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That was last Sunday. Let's see the comparison between these sampling data.", "tokens": [1171, 264, 1674, 10938, 611, 321, 7126, 1451, 3467, 11, 4974, 6889, 11, 27249, 11, 23674, 2587, 293, 596, 38624, 21179, 13, 663, 390, 1036, 7776, 13, 961, 311, 536, 264, 9660, 1296, 613, 21179, 1412, 13], "avg_logprob": -0.34457237704804067, "compression_ratio": 1.3941605839416058, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 35.1, "end": 35.98, "word": " For", "probability": 0.452880859375}, {"start": 35.98, "end": 36.24, "word": " the", "probability": 0.82421875}, {"start": 36.24, "end": 36.58, "word": " product", "probability": 0.63525390625}, {"start": 36.58, "end": 37.0, "word": " samples", "probability": 0.8076171875}, {"start": 37.0, "end": 37.36, "word": " also", "probability": 0.448974609375}, {"start": 37.36, "end": 37.76, "word": " we", "probability": 0.66748046875}, {"start": 37.76, "end": 38.8, "word": " produced", "probability": 0.424072265625}, {"start": 38.8, "end": 39.5, "word": " four", "probability": 0.6767578125}, {"start": 39.5, "end": 39.96, "word": " types,", "probability": 0.81396484375}, {"start": 40.74, "end": 41.32, "word": " random", "probability": 0.149658203125}, {"start": 41.32, "end": 41.82, "word": " sample,", "probability": 0.55712890625}, {"start": 42.74, "end": 43.46, "word": " systematic,", "probability": 0.9296875}, {"start": 44.68, "end": 45.92, "word": " stratified", "probability": 0.977294921875}, {"start": 45.92, "end": 46.56, "word": " and", "probability": 0.685546875}, {"start": 46.56, "end": 47.16, "word": " clustered", "probability": 0.641845703125}, {"start": 47.16, "end": 48.1, "word": " sampling.", "probability": 0.4765625}, {"start": 48.74, "end": 49.36, "word": " That", "probability": 0.81201171875}, {"start": 49.36, "end": 49.92, "word": " was", "probability": 0.95166015625}, {"start": 49.92, "end": 51.88, "word": " last", "probability": 0.822265625}, {"start": 51.88, "end": 52.84, "word": " Sunday.", "probability": 0.8818359375}, {"start": 53.9, "end": 54.4, "word": " Let's", "probability": 0.916015625}, {"start": 54.4, "end": 54.64, "word": " see", "probability": 0.92138671875}, {"start": 54.64, "end": 55.48, "word": " the", "probability": 0.908203125}, {"start": 55.48, "end": 56.12, "word": " comparison", "probability": 0.8818359375}, {"start": 56.12, "end": 56.74, "word": " between", "probability": 0.89404296875}, {"start": 56.74, "end": 59.6, "word": " these", "probability": 0.8134765625}, {"start": 59.6, "end": 60.16, "word": " sampling", "probability": 0.82421875}, {"start": 60.16, "end": 60.4, "word": " data.", "probability": 0.364990234375}], "temperature": 1.0}, {"id": 3, "seek": 8849, "start": 62.25, "end": 88.49, "text": " A simple, random sample, systematic random sample, first, for these two techniques. First of all, they are simple to use because we just use the random tables, random number tables, or by using any statistical software. 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So this is the mainly disadvantage of this sampling technique. So it can be used", "tokens": [407, 309, 1062, 312, 341, 6889, 307, 406, 12424, 295, 264, 2302, 4415, 13, 407, 341, 307, 264, 8704, 24292, 295, 341, 21179, 6532, 13, 407, 309, 393, 312, 1143], "avg_logprob": -0.32888104838709675, "compression_ratio": 1.3565217391304347, "no_speech_prob": 0.0, "words": [{"start": 97.59, "end": 98.25, "word": " So", "probability": 0.0596923828125}, {"start": 98.25, "end": 98.91, "word": " it", "probability": 0.359130859375}, {"start": 98.91, "end": 99.15, "word": " might", "probability": 0.59130859375}, {"start": 99.15, "end": 99.37, "word": " be", "probability": 0.8984375}, {"start": 99.37, "end": 99.67, "word": " this", "probability": 0.55859375}, {"start": 99.67, "end": 99.91, "word": " sample", "probability": 0.83984375}, {"start": 99.91, "end": 100.09, "word": " is", "probability": 0.90478515625}, {"start": 100.09, "end": 100.25, "word": " not", "probability": 0.9384765625}, {"start": 