249.6, "word": " have", "probability": 0.94921875}, {"start": 3249.6, "end": 3249.74, "word": " to", "probability": 0.96435546875}, {"start": 3249.74, "end": 3250.12, "word": " use", "probability": 0.8740234375}, {"start": 3250.12, "end": 3252.7, "word": " 0", "probability": 0.9130859375}, {"start": 3252.7, "end": 3252.84, "word": " to", "probability": 0.84814453125}, {"start": 3252.84, "end": 3253.26, "word": " 5", "probability": 0.99267578125}, {"start": 3253.26, "end": 3254.76, "word": " and", "probability": 0.83154296875}, {"start": 3254.76, "end": 3255.18, "word": " 19.", "probability": 0.96337890625}], "temperature": 1.0}, {"id": 114, "seek": 328372, "start": 3256.2, "end": 3283.72, "text": " By this value here, you'll get the exact answer. Part number two. Given a sample mean of 2.1. So x bar is 2.1. Excuse me? Because n is small. Now, this sample,", "tokens": [3146, 341, 2158, 510, 11, 291, 603, 483, 264, 1900, 1867, 13, 4100, 1230, 732, 13, 18600, 257, 6889, 914, 295, 568, 13, 16, 13, 407, 2031, 2159, 307, 568, 13, 16, 13, 11359, 385, 30, 1436, 297, 307, 1359, 13, 823, 11, 341, 6889, 11], "avg_logprob": -0.3138297999158819, "compression_ratio": 1.2213740458015268, "no_speech_prob": 0.0, "words": [{"start": 3256.2, "end": 3256.52, "word": " By", "probability": 0.181396484375}, {"start": 3256.52, "end": 3256.76, "word": " this", "probability": 0.9169921875}, {"start": 3256.76, "end": 3257.02, "word": " value", "probability": 0.927734375}, {"start": 3257.02, "end": 3257.32, "word": " here,", "probability": 0.78466796875}, {"start": 3257.36, "end": 3257.56, "word": " you'll", "probability": 0.44140625}, {"start": 3257.56, "end": 3257.82, "word": " get", "probability": 0.94091796875}, {"start": 3257.82, "end": 3258.48, "word": " the", "probability": 0.81201171875}, {"start": 3258.48, "end": 3258.86, "word": " exact", "probability": 0.9365234375}, {"start": 3258.86, "end": 3259.32, "word": " answer.", "probability": 0.95556640625}, {"start": 3260.54, "end": 3261.3, "word": " Part", "probability": 0.5390625}, {"start": 3261.3, "end": 3261.84, "word": " number", "probability": 0.73583984375}, {"start": 3261.84, "end": 3262.16, "word": " two.", "probability": 0.50390625}, {"start": 3264.98, "end": 3265.48, "word": " Given", "probability": 0.53955078125}, {"start": 3265.48, "end": 3265.74, "word": " a", "probability": 0.9794921875}, {"start": 3265.74, "end": 3266.02, "word": " sample", "probability": 0.890625}, {"start": 3266.02, "end": 3266.42, "word": " mean", "probability": 0.9462890625}, {"start": 3266.42, "end": 3267.2, "word": " of", "probability": 0.96875}, {"start": 3267.2, "end": 3267.42, "word": " 2", "probability": 0.9296875}, {"start": 3267.42, "end": 3267.96, "word": ".1.", "probability": 0.9873046875}, {"start": 3269.98, "end": 3270.48, "word": " So", "probability": 0.77392578125}, {"start": 3270.48, "end": 3270.72, "word": " x", "probability": 0.7060546875}, {"start": 3270.72, "end": 3271.02, "word": " bar", "probability": 0.265869140625}, {"start": 3271.02, "end": 3271.72, "word": " is", "probability": 0.346923828125}, {"start": 3271.72, "end": 3271.92, "word": " 2", "probability": 0.9833984375}, {"start": 3271.92, "end": 3272.38, "word": ".1.", "probability": 0.997314453125}, {"start": 3273.68, "end": 3274.44, "word": " Excuse", "probability": 0.689453125}, {"start": 3274.44, "end": 3274.68, "word": " me?", "probability": 0.96240234375}, {"start": 3278.5, "end": 3279.26, "word": " Because", "probability": 0.85546875}, {"start": 3279.26, "end": 3279.52, "word": " n", "probability": 0.802734375}, {"start": 3279.52, "end": 3279.7, "word": " is", "probability": 0.953125}, {"start": 3279.7, "end": 3280.1, "word": " small.", "probability": 0.92236328125}, {"start": 3282.3, "end": 3282.74, "word": " Now,", "probability": 0.94873046875}, {"start": 3282.98, "end": 3283.24, "word": " this", "probability": 0.92529296875}, {"start": 3283.24, "end": 3283.72, "word": " sample,", "probability": 0.90576171875}], "temperature": 1.0}, {"id": 115, "seek": 331380, "start": 3285.0, "end": 3313.8, "text": " This sample gives an average of 4.85, and standard deviation based on this sample. So S, so X bar, 4.85, and S is equal to 1.47. So this is not sigma, because it says that 20 tests, so random sample is 20.", "tokens": [639, 6889, 2709, 364, 4274, 295, 1017, 13, 19287, 11, 293, 3832, 25163, 2361, 322, 341, 6889, 13, 407, 318, 11, 370, 1783, 2159, 11, 1017, 13, 19287, 11, 293, 318, 307, 2681, 281, 502, 13, 14060, 13, 407, 341, 307, 406, 12771, 11, 570, 309, 1619, 300, 945, 6921, 11, 370, 4974, 6889, 307, 945, 13], "avg_logprob": -0.2248114288367074, "compression_ratio": 1.4206896551724137, "no_speech_prob": 0.0, "words": [{"start": 3285.0, "end": 3285.42, "word": " This", "probability": 0.53955078125}, {"start": 3285.42, "end": 3285.92, "word": " sample", "probability": 0.794921875}, {"start": 3285.92, "end": 3287.44, "word": " gives", "probability": 0.7421875}, {"start": 3287.44, "end": 3287.72, "word": " an", "probability": 0.92431640625}, {"start": 3287.72, "end": 3288.12, "word": " average", "probability": 0.798828125}, {"start": 3288.12, "end": 3288.66, "word": " of", "probability": 0.96630859375}, {"start": 3288.66, "end": 3289.6, "word": " 4", "probability": 0.9658203125}, {"start": 3289.6, "end": 3290.1, "word": ".85,", "probability": 0.992431640625}, {"start": 3290.88, "end": 3291.2, "word": " and", "probability": 0.921875}, {"start": 3291.2, "end": 3291.64, "word": " standard", "probability": 0.69140625}, {"start": 3291.64, "end": 3292.22, "word": " deviation", "probability": 0.8984375}, {"start": 3292.22, "end": 3293.72, "word": " based", "probability": 0.7939453125}, {"start": 3293.72, "end": 3293.94, "word": " on", "probability": 0.947265625}, {"start": 3293.94, "end": 3294.2, "word": " this", "probability": 0.93896484375}, {"start": 3294.2, "end": 3294.52, "word": " sample.", "probability": 0.87890625}, {"start": 3295.12, "end": 3295.32, "word": " So", "probability": 0.95068359375}, {"start": 3295.32, "end": 3295.8, "word": " S,", "probability": 0.421875}, {"start": 3296.58, "end": 3298.62, "word": " so", "probability": 