100.25, "end": 100.83, "word": " representative", "probability": 0.89794921875}, {"start": 100.83, "end": 101.33, "word": " of", "probability": 0.9619140625}, {"start": 101.33, "end": 101.49, "word": " the", "probability": 0.89794921875}, {"start": 101.49, "end": 101.89, "word": " entire", "probability": 0.8974609375}, {"start": 101.89, "end": 102.23, "word": " population.", "probability": 0.830078125}, {"start": 103.23, "end": 103.35, "word": " So", "probability": 0.85302734375}, {"start": 103.35, "end": 103.57, "word": " this", "probability": 0.89013671875}, {"start": 103.57, "end": 103.75, "word": " is", "probability": 0.94091796875}, {"start": 103.75, "end": 103.99, "word": " the", "probability": 0.6142578125}, {"start": 103.99, "end": 104.53, "word": " mainly", "probability": 0.84423828125}, {"start": 104.53, "end": 105.91, "word": " disadvantage", "probability": 0.64892578125}, {"start": 105.91, "end": 107.69, "word": " of", "probability": 0.96240234375}, {"start": 107.69, "end": 108.13, "word": " this", "probability": 0.9326171875}, {"start": 108.13, "end": 108.49, "word": " sampling", "probability": 0.97607421875}, {"start": 108.49, "end": 108.99, "word": " technique.", "probability": 0.94677734375}, {"start": 109.59, "end": 109.93, "word": " So", "probability": 0.90869140625}, {"start": 109.93, "end": 110.05, "word": " it", "probability": 0.90625}, {"start": 110.05, "end": 110.23, "word": " can", "probability": 0.94921875}, {"start": 110.23, "end": 110.39, "word": " be", "probability": 0.9501953125}, {"start": 110.39, "end": 110.71, "word": " used", "probability": 0.919921875}], "temperature": 1.0}, {"id": 5, "seek": 13211, "start": 112.23, "end": 132.11, "text": " unless the population is not symmetric or the population is not heterogeneous. I mean if the population has the same characteristics, then we can use simple or systematic sample. 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In this case, stratified sampling is better than using a simple random sample. Stratified samples ensure representation of individuals across the entire population. 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First level, second level and fourth level, and so on. The last type of sampling was clusters. 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You have to know, number one, what's the purpose of the survey. In this case, you can determine the frame of the population. 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If the answer is yes, then go ahead and use one of the non-probability sampling techniques either similar than some certified cluster or systematic. Next, we have to distinguish between four types of errors, at least now. 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I mean, frame appropriate means that you have all the individual list, then you can choose one of these. For example, suppose we divide Gaza Strip into four governorates. North Gaza, Gaza Middle Area, Khanon and Rafah. 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In this case if you, so that's your frame. Now if you exclude one, for example, and that one is important for you, but you exclude it for some reasons, in this case you will have coverage as well, because you excluded.", "tokens": [10863, 295, 1732, 11280, 13, 682, 341, 1389, 498, 291, 11, 370, 300, 311, 428, 3920, 13, 823, 498, 291, 33536, 472, 11, 337, 1365, 11, 293, 300, 472, 307, 1021, 337, 291, 11, 457, 291, 33536, 309, 337, 512, 4112, 11, 294, 341, 1389, 291, 486, 362, 9645, 382, 731, 11, 570, 291, 29486, 13], "avg_logprob": -0.27206689851325855, "compression_ratio": 1.585987261146497, "no_speech_prob": 3.5762786865234375e-07, "words": [{"start": 309.79, "end": 310.31, "word": " sections", "probability": 0.1644287109375}, {"start": 310.31, "end": 310.55, "word": " of", "probability": 0.6298828125}, {"start": 310.55, "end": 310.83, "word": " five", "probability": 0.69384765625}, {"start": 310.83, "end": 311.31, "word": " governments.", "probability": 0.83056640625}, {"start": 312.51, "end": 312.69, "word": " In", "probability": 0.775390625}, {"start": 312.69, "end": 312.95, "word": " this", "probability": 0.947265625}, {"start": 312.95, "end": 313.23, "word": " case", "probability": 0.9169921875}, {"start": 313.23, "end": 313.45, "word": " if", "probability": 0.54150390625}, {"start": 313.45, "end": 313.67, "word": " you,", "probability": 0.95703125}, {"start": 314.11, "end": 314.39, "word": " so", "probability": 0.603515625}, {"start": 314.39, "end": 314.95, "word": " that's", "probability": 0.90576171875}, {"start": 314.95, "end": 315.29, "word": " your", "probability": 0.90185546875}, {"start": 315.29, "end": 316.39, "word": " frame.", "probability": 0.91748046875}, {"start": 316.91, "end": 317.11, "word": " Now", "probability": 0.9091796875}, {"start": 317.11, "end": 317.25, "word": " if", "probability": 0.8212890625}, {"start": 317.25, "end": 317.43, "word": " you", "probability": 0.96435546875}, {"start": 317.43, "end": 317.65, "word": " exclude", "probability": 0.853515625}, {"start": 317.65, "end": 318.05, "word": " one,", "probability": 0.9326171875}, {"start": 318.27, "end": 318.43, "word": " for", "probability": 0.94287109375}, {"start": 318.43, "end": 318.79, "word": " example,", "probability": 0.97216796875}, {"start": 319.09, "end": 319.23, "word": " and", "probability": 0.92529296875}, {"start": 319.23, "end": 319.41, "word": " that", "probability": 0.93994140625}, {"start": 319.41, "end": 319.63, "word": " one", "probability": 0.92431640625}, {"start": 319.63, "end": 319.89, "word": " is", "probability": 0.94677734375}, {"start": 319.89, "end": 320.45, "word": " important", "probability": 0.87939453125}, {"start": 320.45, "end": 320.75, "word": " for", "probability": 0.92578125}, {"start": 320.75, "end": 320.97, "word": " you,", "probability": 0.96337890625}, {"start": 321.15, "end": 321.29, "word": " but", "probability": 0.8974609375}, {"start": 321.29, "end": 321.45, "word": " you", "probability": 0.57861328125}, {"start": 321.45, "end": 321.73, "word": " exclude", "probability": 0.85693359375}, {"start": 321.73, "end": 321.87, "word": " it", "probability": 0.49609375}, {"start": 321.87, "end": 321.99, "word": " for", "probability": 0.94775390625}, {"start": 321.99, "end": 322.35, "word": " some", "probability": 0.9033203125}, {"start": 322.35, "end": 323.27, "word": " reasons,", "probability": 0.81787109375}, {"start": 323.71, "end": 323.93, "word": " in", "probability": 0.9345703125}, {"start": 323.93, "end": 324.17, "word": " this", "probability": 0.94970703125}, {"start": 324.17, "end": 324.53, "word": " case", "probability": 0.916015625}, {"start": 324.53, "end": 324.77, "word": " you", "probability": 0.7470703125}, {"start": 324.77, "end": 324.91, "word": " will", "probability": 0.85791015625}, {"start": 324.91, "end": 325.19, "word": " have", "probability": 0.94384765625}, {"start": 325.19, "end": 326.01, "word": " coverage", "probability": 0.88623046875}, {"start": 326.01, "end": 326.27, "word": " as", "probability": 0.444091796875}, {"start": 326.27, "end": 326.49, "word": " well,", "probability": 0.951171875}, {"start": 326.97, "end": 327.35, "word": " because", "probability": 0.89599609375}, {"start": 327.35, "end": 327.55, "word": " you", "probability": 0.96435546875}, {"start": 327.55, "end": 327.99, "word": " excluded.", "probability": 0.50830078125}], "temperature": 1.0}, {"id": 14, "seek": 35784, "start": 330.34, "end": 357.84, "text": " one group out of five and that group may be important for your study. Next is called non-response error. Suppose I attributed my questionnaire for 100 students and I gave each one 30 minutes to answer the questionnaire or to fill up the questionnaire, but I didn't follow up.", "tokens": [472, 1594, 484, 295, 1732, 293, 300, 1594, 815, 312, 1021, 337, 428, 2979, 13, 3087, 307, 1219, 2107, 12, 5667, 3739, 6713, 13, 21360, 286, 30976, 452, 44702, 337, 2319, 1731, 293, 286, 2729, 1184, 472, 2217, 2077, 281, 1867, 264, 44702, 420, 281, 2836, 493, 264, 44702, 11, 457, 286, 994, 380, 1524, 493, 