0.87060546875}, {"start": 3298.62, "end": 3298.88, "word": " X", "probability": 0.5400390625}, {"start": 3298.88, "end": 3299.18, "word": " bar,", "probability": 0.853515625}, {"start": 3299.82, "end": 3300.26, "word": " 4", "probability": 0.8056640625}, {"start": 3300.26, "end": 3300.52, "word": ".85,", "probability": 0.9189453125}, {"start": 3301.18, "end": 3302.06, "word": " and", "probability": 0.93505859375}, {"start": 3302.06, "end": 3302.42, "word": " S", "probability": 0.98193359375}, {"start": 3302.42, "end": 3302.74, "word": " is", "probability": 0.92333984375}, {"start": 3302.74, "end": 3303.14, "word": " equal", "probability": 0.89501953125}, {"start": 3303.14, "end": 3303.46, "word": " to", "probability": 0.96337890625}, {"start": 3303.46, "end": 3303.66, "word": " 1", "probability": 0.9853515625}, {"start": 3303.66, "end": 3304.18, "word": ".47.", "probability": 0.82080078125}, {"start": 3305.48, "end": 3306.28, "word": " So", "probability": 0.95849609375}, {"start": 3306.28, "end": 3306.46, "word": " this", "probability": 0.76611328125}, {"start": 3306.46, "end": 3306.56, "word": " is", "probability": 0.92041015625}, {"start": 3306.56, "end": 3306.72, "word": " not", "probability": 0.93896484375}, {"start": 3306.72, "end": 3307.02, "word": " sigma,", "probability": 0.82177734375}, {"start": 3308.78, "end": 3309.5, "word": " because", "probability": 0.8984375}, {"start": 3309.5, "end": 3309.64, "word": " it", "probability": 0.90771484375}, {"start": 3309.64, "end": 3309.88, "word": " says", "probability": 0.88037109375}, {"start": 3309.88, "end": 3310.22, "word": " that", "probability": 0.896484375}, {"start": 3310.22, "end": 3311.22, "word": " 20", "probability": 0.533203125}, {"start": 3311.22, "end": 3311.82, "word": " tests,", "probability": 0.8603515625}, {"start": 3312.28, "end": 3312.52, "word": " so", "probability": 0.939453125}, {"start": 3312.52, "end": 3312.88, "word": " random", "probability": 0.31982421875}, {"start": 3312.88, "end": 3313.22, "word": " sample", "probability": 0.91162109375}, {"start": 3313.22, "end": 3313.42, "word": " is", "probability": 0.93994140625}, {"start": 3313.42, "end": 3313.8, "word": " 20.", "probability": 0.95849609375}], "temperature": 1.0}, {"id": 116, "seek": 334363, "start": 3314.79, "end": 3343.63, "text": " This sample gives an average of this amount and standard deviation of this amount. We are looking for the continence interval, and we have two cases. First case, if sigma is known,", "tokens": [639, 6889, 2709, 364, 4274, 295, 341, 2372, 293, 3832, 25163, 295, 341, 2372, 13, 492, 366, 1237, 337, 264, 1421, 655, 15035, 11, 293, 321, 362, 732, 3331, 13, 2386, 1389, 11, 498, 12771, 307, 2570, 11], "avg_logprob": -0.19260817154859886, "compression_ratio": 1.4031007751937985, "no_speech_prob": 0.0, "words": [{"start": 3314.79, "end": 3315.21, "word": " This", "probability": 0.6689453125}, {"start": 3315.21, "end": 3315.55, "word": " sample", "probability": 0.83154296875}, {"start": 3315.55, "end": 3315.89, "word": " gives", "probability": 0.9033203125}, {"start": 3315.89, "end": 3316.13, "word": " an", "probability": 0.89404296875}, {"start": 3316.13, "end": 3316.49, "word": " average", "probability": 0.77978515625}, {"start": 3316.49, "end": 3316.93, "word": " of", "probability": 0.96484375}, {"start": 3316.93, "end": 3317.55, "word": " this", "probability": 0.9306640625}, {"start": 3317.55, "end": 3318.03, "word": " amount", "probability": 0.90771484375}, {"start": 3318.03, "end": 3319.39, "word": " and", "probability": 0.78076171875}, {"start": 3319.39, "end": 3319.89, "word": " standard", "probability": 0.81396484375}, {"start": 3319.89, "end": 3320.35, "word": " deviation", "probability": 0.91552734375}, {"start": 3320.35, "end": 3320.73, "word": " of", "probability": 0.96435546875}, {"start": 3320.73, "end": 3320.95, "word": " this", "probability": 0.9345703125}, {"start": 3320.95, "end": 3321.35, "word": " amount.", "probability": 0.89599609375}, {"start": 3329.71, "end": 3330.31, "word": " We", "probability": 0.87158203125}, {"start": 3330.31, "end": 3330.45, "word": " are", "probability": 0.8984375}, {"start": 3330.45, "end": 3330.71, "word": " looking", "probability": 0.9072265625}, {"start": 3330.71, "end": 3331.23, "word": " for", "probability": 0.95263671875}, {"start": 3331.23, "end": 3334.61, "word": " the", "probability": 0.86083984375}, {"start": 3334.61, "end": 3335.13, "word": " continence", "probability": 0.775634765625}, {"start": 3335.13, "end": 3335.59, "word": " interval,", "probability": 0.95458984375}, {"start": 3337.07, "end": 3337.33, "word": " and", "probability": 0.9140625}, {"start": 3337.33, "end": 3337.49, "word": " we", "probability": 0.9560546875}, {"start": 3337.49, "end": 3337.87, "word": " have", "probability": 0.94970703125}, {"start": 3337.87, "end": 3338.15, "word": " two", "probability": 0.85302734375}, {"start": 3338.15, "end": 3338.63, "word": " cases.", "probability": 0.89892578125}, {"start": 3339.97, "end": 3340.47, "word": " First", "probability": 0.81494140625}, {"start": 3340.47, "end": 3340.87, "word": " case,", "probability": 0.91845703125}, {"start": 3342.59, "end": 3342.85, "word": " if", "probability": 0.94873046875}, {"start": 3342.85, "end": 3343.15, "word": " sigma", "probability": 0.74951171875}, {"start": 3343.15, "end": 3343.39, "word": " is", "probability": 0.9404296875}, {"start": 3343.39, "end": 3343.63, "word": " known,", "probability": 0.40966796875}], "temperature": 1.0}, {"id": 117, "seek": 337640, "start": 3347.22, "end": 3376.4, "text": " Sigma is unknown. Now for this example, sigma is unknown. So since sigma is unknown, we have to use T distribution if the distribution is normal or if N is large enough. Now for this example, N is 20. 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So we have to use t. So my confidence interval should be x bar plus or minus 3s over root n. Now, number two. Given a sample mean of 2.1 and a population standard deviation. I mentioned that population standard deviation is given. So sigma is 0.7. 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Now, from a sample of 10 data points, we are looking for 90% confidence interval. 