13], "avg_logprob": -0.20177802366429362, "compression_ratio": 1.5164835164835164, "no_speech_prob": 0.0, "words": [{"start": 330.34, "end": 330.7, "word": " one", "probability": 0.436767578125}, {"start": 330.7, "end": 331.1, "word": " group", "probability": 0.9541015625}, {"start": 331.1, "end": 332.06, "word": " out", "probability": 0.572265625}, {"start": 332.06, "end": 332.28, "word": " of", "probability": 0.97314453125}, {"start": 332.28, "end": 332.6, "word": " five", "probability": 0.6865234375}, 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The other type of error is called measurement error, which is one of the most important errors, and we have to avoid. It's called measurement error. Good questions elicit good responses. It means suppose, for example, my question is,", "tokens": [456, 307, 364, 6713, 11, 293, 300, 6713, 307, 1219, 2107, 12, 5667, 3739, 13, 440, 661, 2010, 295, 6713, 307, 1219, 13160, 6713, 11, 597, 307, 472, 295, 264, 881, 1021, 13603, 11, 293, 321, 362, 281, 5042, 13, 467, 311, 1219, 13160, 6713, 13, 2205, 1651, 806, 8876, 665, 13019, 13, 467, 1355, 7297, 11, 337, 1365, 11, 452, 1168, 307, 11], "avg_logprob": -0.2308894230769231, "compression_ratio": 1.7380952380952381, "no_speech_prob": 0.0, "words": [{"start": 388.09, "end": 388.47, "word": " there", "probability": 0.3994140625}, {"start": 388.47, "end": 388.79, "word": " is", "probability": 0.92236328125}, {"start": 388.79, "end": 389.03, "word": " an", "probability": 0.90625}, {"start": 389.03, "end": 389.25, "word": " error,", "probability": 0.87109375}, {"start": 389.39, "end": 389.41, "word": " and", "probability": 0.85693359375}, {"start": 389.41, "end": 389.59, "word": " that", "probability": 0.90673828125}, {"start": 389.59, "end": 389.75, "word": " error", "probability": 0.8466796875}, {"start": 389.75, "end": 389.91, "word": " is", "probability": 0.9140625}, {"start": 389.91, "end": 390.25, "word": " called", "probability": 0.85400390625}, {"start": 390.25, "end": 390.55, "word": " non", "probability": 0.70361328125}, {"start": 390.55, "end": 391.07, "word": "-response.", "probability": 0.73486328125}, {"start": 391.85, "end": 392.49, "word": " The", "probability": 0.875}, {"start": 392.49, "end": 392.75, "word": " other", "probability": 0.89013671875}, {"start": 392.75, "end": 393.07, "word": " type", "probability": 0.95849609375}, {"start": 393.07, "end": 393.23, "word": " of", "probability": 0.96484375}, {"start": 393.23, "end": 393.51, "word": " error", "probability": 0.88330078125}, {"start": 393.51, "end": 394.95, "word": " is", "probability": 0.75341796875}, {"start": 394.95, "end": 395.17, "word": " called", "probability": 0.82275390625}, {"start": 395.17, "end": 395.59, "word": " measurement", "probability": 0.767578125}, {"start": 395.59, "end": 395.99, "word": " error,", "probability": 0.79150390625}, {"start": 396.17, "end": 396.21, "word": " which", "probability": 0.64794921875}, {"start": 396.21, "end": 396.31, "word": " is", "probability": 0.9404296875}, {"start": 396.31, "end": 396.51, "word": " one", "probability": 0.92822265625}, {"start": 396.51, "end": 396.65, "word": " of", "probability": 0.9658203125}, {"start": 396.65, "end": 396.81, "word": " the", "probability": 0.9208984375}, {"start": 396.81, "end": 397.15, "word": " most", "probability": 0.89306640625}, {"start": 397.15, "end": 397.87, "word": " important", "probability": 0.88232421875}, {"start": 397.87, "end": 398.33, "word": " errors,", "probability": 0.86328125}, {"start": 398.83, "end": 398.91, "word": " and", "probability": 0.919921875}, {"start": 398.91, "end": 399.03, "word": " we", "probability": 0.87060546875}, {"start": 399.03, "end": 399.19, "word": " have", "probability": 0.94873046875}, {"start": 399.19, "end": 399.33, "word": " to", "probability": 0.97265625}, {"start": 399.33, "end": 399.91, "word": " avoid.", "probability": 0.9140625}, {"start": 402.95, "end": 403.29, "word": " It's", "probability": 0.888671875}, {"start": 403.29, "end": 403.49, "word": " called", "probability": 0.86572265625}, {"start": 403.49, "end": 403.87, "word": " measurement", "probability": 0.84423828125}, {"start": 403.87, "end": 404.23, "word": " error.", "probability": 0.90185546875}, {"start": 405.07, "end": 405.23, "word": " Good", "probability": 0.262451171875}, {"start": 405.23, "end": 405.83, "word": " questions", "probability": 0.94873046875}, {"start": 405.83, "end": 406.73, "word": " elicit", "probability": 0.935791015625}, {"start": 406.73, "end": 408.05, "word": " good", "probability": 0.9150390625}, {"start": 408.05, "end": 408.63, "word": " responses.", "probability": 0.93310546875}, {"start": 408.95, "end": 409.07, "word": " It", "probability": 0.89599609375}, {"start": 409.07, "end": 409.37, "word": " means", "probability": 0.92919921875}, {"start": 409.37, "end": 410.51, "word": " suppose,", "probability": 0.31884765625}, {"start": 410.65, "end": 410.71, "word": " for", "probability": 0.95263671875}, {"start": 410.71, "end": 411.11, "word": " example,", "probability": 0.9755859375}, {"start": 412.21, "end": 412.51, "word": " my", "probability": 0.96630859375}, {"start": 412.51, "end": 412.83, "word": " question", "probability": 0.97021484375}, {"start": 412.83, "end": 413.21, "word": " is,", "probability": 0.95068359375}], "temperature": 1.0}, {"id": 17, "seek": 43824, "start": 414.72, "end": 438.24, "text": " I feel this candidate is good for us. What do you think? It's my question. I feel this candidate, candidate A, whatever he is, is good for us. What do you think? For sure there's abundant answer will be yes. 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So it means leading question. So measurement error. So but if we have good questions, just ask any question for the respondent and let him or let his answer based on", "tokens": [407, 300, 1355, 291, 1715, 264, 1168, 294, 264, 636, 300, 291, 486, 458, 436, 4196, 3838, 300, 415, 486, 1867, 2086, 420, 572, 5946, 322, 428, 1715, 295, 264, 1168, 13, 407, 309, 1355, 5775, 1168, 13, 407, 13160, 6713, 13, 407, 457, 498, 321, 362, 665, 1651, 11, 445, 1029, 604, 1168, 337, 264, 4196, 317, 293, 718, 796, 420, 718, 702, 1867, 2361, 322], "avg_logprob": -0.19485294008079698, "compression_ratio": 1.7912087912087913, "no_speech_prob": 0.0, "words": [{"start": 439.1, "end": 439.58, "word": " So", "probability": 0.67724609375}, {"start": 439.58, "end": 439.86, "word": " that", "probability": 0.76708984375}, {"start": 439.86, "end": 440.14, "word": " means", "probability": 0.93017578125}, {"start": 440.14, "end": 440.42, "word": " you", "probability": 0.91064453125}, {"start": 440.42, "end": 441.34, "word": " design", "probability": 0.83251953125}, 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So don't force the respondent to answer the question in the direction you want to be. Otherwise you will get something called Measurement Error. Do you think? Give me an example of Measurement Error. Give me an example of Measurement Error. 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Maybe I like coffee, do you like coffee or tea? So maybe he will go with your answer, in this case it's measurement. Another example.", "tokens": [286, 914, 702, 1867, 486, 312, 264, 912, 382, 291, 519, 466, 309, 13, 2704, 286, 411, 4982, 11, 360, 291, 411, 4982, 420, 5817, 30, 407, 1310, 415, 486, 352, 365, 428, 1867, 11, 294, 341, 1389, 309, 311, 13160, 13, 3996, 1365, 13], "avg_logprob": -0.21569292830384296, "compression_ratio": 1.3714285714285714, "no_speech_prob": 0.0, "words": [{"start": 498.23, "end": 498.57, "word": " I", "probability": 0.67822265625}, {"start": 498.57, "end": 498.91, "word": " mean", "probability": 0.9658203125}, {"start": 498.91, "end": 499.37, "word": " his", "probability": 0.6083984375}, {"start": 499.37, "end": 499.71, "word": " answer", "probability": 0.953125}, {"start": 499.71, "end": 499.89, "word": " will", "probability": 0.759765625}, {"start": 499.89, "end": 500.01, "word": " be", "probability": 0.95068359375}, {"start": 500.01, "end": 500.19, "word": " the", "probability": 0.876953125}, {"start": 500.19, "end": 500.39, "word": " same", "probability": 