90% confidence interval will have a width of 2.36.", "tokens": [407, 294, 644, 732, 11, 12771, 307, 2212, 13, 823, 11, 490, 257, 6889, 295, 1266, 1412, 2793, 11, 321, 366, 1237, 337, 4289, 4, 6687, 15035, 13, 4289, 4, 6687, 15035, 486, 362, 257, 11402, 295, 568, 13, 11309, 13], "avg_logprob": -0.23251487740448543, "compression_ratio": 1.3306451612903225, "no_speech_prob": 0.0, "words": [{"start": 3405.37, "end": 3405.75, "word": " So", "probability": 0.261962890625}, {"start": 3405.75, "end": 3406.09, "word": " in", "probability": 0.268798828125}, {"start": 3406.09, "end": 3406.29, "word": " part", "probability": 0.7666015625}, {"start": 3406.29, "end": 3406.59, "word": " two,", "probability": 0.4609375}, {"start": 3406.83, "end": 3407.01, "word": " sigma", "probability": 0.5634765625}, {"start": 3407.01, "end": 3407.17, "word": " is", "probability": 0.9130859375}, {"start": 3407.17, "end": 3407.33, "word": " given.", "probability": 0.88916015625}, {"start": 3408.27, "end": 3408.93, "word": " Now,", "probability": 0.8251953125}, {"start": 3408.99, "end": 3409.17, "word": " from", "probability": 0.8818359375}, {"start": 3409.17, "end": 3409.35, "word": " a", "probability": 0.9765625}, {"start": 3409.35, "end": 3409.57, "word": " sample", "probability": 0.85986328125}, {"start": 3409.57, "end": 3409.79, "word": " of", "probability": 0.97021484375}, {"start": 3409.79, "end": 3410.13, "word": " 10", "probability": 0.708984375}, {"start": 3410.13, "end": 3410.57, "word": " data", "probability": 0.94775390625}, {"start": 3410.57, "end": 3410.89, "word": " points,", "probability": 0.9013671875}, {"start": 3413.73, "end": 3414.03, "word": " we", "probability": 0.93701171875}, {"start": 3414.03, "end": 3414.15, "word": " are", "probability": 0.91162109375}, {"start": 3414.15, "end": 3414.39, "word": " looking", "probability": 0.92236328125}, {"start": 3414.39, "end": 3414.61, "word": " for", "probability": 0.94140625}, {"start": 3414.61, "end": 3414.91, "word": " 90", "probability": 0.9013671875}, {"start": 3414.91, "end": 3415.19, "word": "%", "probability": 0.83056640625}, {"start": 3415.19, "end": 3415.71, "word": " confidence", "probability": 0.96435546875}, {"start": 3415.71, "end": 3416.19, "word": " interval.", "probability": 0.8583984375}, {"start": 3418.79, "end": 3419.45, "word": " 90", "probability": 0.939453125}, {"start": 3419.45, "end": 3420.07, "word": "%", "probability": 0.99169921875}, {"start": 3420.07, "end": 3422.03, "word": " confidence", "probability": 0.9716796875}, {"start": 3422.03, "end": 3422.57, "word": " interval", "probability": 0.96337890625}, {"start": 3422.57, "end": 3423.15, "word": " will", "probability": 0.83740234375}, {"start": 3423.15, "end": 3423.49, "word": " have", "probability": 0.9423828125}, {"start": 3423.49, "end": 3423.69, "word": " a", "probability": 0.9873046875}, {"start": 3423.69, "end": 3423.95, "word": " width", "probability": 0.96484375}, {"start": 3423.95, "end": 3425.63, "word": " of", "probability": 0.96728515625}, {"start": 3425.63, "end": 3426.49, "word": " 2", "probability": 0.95361328125}, {"start": 3426.49, "end": 3427.23, "word": ".36.", "probability": 0.981201171875}], "temperature": 1.0}, {"id": 120, "seek": 345412, "start": 3436.46, "end": 3454.12, "text": " What is two times the assembling error? So the answer is given. So the error here, error A equals W. So the answer is 1.16.", "tokens": [708, 307, 732, 1413, 264, 43867, 6713, 30, 407, 264, 1867, 307, 2212, 13, 407, 264, 6713, 510, 11, 6713, 316, 6915, 343, 13, 407, 264, 1867, 307, 502, 13, 6866, 13], "avg_logprob": -0.2821969696969697, "compression_ratio": 1.3333333333333333, "no_speech_prob": 0.0, "words": [{"start": 3436.46, "end": 3436.9, "word": " What", "probability": 0.1990966796875}, {"start": 3436.9, "end": 3437.16, "word": " is", "probability": 0.880859375}, {"start": 3437.16, "end": 3437.56, "word": " two", "probability": 0.64111328125}, {"start": 3437.56, "end": 3437.92, "word": " times", "probability": 0.92529296875}, {"start": 3437.92, "end": 3438.36, "word": " the", "probability": 0.8798828125}, {"start": 3438.36, "end": 3438.88, "word": " assembling", "probability": 0.40380859375}, {"start": 3438.88, "end": 3439.18, "word": " error?", "probability": 0.89111328125}, {"start": 3442.5, "end": 3442.86, "word": " So", "probability": 0.65576171875}, {"start": 3442.86, "end": 3442.98, "word": " the", "probability": 0.357177734375}, {"start": 3442.98, "end": 3443.16, "word": " answer", "probability": 0.8408203125}, {"start": 3443.16, "end": 3443.32, "word": " is", "probability": 0.76708984375}, {"start": 3443.32, "end": 3443.5, "word": " given.", "probability": 0.89501953125}, {"start": 3445.32, "end": 3446.04, "word": " So", "probability": 0.912109375}, {"start": 3446.04, "end": 3446.28, "word": " the", "probability": 0.7265625}, {"start": 3446.28, "end": 3446.5, "word": " error", "probability": 0.86767578125}, {"start": 3446.5, "end": 3446.84, "word": " here,", "probability": 0.62158203125}, {"start": 3447.48, "end": 3447.78, "word": " error", "probability": 0.87451171875}, {"start": 3447.78, "end": 3448.04, "word": " A", "probability": 0.642578125}, {"start": 3448.04, "end": 3448.6, "word": " equals", "probability": 0.78955078125}, {"start": 3448.6, "end": 3450.16, "word": " W.", "probability": 0.408447265625}, {"start": 3452.06, "end": 3452.66, "word": " So", "probability": 0.94384765625}, {"start": 3452.66, "end": 3452.82, "word": " the", "probability": 0.8984375}, {"start": 3452.82, "end": 3453.02, "word": " answer", "probability": 0.96142578125}, {"start": 3453.02, "end": 3453.2, "word": " is", "probability": 0.93896484375}, {"start": 3453.2, "end": 3453.42, "word": " 1", "probability": 0.94677734375}, {"start": 3453.42, "end": 3454.12, "word": ".16.", "probability": 0.990966796875}], "temperature": 1.0}, {"id": 121, "seek": 348866, "start": 3460.52, "end": 3488.66, "text": " So he asked about given a sample, 90% confidence interval will have a width of 2.36. Let's see if the exact width is 2.36 or not. Now we have x bar plus or minus z, sigma 1.8. x bar is 2.1, plus or minus. 