0.90478515625}, {"start": 500.39, "end": 500.61, "word": " as", "probability": 0.96044921875}, {"start": 500.61, "end": 500.75, "word": " you", "probability": 0.93798828125}, {"start": 500.75, "end": 501.03, "word": " think", "probability": 0.90625}, {"start": 501.03, "end": 501.27, "word": " about", "probability": 0.904296875}, {"start": 501.27, "end": 504.77, "word": " it.", "probability": 0.85107421875}, {"start": 510.13, "end": 510.49, "word": " Maybe", "probability": 0.37060546875}, {"start": 510.49, "end": 510.91, "word": " I", "probability": 0.39453125}, {"start": 510.91, "end": 511.17, "word": " like", "probability": 0.93212890625}, {"start": 511.17, "end": 511.49, "word": " coffee,", "probability": 0.89208984375}, {"start": 511.93, "end": 512.13, "word": " do", "probability": 0.87890625}, {"start": 512.13, "end": 512.19, "word": " you", "probability": 0.9619140625}, {"start": 512.19, "end": 512.31, "word": " like", "probability": 0.93798828125}, {"start": 512.31, "end": 512.57, "word": " coffee", "probability": 0.86376953125}, {"start": 512.57, "end": 512.79, "word": " or", "probability": 0.95654296875}, {"start": 512.79, "end": 513.03, "word": " tea?", "probability": 0.94775390625}, {"start": 514.67, "end": 515.13, "word": " So", "probability": 0.7958984375}, {"start": 515.13, "end": 515.43, "word": " maybe", "probability": 0.822265625}, {"start": 515.43, "end": 515.73, "word": " he", "probability": 0.93310546875}, {"start": 515.73, "end": 515.87, "word": " will", "probability": 0.8876953125}, {"start": 515.87, "end": 516.05, "word": " go", "probability": 0.96728515625}, {"start": 516.05, "end": 516.23, "word": " with", "probability": 0.8896484375}, {"start": 516.23, "end": 516.41, "word": " your", "probability": 0.88134765625}, {"start": 516.41, "end": 516.81, "word": " answer,", "probability": 0.96044921875}, {"start": 516.89, "end": 516.97, "word": " in", "probability": 0.91748046875}, {"start": 516.97, "end": 517.17, "word": " this", "probability": 0.94091796875}, {"start": 517.17, "end": 517.39, "word": " case", "probability": 0.92236328125}, {"start": 517.39, "end": 519.55, "word": " it's", "probability": 0.855224609375}, {"start": 519.55, "end": 520.51, "word": " measurement.", "probability": 0.34228515625}, {"start": 520.87, "end": 521.23, "word": " Another", "probability": 0.841796875}, {"start": 521.23, "end": 521.63, "word": " example.", "probability": 0.97021484375}], "temperature": 1.0}, {"id": 21, "seek": 55594, "start": 540.26, "end": 555.94, "text": " Exactly. So it means that if you design a question in the way that you will get the same answer you think about it,", "tokens": [7587, 13, 407, 309, 1355, 300, 498, 291, 1715, 257, 1168, 294, 264, 636, 300, 291, 486, 483, 264, 912, 1867, 291, 519, 466, 309, 11], "avg_logprob": -0.21122685405943128, "compression_ratio": 1.2210526315789474, "no_speech_prob": 0.0, "words": [{"start": 540.26, "end": 540.86, "word": " Exactly.", "probability": 0.08843994140625}, {"start": 547.96, "end": 548.22, "word": " So", "probability": 0.900390625}, {"start": 548.22, "end": 548.6, "word": " it", "probability": 0.7568359375}, {"start": 548.6, "end": 548.96, "word": " means", "probability": 0.916015625}, {"start": 548.96, "end": 549.3, "word": " that", "probability": 0.91845703125}, {"start": 549.3, "end": 549.74, "word": " if", "probability": 0.9072265625}, {"start": 549.74, "end": 549.96, "word": " you", "probability": 0.96337890625}, {"start": 549.96, "end": 550.38, "word": " design", "probability": 0.96435546875}, {"start": 550.38, "end": 550.54, "word": " a", "probability": 0.98779296875}, {"start": 550.54, "end": 551.3, "word": " question", "probability": 0.92822265625}, {"start": 551.3, "end": 552.26, "word": " in", "probability": 0.69775390625}, {"start": 552.26, "end": 552.42, "word": " the", "probability": 0.81787109375}, {"start": 552.42, "end": 552.62, "word": " way", "probability": 0.9541015625}, {"start": 552.62, "end": 552.9, "word": " that", "probability": 0.9287109375}, {"start": 552.9, "end": 553.48, "word": " you", "probability": 0.9443359375}, {"start": 553.48, "end": 553.64, "word": " will", "probability": 0.8837890625}, {"start": 553.64, "end": 554.04, "word": " get", "probability": 0.94189453125}, {"start": 554.04, "end": 554.34, "word": " the", "probability": 0.91796875}, {"start": 554.34, "end": 554.64, "word": " same", "probability": 0.904296875}, {"start": 554.64, "end": 554.98, "word": " answer", "probability": 0.95703125}, {"start": 554.98, "end": 555.14, "word": " you", "probability": 0.73193359375}, {"start": 555.14, "end": 555.42, "word": " think", "probability": 0.88720703125}, {"start": 555.42, "end": 555.7, "word": " about", "probability": 0.9091796875}, {"start": 555.7, "end": 555.94, "word": " it,", "probability": 0.9453125}], "temperature": 1.0}, {"id": 22, "seek": 58409, "start": 556.37, "end": 584.09, "text": " It means that you will have something called measurement error. The last type is sampling error. Sampling error always happens, always exists. For example, suppose you are around 50 students in this class. Suppose I select randomly 20 of you. And I am interested suppose in your age. Maybe for this sample.", "tokens": [467, 1355, 300, 291, 486, 362, 746, 1219, 13160, 6713, 13, 440, 1036, 2010, 307, 21179, 6713, 13, 4832, 11970, 6713, 1009, 2314, 11, 1009, 8198, 13, 1171, 1365, 11, 7297, 291, 366, 926, 2625, 1731, 294, 341, 1508, 13, 21360, 286, 3048, 16979, 945, 295, 291, 13, 400, 286, 669, 3102, 7297, 294, 428, 3205, 13, 2704, 337, 341, 6889, 13], "avg_logprob": -0.17547122779346647, "compression_ratio": 1.5198019801980198, "no_speech_prob": 0.0, "words": [{"start": 556.37, "end": 556.63, "word": " It", "probability": 0.373291015625}, {"start": 556.63, "end": 556.97, "word": " means", "probability": 0.91552734375}, {"start": 556.97, "end": 557.39, "word": " that", "probability": 0.912109375}, {"start": 557.39, "end": 558.01, "word": " you", "probability": 0.88916015625}, {"start": 558.01, "end": 558.19, "word": " will", "probability": 0.85791015625}, {"start": 558.19, "end": 558.55, "word": " have", "probability": 0.951171875}, {"start": 558.55, "end": 558.91, 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So the first one, second tier, each of them has different sample statistics, I mean different sample means. This difference or this error actually is called sampling error and always happens.", "tokens": [8734, 1646, 1310, 611, 3048, 264, 912, 1230, 295, 1731, 11, 457, 264, 4274, 295, 264, 1508, 1062, 312, 945, 924, 13, 407, 264, 700, 472, 11, 1150, 12362, 11, 1184, 295, 552, 575, 819, 6889, 12523, 11, 286, 914, 819, 6889, 1355, 13, 639, 2649, 420, 341, 6713, 767, 307, 1219, 21179, 6713, 293, 1009, 2314, 13], "avg_logprob": -0.23450741676960962, "compression_ratio": 1.5957446808510638, "no_speech_prob": 0.0, "words": [{"start": 619.33, "end": 619.73, "word": " Someone", "probability": 0.5029296875}, {"start": 619.73, "end": 620.13, "word": " else", "probability": 0.91162109375}, {"start": 620.13, "end": 620.41, "word": " maybe", "probability": 0.5888671875}, {"start": 620.41, "end": 622.35, "word": " also", "probability": 0.289794921875}, {"start": 622.35, "end": 622.93, "word": " select", "probability": 0.84130859375}, {"start": 622.93, "end": 623.37, "word": " the", "probability": 0.350341796875}, {"start": 623.37, "end": 623.55, "word": " same", "probability": 0.90478515625}, {"start": 623.55, "end": 623.91, "word": " number", "probability": 0.93505859375}, {"start": 623.91, "end": 624.79, "word": " of", "probability": 0.95458984375}, {"start": 624.79, "end": 625.29, "word": " students,", "probability": 0.88525390625}, {"start": 626.15, "end": 626.47, "word": " but", "probability": 0.845703125}, {"start": 626.47, "end": 626.61, "word": " the", "probability": 0.62060546875}, {"start": 626.61, "end": 626.93, "word": " average", "probability": 0.7509765625}, {"start": 626.93, "end": 627.45, "word": " of", "probability": 0.95263671875}, {"start": 627.45, "end": 627.59, "word": " the", "probability": 0.84423828125}, {"start": 