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given to be 2.36. So E is 1.18. So that saves time in order to compute the error term. So now 2.1 minus 1.8. 2.1 plus 1.8. That F, the width, is 2.36.", "tokens": [583, 291, 500, 380, 643, 281, 360, 300, 570, 264, 11402, 307, 2212, 281, 312, 568, 13, 11309, 13, 407, 462, 307, 502, 13, 6494, 13, 407, 300, 19155, 565, 294, 1668, 281, 14722, 264, 6713, 1433, 13, 407, 586, 568, 13, 16, 3175, 502, 13, 23, 13, 568, 13, 16, 1804, 502, 13, 23, 13, 663, 479, 11, 264, 11402, 11, 307, 568, 13, 11309, 13], "avg_logprob": -0.1500459499657154, "compression_ratio": 1.4125874125874125, "no_speech_prob": 0.0, "words": [{"start": 3514.01, "end": 3514.31, "word": " But", "probability": 0.818359375}, {"start": 3514.31, "end": 3514.47, "word": " you", "probability": 0.560546875}, {"start": 3514.47, "end": 3514.67, "word": " don't", "probability": 0.974365234375}, {"start": 3514.67, "end": 3514.91, "word": " need", "probability": 0.92578125}, {"start": 3514.91, "end": 3515.07, "word": " to", "probability": 0.96826171875}, {"start": 3515.07, "end": 3515.21, "word": " do", "probability": 0.9521484375}, {"start": 3515.21, "end": 3515.43, "word": " that", "probability": 0.93896484375}, {"start": 3515.43, "end": 3515.77, "word": " because", "probability": 0.61328125}, {"start": 3515.77, "end": 3515.97, "word": " the", "probability": 0.9033203125}, {"start": 3515.97, "end": 3516.19, "word": " width", "probability": 0.96435546875}, {"start": 3516.19, "end": 3516.37, "word": " is", "probability": 0.92236328125}, {"start": 3516.37, "end": 3516.69, "word": " given", "probability": 0.90234375}, {"start": 3516.69, "end": 3517.51, "word": " to", "probability": 0.95654296875}, {"start": 3517.51, "end": 3517.65, "word": " be", "probability": 0.9443359375}, {"start": 3517.65, "end": 3517.83, "word": " 2", "probability": 0.97412109375}, {"start": 3517.83, "end": 3518.41, "word": ".36.", "probability": 0.994384765625}, {"start": 3519.25, "end": 3519.75, "word": " So", "probability": 0.95654296875}, {"start": 3519.75, "end": 3520.11, "word": " E", "probability": 0.63916015625}, {"start": 3520.11, "end": 3520.37, "word": " is", "probability": 0.90966796875}, {"start": 3520.37, "end": 3520.57, "word": " 1", "probability": 0.96826171875}, {"start": 3520.57, "end": 3521.09, "word": ".18.", "probability": 0.9375}, {"start": 3522.79, "end": 3523.39, "word": " So", "probability": 0.9404296875}, {"start": 3523.39, "end": 3523.63, "word": " that", "probability": 0.8603515625}, {"start": 3523.63, "end": 3523.91, "word": " saves", "probability": 0.36376953125}, {"start": 3523.91, "end": 3524.33, "word": " time", "probability": 0.8857421875}, {"start": 3524.33, "end": 3524.57, "word": " in", "probability": 0.78564453125}, {"start": 3524.57, "end": 3524.73, "word": " order", "probability": 0.90185546875}, {"start": 3524.73, "end": 3524.95, "word": " to", "probability": 0.96728515625}, {"start": 3524.95, "end": 3525.43, "word": " compute", "probability": 0.880859375}, {"start": 3525.43, "end": 3526.43, "word": " the", "probability": 0.87939453125}, {"start": 3526.43, "end": 3526.65, "word": " error", "probability": 0.6923828125}, {"start": 3526.65, "end": 3526.99, "word": " term.", "probability": 0.64892578125}, {"start": 3527.23, "end": 3527.39, "word": " So", "probability": 0.95556640625}, {"start": 3527.39, "end": 3527.67, "word": " now", "probability": 0.89404296875}, {"start": 3527.67, "end": 3527.93, "word": " 2", "probability": 0.66796875}, {"start": 3527.93, "end": 3528.45, "word": ".1", "probability": 0.993896484375}, {"start": 3528.45, "end": 3530.59, "word": " minus", "probability": 0.8984375}, {"start": 3530.59, "end": 3530.87, "word": " 1", "probability": 0.98876953125}, {"start": 3530.87, "end": 3531.51, "word": ".8.", "probability": 0.979736328125}, {"start": 3532.59, "end": 3533.07, "word": " 2", "probability": 0.9345703125}, {"start": 3533.07, "end": 3533.67, "word": ".1", "probability": 0.99560546875}, {"start": 3533.67, "end": 3534.49, "word": " plus", "probability": 0.93017578125}, {"start": 3534.49, "end": 3534.79, "word": " 1", "probability": 0.95263671875}, {"start": 3534.79, "end": 3535.19, "word": ".8.", "probability": 0.978271484375}, {"start": 3536.35, "end": 3536.71, "word": " That", "probability": 0.64794921875}, {"start": 3536.71, "end": 3537.03, "word": " F,", "probability": 0.38134765625}, {"start": 3537.15, "end": 3537.29, "word": " the", "probability": 0.91455078125}, {"start": 3537.29, "end": 3537.59, "word": " width,", "probability": 0.95947265625}, {"start": 3537.75, "end": 3538.21, "word": " is", "probability": 0.94580078125}, {"start": 3538.21, "end": 3538.55, "word": " 2", "probability": 0.9990234375}, {"start": 3538.55, "end": 3539.07, "word": ".36.", "probability": 0.998291015625}], "temperature": 1.0}, {"id": 124, "seek": 356823, "start": 3542.01, "end": 3568.23, "text": " that if the width equals this value. 2.36. So I solved the problem if the width. But he asked about, do you know this value? I don't know that one, so we have to compute the exact answer now. So x bar 2.1 plus 1645 sigma", "tokens": [300, 498, 264, 11402, 6915, 341, 2158, 13, 568, 13, 11309, 13, 407, 286, 13041, 264, 1154, 498, 264, 11402, 13, 583, 415, 2351, 466, 11, 360, 291, 458, 341, 2158, 30, 286, 500, 380, 458, 300, 472, 11, 370, 321, 362, 281, 14722, 264, 1900, 1867, 586, 13, 407, 2031, 2159, 568, 13, 16, 1804, 3165, 8465, 12771], "avg_logprob": -0.24049478769302368, "compression_ratio": 1.389937106918239, "no_speech_prob": 0.0, "words": [{"start": 3542.01, "end": 3542.41, "word": " that", "probability": 0.412353515625}, {"start": 3542.41, "end": 3542.73, "word": " if", "probability": 0.84716796875}, {"start": 3542.73, "end": 3542.95, "word": " the", "probability": 0.89697265625}, {"start": 3542.95, "end": 3543.19, "word": " width", "probability": 0.904296875}, {"start": 3543.19, "end": 3543.59, "word": " equals", "probability": 0.74365234375}, {"start": 3543.59, "end": 3543.83, "word": " this", "probability": 0.90966796875}, {"start": 3543.83, "end": 3544.17, "word": " value.", "probability": 0.9404296875}, {"start": 3550.41, "end": 3550.57, "word": " 2", "probability": 0.39111328125}, {"start": 3550.57, "end": 3551.07, "word": ".36.", "probability": 0.980712890625}, {"start": 3551.75, "end": 3552.29, "word": " So", "probability": 0.56884765625}, {"start": 3552.29, "end": 3552.75, "word": " I", "probability": 0.763671875}, {"start": 3552.75, "end": 3553.03, "word": " solved", "probability": 0.60546875}, {"start": 3553.03, "end": 3553.15, "word": " the", "probability": 0.89501953125}, {"start": 3553.15, "end": 3553.45, "word": " problem", "probability": 0.8662109375}, {"start": 3553.45, "end": 3553.85, "word": " if", "probability": 0.474365234375}, {"start": 3553.85, "end": 3554.01, "word": " the", "probability": 0.8720703125}, {"start": 3554.01, "end": 3554.27, "word": " width.", "probability": 0.95751953125}, {"start": 3554.91, "end": 3555.13, "word": " But", "probability": 0.90380859375}, {"start": 3555.13, "end": 3555.27, "word": " he", "probability": 0.8759765625}, {"start": 3555.27, "end": 3555.45, "word": " asked", "probability": 0.67724609375}, {"start": 3555.45, "end": 3555.79, "word": " about,", "probability": 0.865234375}, {"start": 3556.39, "end": 3556.91, "word": " do", "probability": 0.468017578125}, {"start": 3556.91, "end": 3556.99, "word": " you", "probability": 0.9638671875}, {"start": 3556.99, "end": 3557.13, "word": " know", "probability": 0.884765625}, {"start": 3557.13, "end": 3557.35, "word": " this", "probability": 0.8935546875}, {"start": 3557.35, "end": 3557.69, "word": " value?", "probability": 0.974609375}, {"start": 3557.81, "end": 3557.87, "word": " I", "probability": 0.970703125}, {"start": 3557.87, "end": 3558.25, "word": " don't", "probability": 0.975341796875}, {"start": 3558.25, "end": 3558.43, "word": " know", "probability": 0.892578125}, {"start": 3558.43, "end": 3558.63, "word": " that", "probability": 0.93603515625}, {"start": 3558.63, "end": 3558.83, "word": " one,", "probability": 0.912109375}, {"start": 3558.91, "end": 3559.01, "word": " so", "probability": 0.93994140625}, {"start": 3559.01, "end": 3559.17, "word": " we", "probability": 0.93798828125}, {"start": 3559.17, "end": 3559.37, "word": " have", "probability": 0.87060546875}, {"start": 3559.37, "end": 3559.85, "word": " to", "probability": 0.9658203125}, {"start": 3559.85, "end": 3560.27, "word": " compute", "probability": 0.94189453125}, {"start": 3560.27, "end": 3560.47, "word": " the", "probability": 0.892578125}, {"start": 3560.47, "end": 3560.87, "word": " exact", "probability": 0.93212890625}, {"start": 3560.87, "end": 3561.23, "word": " answer", "probability": 0.9482421875}, {"start": 3561.23, "end": 3561.51, "word": " now.", "probability": 0.89404296875}, {"start": 3562.35, "end": 3562.55, "word": " So", "probability": 0.94677734375}, {"start": 3562.55, "end": 3562.79, "word": " x", "probability": 0.68310546875}, {"start": 3562.79, "end": 3563.09, "word": " bar", "probability": 0.75830078125}, {"start": 3563.09, "end": 3564.07, "word": " 2", "probability": 0.4208984375}, {"start": 3564.07, "end": 3564.61, "word": ".1", "probability": 0.971923828125}, {"start": 3564.61, "end": 3565.63, "word": " plus", "probability": 0.873046875}, {"start": 3565.63, "end": 3566.69, "word": " 1645", "probability": 0.80810546875}, {"start": 3566.69, "end": 3568.23, "word": " sigma", "probability": 0.67333984375}], "temperature": 1.0}, {"id": 125, "seek": 360068, "start": 3574.48, "end": 3600.68, "text": " My calculator can find the error now. What's the value for this amount? My calculator. It's 5.75. 5.75. So this is your error. So E equals this amount.", "tokens": [1222, 24993, 393, 915, 264, 6713, 586, 13, 708, 311, 264, 2158, 337, 341, 2372, 30, 1222, 24993, 13, 467, 311, 1025, 13, 11901, 13, 1025, 13, 11901, 13, 407, 341, 307, 428, 6713, 13, 407, 462, 6915, 341, 2372, 13], "avg_logprob": -0.27418153342746554, "compression_ratio": 1.345132743362832, "no_speech_prob": 0.0, "words": [{"start": 3574.48, "end": 3574.8, "word": " My", "probability": 0.1298828125}, {"start": 3574.8, "end": 3575.28, "word": " calculator", "probability": 0.82275390625}, {"start": 3575.28, "end": 3575.56, "word": " can", "probability": 0.81298828125}, {"start": 3575.56, "end": 3575.9, "word": " find", "probability": 0.869140625}, {"start": 3575.9, "end": 3576.2, "word": " the", "probability": 0.67626953125}, {"start": 3576.2, "end": 3576.48, "word": " error", "probability": 0.8662109375}, {"start": 3576.48, "end": 3576.92, "word": " now.", "probability": 0.744140625}, {"start": 3577.84, "end": 3578.48, "word": " What's", "probability": 0.745849609375}, {"start": 3578.48, "end": 3578.6, "word": " the", "probability": 0.9208984375}, {"start": 3578.6, "end": 3578.74, "word": " value", "probability": 0.96923828125}, {"start": 3578.74, "end": 3578.96, "word": " for", "probability": 0.82080078125}, {"start": 3578.96, "end": 3579.12, "word": " this", "probability": 0.94580078125}, {"start": 3579.12, "end": 3579.44, "word": " amount?", "probability": 0.90478515625}, {"start": 3580.66, "end": 3580.86, "word": " My", "probability": 0.75439453125}, {"start": 3580.86, "end": 3581.26, "word": " calculator.", "probability": 0.94580078125}, {"start": 3590.7, "end": 3591.34, "word": " It's", "probability": 0.624755859375}, {"start": 3591.34, "end": 3591.78, "word": " 5", "probability": 0.4765625}, {"start": 3591.78, "end": 3593.02, "word": ".75.", "probability": 0.7255859375}, {"start": 3593.66, "end": 3594.3, "word": " 5", "probability": 0.6728515625}, {"start": 3594.3, "end": 3596.44, "word": ".75.", "probability": 0.87548828125}, {"start": 3597.64, "end": 3598.28, "word": " So", "probability": 0.9228515625}, {"start": 3598.28, "end": 3598.54, "word": " this", "probability": 0.8466796875}, {"start": 3598.54, "end": 3598.66, "word": " is", "probability": 0.93896484375}, {"start": 3598.66, "end": 3598.84, "word": " your", "probability": 0.90673828125}, {"start": 3598.84, "end": 3599.1, "word": " error.", "probability": 0.89794921875}, {"start": 3599.42, "end": 3599.64, "word": " So", "probability": 0.80126953125}, {"start": 3599.64, "end": 3599.82, "word": " E", "probability": 0.7314453125}, {"start": 3599.82, "end": 3600.16, "word": " equals", "probability": 0.7275390625}, {"start": 3600.16, "end": 3600.44, "word": " this", "probability": 0.9267578125}, {"start": 3600.44, "end": 3600.68, "word": " amount.", "probability": 0.904296875}], "temperature": 1.0}, {"id": 126, "seek": 362657, "start": 3601.55, "end": 3626.57, "text": " So W equals 2 plus 4. So the error is 5.74. So what's the width? The width equals 2 times E. Again.", "tokens": [407, 343, 6915, 568, 1804, 1017, 13, 407, 264, 6713, 307, 1025, 13, 34026, 13, 407, 437, 311, 264, 11402, 30, 440, 11402, 6915, 568, 1413, 462, 13, 3764, 13], "avg_logprob": -0.23450100614178565, "compression_ratio": 1.1764705882352942, "no_speech_prob": 0.0, "words": [{"start": 3601.55, "end": 3601.83, "word": " So", "probability": 0.90234375}, {"start": 3601.83, "end": 3602.25, "word": " W", "probability": 0.466552734375}, {"start": 3602.25, "end": 3603.81, "word": " equals", "probability": 0.21630859375}, {"start": 3603.81, "end": 3604.53, "word": " 2", "probability": 0.41650390625}, {"start": 3604.53, "end": 3605.07, "word": " plus", "probability": 0.76513671875}, {"start": 3605.07, "end": 3605.37, "word": " 4.", "probability": 0.73828125}, {"start": 3608.35, "end": 3609.33, "word": " So", "probability": 0.8681640625}, {"start": 3609.33, "end": 3609.47, "word": " the", "probability": 0.79296875}, {"start": 3609.47, "end": 3609.77, "word": " error", "probability": 0.8935546875}, {"start": 3609.77, "end": 3611.83, "word": " is", "probability": 0.92041015625}, {"start": 3611.83, "end": 3612.27, "word": " 5", "probability": 0.96240234375}, {"start": 3612.27, "end": 3613.41, "word": ".74.", "probability": 0.97998046875}, {"start": 3614.11, "end": 3614.49, "word": " So", "probability": 0.8623046875}, {"start": 3614.49, "end": 3614.71, "word": " what's", "probability": 0.883056640625}, {"start": 3614.71, "end": 3614.85, "word": " the", "probability": 0.89404296875}, {"start": 3614.85, "end": 3615.03, "word": " width?", "probability": 0.74951171875}, {"start": 3616.07, "end": 3617.05, "word": " The", "probability": 0.86669921875}, {"start": 3617.05, "end": 3617.37, "word": " width", "probability": 0.962890625}, {"start": 3617.37, "end": 3618.25, "word": " equals", "probability": 0.84912109375}, {"start": 3618.25, "end": 3619.57, "word": " 2", "probability": 0.8916015625}, {"start": 3619.57, "end": 3619.93, "word": " times", "probability": 0.90869140625}, {"start": 3619.93, "end": 3620.21, "word": " E.", "probability": 0.673828125}, {"start": 3625.59, "end": 3626.57, "word": " Again.", "probability": 0.9287109375}], "temperature": 1.0}, {"id": 127, "seek": 365354, "start": 3627.06, "end": 3653.54, "text": " This value, 1.645 times 1.7 divided by root 10. Three point. So again, arrow is 3.64. So what's the width? Twice this value, so two times this one.", "tokens": [639, 2158, 11, 502, 13, 21, 8465, 1413, 502, 13, 22, 6666, 538, 5593, 1266, 13, 6244, 935, 13, 407, 797, 11, 11610, 307, 805, 13, 19395, 13, 407, 437, 311, 264, 11402, 30, 46964, 341, 2158, 11, 370, 732, 1413, 341, 472, 13], "avg_logprob": -0.2875000026490953, "compression_ratio": 1.2436974789915967, "no_speech_prob": 0.0, "words": [{"start": 3627.06, "end": 3627.48, "word": " This", "probability": 0.38720703125}, {"start": 3627.48, "end": 3627.76, "word": " value,", "probability": 0.888671875}, {"start": 3627.82, "end": 3628.0, "word": " 1", "probability": 0.896484375}, {"start": 3628.0, "end": 3628.7, "word": ".645", "probability": 0.9376627604166666}, {"start": 3628.7, "end": 3629.18, "word": " times", "probability": 0.47509765625}, {"start": 3629.18, "end": 3629.42, "word": " 1", "probability": 0.380126953125}, {"start": 3629.42, "end": 3629.66, "word": ".7", "probability": 0.951416015625}, {"start": 3629.66, "end": 3629.94, "word": " divided", "probability": 0.58984375}, {"start": 3629.94, "end": 3630.12, "word": " by", "probability": 0.9736328125}, {"start": 3630.12, "end": 3630.34, "word": " root", "probability": 0.8955078125}, {"start": 3630.34, "end": 3630.58, "word": " 10.", "probability": 0.8486328125}, {"start": 3637.28, "end": 3637.88, "word": " Three", "probability": 0.263916015625}, {"start": 3637.88, "end": 3638.28, "word": " point.", "probability": 0.83251953125}, {"start": 3644.02, "end": 3644.62, "word": " So", "probability": 0.74267578125}, {"start": 3644.62, "end": 3645.18, "word": " again,", "probability": 0.78369140625}, {"start": 3645.54, "end": 3645.9, "word": " arrow", "probability": 0.384521484375}, {"start": 3645.9, "end": 3646.4, "word": " is", "probability": 0.90576171875}, {"start": 3646.4, "end": 3646.78, "word": " 3", "probability": 0.91357421875}, {"start": 3646.78, "end": 3647.62, "word": ".64.", "probability": 0.982421875}, {"start": 3648.94, "end": 3649.18, "word": " So", "probability": 0.64453125}, {"start": 3649.18, "end": 3649.38, "word": " what's", "probability": 0.895263671875}, {"start": 3649.38, "end": 3649.5, "word": " the", "probability": 0.92431640625}, {"start": 3649.5, "end": 3649.7, "word": " width?", "probability": 0.8564453125}, {"start": 3651.16, "end": 3651.76, "word": " Twice", "probability": 0.9658203125}, {"start": 3651.76, "end": 3652.04, "word": " this", "probability": 0.9130859375}, {"start": 3652.04, "end": 3652.34, "word": " value,", "probability": 0.95947265625}, {"start": 3652.44, "end": 3652.58, "word": " so", "probability": 0.884765625}, {"start": 3652.58, "end": 3652.78, "word": " two", "probability": 0.693359375}, {"start": 3652.78, "end": 3653.1, "word": " times", "probability": 0.93359375}, {"start": 3653.1, "end": 3653.32, "word": " this", "probability": 0.7109375}, {"start": 3653.32, "end": 3653.54, "word": " one.", "probability": 0.9150390625}], "temperature": 1.0}, {"id": 128, "seek": 368390, "start": 3657.88, "end": 3683.9, "text": " 7.28. Now it says in the problem here we have width of 2.36. So it's incorrect. So just simple calculation gives width of 7.28, not 2.36. Number three.", "tokens": [1614, 13, 11205, 13, 823, 309, 1619, 294, 264, 1154, 510, 321, 362, 11402, 295, 568, 13, 11309, 13, 407, 309, 311, 18424, 13, 407, 445, 2199, 17108, 2709, 11402, 295, 1614, 13, 11205, 11, 406, 568, 13, 11309, 13, 5118, 1045, 13], "avg_logprob": -0.2560369446873665, "compression_ratio": 1.2258064516129032, "no_speech_prob": 0.0, "words": [{"start": 3657.8799999999997, "end": 3658.72, "word": " 7", "probability": 0.391845703125}, {"start": 3658.72, "end": 3659.56, "word": ".28.", "probability": 0.89208984375}, {"start": 3662.12, "end": 3662.96, "word": " Now", "probability": 0.8056640625}, {"start": 3662.96, "end": 3663.18, "word": " it", "probability": 0.515625}, {"start": 3663.18, "end": 3663.42, "word": " says", "probability": 0.7900390625}, {"start": 3663.42, "end": 3663.98, "word": " in", "probability": 0.57763671875}, {"start": 3663.98, "end": 3664.1, "word": " the", "probability": 0.90380859375}, {"start": 3664.1, "end": 3664.4, "word": " problem", "probability": 0.91650390625}, {"start": 3664.4, "end": 3664.66, "word": " here", "probability": 0.80078125}, {"start": 3664.66, "end": 3664.84, "word": " we", "probability": 0.52734375}, {"start": 3664.84, "end": 3665.06, "word": " have", "probability": 0.947265625}, {"start": 3665.06, "end": 3665.4, "word": " width", "probability": 0.78955078125}, {"start": 3665.4, "end": 3665.82, "word": " of", "probability": 0.97119140625}, {"start": 3665.82, "end": 3667.18, "word": " 2", "probability": 0.363037109375}, {"start": 3667.18, "end": 3667.86, "word": ".36.", "probability": 0.962646484375}, {"start": 3668.16, "end": 3668.5, "word": " So", "probability": 0.92919921875}, {"start": 3668.5, "end": 3668.78, "word": " it's", "probability": 0.840576171875}, {"start": 3668.78, "end": 3669.2, "word": " incorrect.", "probability": 0.90478515625}, {"start": 3671.84, "end": 3672.18, "word": " So", "probability": 0.8828125}, {"start": 3672.18, "end": 3672.52, "word": " just", "probability": 0.818359375}, {"start": 3672.52, "end": 3672.96, "word": " simple", "probability": 0.70849609375}, {"start": 3672.96, "end": 3673.56, "word": " calculation", "probability": 0.912109375}, {"start": 3673.56, "end": 3673.98, "word": " gives", "probability": 0.8212890625}, {"start": 3673.98, "end": 3674.44, "word": " width", "probability": 0.916015625}, {"start": 3674.44, "end": 3674.9, "word": " of", "probability": 0.966796875}, {"start": 3674.9, "end": 3675.36, "word": " 7", "probability": 0.96533203125}, {"start": 3675.36, "end": 3676.32, "word": ".28,", "probability": 0.99169921875}, {"start": 3677.18, "end": 3677.54, "word": " not", "probability": 0.9052734375}, {"start": 3677.54, "end": 3679.94, "word": " 2", "probability": 0.69189453125}, {"start": 3679.94, "end": 3681.2, "word": ".36.", "probability": 0.99462890625}, {"start": 3682.72, "end": 3683.56, "word": " Number", "probability": 0.8583984375}, {"start": 3683.56, "end": 3683.9, "word": " three.", "probability": 0.517578125}], "temperature": 1.0}, {"id": 129, "seek": 371379, "start": 3687.95, "end": 3713.79, "text": " Look at number four. Other things be equal. As the confidence level for a confidence interval increases, the width of the interval increases. As the confidence level increases, confidence interval increases, the width of the interval increases. Correct. So that's true. Let's do number seven.", "tokens": [2053, 412, 1230, 1451, 13, 5358, 721, 312, 2681, 13, 1018, 264, 6687, 1496, 337, 257, 6687, 15035, 8637, 11, 264, 11402, 295, 264, 15035, 8637, 13, 1018, 264, 6687, 1496, 8637, 11, 6687, 15035, 8637, 11, 264, 11402, 295, 264, 15035, 8637, 13, 12753, 13, 407, 300, 311, 2074, 13, 961, 311, 360, 1230, 3407, 13], "avg_logprob": -0.14345365839785543, "compression_ratio": 2.092857142857143, "no_speech_prob": 0.0, "words": [{"start": 3687.95, "end": 3688.17, "word": " Look", "probability": 0.689453125}, {"start": 3688.17, "end": 3688.31, "word": " at", "probability": 0.96337890625}, {"start": 3688.31, "end": 3688.51, "word": " number", "probability": 0.7998046875}, {"start": 3688.51, "end": 3688.89, "word": " four.", "probability": 0.63427734375}, {"start": 3689.51, "end": 3689.75, "word": " Other", "probability": 0.56494140625}, {"start": 3689.75, "end": 3690.19, "word": " things", "probability": 0.8662109375}, {"start": 3690.19, "end": 3690.41, "word": " be", "probability": 0.84423828125}, {"start": 3690.41, "end": 3690.77, "word": " equal.", "probability": 0.8740234375}, {"start": 3692.39, "end": 3692.69, "word": " As", "probability": 0.96240234375}, {"start": 3692.69, "end": 3692.85, "word": " the", "probability": 0.90283203125}, {"start": 3692.85, "end": 3693.31, "word": " confidence", "probability": 0.966796875}, {"start": 3693.31, "end": 3693.65, "word": " level", "probability": 0.90966796875}, {"start": 3693.65, "end": 3694.51, "word": " for", "probability": 0.8955078125}, {"start": 3694.51, "end": 3694.71, "word": " a", "probability": 0.9228515625}, {"start": 3694.71, "end": 3695.11, "word": " confidence", "probability": 0.97705078125}, {"start": 3695.11, "end": 3695.55, "word": " interval", "probability": 0.958984375}, {"start": 3695.55, "end": 3696.07, "word": " increases,", "probability": 0.92236328125}, {"start": 3696.73, "end": 3697.25, "word": " the", "probability": 0.92041015625}, {"start": 3697.25, "end": 3697.55, "word": " width", "probability": 0.6669921875}, {"start": 3697.55, "end": 3697.81, "word": " of", "probability": 0.96826171875}, {"start": 3697.81, "end": 3697.97, "word": " the", "probability": 0.91162109375}, {"start": 3697.97, "end": 3698.33, "word": " interval", "probability": 0.98388671875}, {"start": 3698.33, "end": 3698.93, "word": " increases.", "probability": 0.92236328125}, {"start": 3700.57, "end": 3701.25, "word": " As", "probability": 0.9384765625}, {"start": 3701.25, "end": 3701.41, "word": " the", "probability": 0.90576171875}, {"start": 3701.41, "end": 3701.77, "word": " confidence", "probability": 0.9765625}, {"start": 3701.77, "end": 3702.11, "word": " level", "probability": 0.806640625}, {"start": 3702.11, "end": 3702.63, "word": " increases,", "probability": 0.7822265625}, {"start": 3702.85, "end": 3705.31, "word": " confidence", "probability": 0.3291015625}, {"start": 3705.31, "end": 3705.77, "word": " interval", "probability": 0.95263671875}, {"start": 3705.77, "end": 3706.29, "word": " increases,", "probability": 0.923828125}, {"start": 3706.67, "end": 3706.83, "word": " the", "probability": 0.9150390625}, {"start": 3706.83, "end": 3707.09, "word": " width", "probability": 0.9736328125}, {"start": 3707.09, "end": 3707.25, "word": " of", "probability": 0.958984375}, {"start": 3707.25, "end": 3707.37, "word": " the", "probability": 0.828125}, {"start": 3707.37, "end": 3707.65, "word": " interval", "probability": 0.9892578125}, {"start": 3707.65, "end": 3708.09, "word": " increases.", "probability": 0.89453125}, {"start": 3708.35, "end": 3708.53, "word": " Correct.", "probability": 0.7294921875}, {"start": 3709.67, "end": 3709.93, "word": " So", "probability": 0.9287109375}, {"start": 3709.93, "end": 3710.17, "word": " that's", "probability": 0.912841796875}, {"start": 3710.17, "end": 3710.41, "word": " true.", "probability": 0.95654296875}, {"start": 3711.77, "end": 3712.45, "word": " Let's", "probability": 0.972412109375}, {"start": 3712.45, "end": 3712.75, "word": " do", "probability": 0.958984375}, {"start": 3712.75, "end": 3713.49, "word": " number", "probability": 0.92822265625}, {"start": 3713.49, "end": 3713.79, "word": " seven.", "probability": 0.89599609375}], "temperature": 1.0}, {"id": 130, "seek": 374366, "start": 3716.84, "end": 3743.66, "text": " A point estimate consists of a single sample statistic that is used to estimate the true population parameter. That's correct because any point estimate, for example x bar, is used to determine the confidence interval for the unknown parameter mu.", "tokens": [316, 935, 12539, 14689, 295, 257, 2167, 6889, 29588, 300, 307, 1143, 281, 12539, 264, 2074, 4415, 13075, 13, 663, 311, 3006, 570, 604, 935, 12539, 11, 337, 1365, 2031, 2159, 11, 307, 1143, 281, 6997, 264, 6687, 15035, 337, 264, 9841, 13075, 2992, 13], "avg_logprob": -0.17051630693933237, "compression_ratio": 1.5897435897435896, "no_speech_prob": 0.0, "words": [{"start": 3716.84, "end": 3717.3, "word": " A", "probability": 0.36572265625}, {"start": 3717.3, "end": 3717.66, "word": " point", "probability": 0.94287109375}, {"start": 3717.66, "end": 3718.36, "word": " estimate", "probability": 0.9248046875}, {"start": 3718.36, "end": 3722.3, "word": " consists", "probability": 0.6748046875}, {"start": 3722.3, "end": 3723.02, "word": " of", "probability": 0.9716796875}, {"start": 3723.02, "end": 3723.34, "word": " a", "probability": 0.98583984375}, {"start": 3723.34, "end": 3723.68, "word": " single", "probability": 0.9580078125}, {"start": 3723.68, "end": 3724.14, "word": " sample", "probability": 0.61279296875}, {"start": 3724.14, "end": 3724.74, "word": " statistic", "probability": 0.84228515625}, {"start": 3724.74, "end": 3725.9, "word": " that", "probability": 0.84375}, {"start": 3725.9, "end": 3726.14, "word": " is", "probability": 0.94189453125}, {"start": 3726.14, "end": 3726.48, "word": " used", "probability": 0.91162109375}, {"start": 3726.48, "end": 3726.7, "word": " to", "probability": 0.96630859375}, {"start": 3726.7, "end": 3727.16, "word": " estimate", "probability": 0.9169921875}, {"start": 3727.16, "end": 3727.44, "word": " the", "probability": 0.79345703125}, {"start": 3727.44, "end": 3727.62, "word": " true", "probability": 0.91650390625}, {"start": 3727.62, "end": 3728.04, "word": " population", "probability": 0.9091796875}, {"start": 3728.04, "end": 3729.8, "word": " parameter.", "probability": 0.8740234375}, {"start": 3730.62, "end": 3731.0, "word": " That's", "probability": 0.77294921875}, {"start": 3731.0, "end": 3731.52, "word": " correct", "probability": 0.90625}, {"start": 3731.52, "end": 3732.86, "word": " because", "probability": 0.5185546875}, {"start": 3732.86, "end": 3734.56, "word": " any", "probability": 0.7529296875}, {"start": 3734.56, "end": 3734.84, "word": " point", "probability": 0.97265625}, {"start": 3734.84, "end": 3735.18, "word": " estimate,", "probability": 0.9228515625}, {"start": 3735.26, "end": 3735.44, "word": " for", "probability": 0.947265625}, {"start": 3735.44, "end": 3735.7, "word": " example", "probability": 0.9716796875}, {"start": 3735.7, "end": 3735.94, "word": " x", "probability": 0.56689453125}, {"start": 3735.94, "end": 3736.26, "word": " bar,", "probability": 0.80078125}, {"start": 3737.46, "end": 3737.82, "word": " is", "probability": 0.93603515625}, {"start": 3737.82, "end": 3738.22, "word": " used", "probability": 0.91552734375}, {"start": 3738.22, "end": 3739.6, "word": " to", "probability": 0.96533203125}, {"start": 3739.6, "end": 3740.04, "word": " determine", "probability": 0.91748046875}, {"start": 3740.04, "end": 3740.44, "word": " the", "probability": 0.91943359375}, {"start": 3740.44, "end": 3740.9, "word": " confidence", "probability": 0.97265625}, {"start": 3740.9, "end": 3741.36, "word": " interval", "probability": 0.966796875}, {"start": 3741.36, "end": 3741.92, "word": " for", "probability": 0.916015625}, {"start": 3741.92, "end": 3742.66, "word": " the", "probability": 0.90869140625}, {"start": 3742.66, "end": 3742.94, "word": " unknown", "probability": 0.88232421875}, {"start": 3742.94, "end": 3743.4, "word": " parameter", "probability": 0.9677734375}, {"start": 3743.4, "end": 3743.66, "word": " mu.", "probability": 0.47998046875}], "temperature": 1.0}, {"id": 131, "seek": 376574, "start": 3744.68, "end": 3765.74, "text": " So a single statistic can be used to estimate the true population parameter, either X bar as a point estimate or P. So that's true. 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A population parameter is used to estimate a confidence interval? No way. Because we use statistics to estimate the confidence interval. These are statistics. So we are using statistics to construct the confidence interval. Number 12. 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That's true. 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So it's false. So that's for section two. One section is left, free response problems or questions, you can do it at home. So next time, inshallah, we'll start chapter nine. 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