627.59, "end": 627.91, "word": " class", "probability": 0.9580078125}, {"start": 627.91, "end": 628.41, "word": " might", "probability": 0.9052734375}, {"start": 628.41, "end": 628.65, "word": " be", "probability": 0.94873046875}, {"start": 628.65, "end": 628.91, "word": " 20", "probability": 0.7802734375}, {"start": 628.91, "end": 629.23, "word": " years.", "probability": 0.78369140625}, {"start": 630.27, "end": 630.63, "word": " So", "probability": 0.93994140625}, {"start": 630.63, "end": 630.79, "word": " the", "probability": 0.7587890625}, {"start": 630.79, "end": 631.03, "word": " first", "probability": 0.876953125}, {"start": 631.03, "end": 631.29, "word": " one,", "probability": 0.9345703125}, {"start": 631.69, "end": 632.11, "word": " second", "probability": 0.7197265625}, {"start": 632.11, "end": 632.59, "word": " tier,", "probability": 0.58544921875}, {"start": 633.07, "end": 633.37, "word": " each", "probability": 0.94287109375}, {"start": 633.37, "end": 633.51, "word": " of", "probability": 0.919921875}, {"start": 633.51, "end": 633.69, "word": " them", "probability": 0.89306640625}, {"start": 633.69, "end": 634.15, "word": " has", "probability": 0.9326171875}, {"start": 634.15, "end": 635.45, "word": " different", "probability": 0.87060546875}, {"start": 635.45, "end": 636.13, "word": " sample", "probability": 0.75732421875}, {"start": 636.13, "end": 636.75, "word": " statistics,", "probability": 0.7646484375}, {"start": 637.07, "end": 637.15, "word": " I", "probability": 0.931640625}, {"start": 637.15, "end": 637.25, "word": " mean", "probability": 0.9580078125}, {"start": 637.25, "end": 637.83, "word": " different", "probability": 0.671875}, {"start": 637.83, "end": 638.75, "word": " sample", "probability": 0.87744140625}, {"start": 638.75, "end": 639.09, "word": " means.", "probability": 0.74658203125}, {"start": 639.85, "end": 640.29, "word": " This", "probability": 0.87353515625}, {"start": 640.29, "end": 640.95, "word": " difference", "probability": 0.8896484375}, {"start": 640.95, "end": 642.21, "word": " or", "probability": 0.51513671875}, {"start": 642.21, "end": 642.45, "word": " this", "probability": 0.94775390625}, {"start": 642.45, "end": 642.71, "word": " error", "probability": 0.86669921875}, {"start": 642.71, "end": 643.21, "word": " actually", "probability": 0.79931640625}, {"start": 643.21, "end": 643.71, "word": " is", "probability": 0.84228515625}, {"start": 643.71, "end": 644.09, "word": " called", "probability": 0.89501953125}, {"start": 644.09, "end": 645.03, "word": " sampling", "probability": 0.7509765625}, {"start": 645.03, "end": 645.33, "word": " error", "probability": 0.94775390625}, {"start": 645.33, "end": 646.01, "word": " and", "probability": 0.50830078125}, {"start": 646.01, "end": 646.47, "word": " always", "probability": 0.8798828125}, {"start": 646.47, "end": 646.83, "word": " happens.", "probability": 0.927734375}], "temperature": 1.0}, {"id": 25, "seek": 66662, "start": 648.86, "end": 666.62, "text": " So now we have five types of errors. One is called coverage error. In this case, you have problem with the frame. The other type is called non-response error. It means you have problem with following up. Measurement error, it means you have", "tokens": [407, 586, 321, 362, 1732, 3467, 295, 13603, 13, 1485, 307, 1219, 9645, 6713, 13, 682, 341, 1389, 11, 291, 362, 1154, 365, 264, 3920, 13, 440, 661, 2010, 307, 1219, 2107, 12, 5667, 3739, 6713, 13, 467, 1355, 291, 362, 1154, 365, 3480, 493, 13, 41436, 518, 6713, 11, 309, 1355, 291, 362], "avg_logprob": -0.1955965909090909, "compression_ratio": 1.6394557823129252, "no_speech_prob": 0.0, "words": [{"start": 648.86, "end": 649.12, "word": " So", "probability": 0.450439453125}, {"start": 649.12, "end": 649.9, "word": " now", "probability": 0.71630859375}, {"start": 649.9, "end": 650.08, "word": " we", "probability": 0.86669921875}, {"start": 650.08, "end": 650.32, "word": " have", "probability": 0.94873046875}, {"start": 650.32, "end": 650.66, "word": " five", "probability": 0.68798828125}, {"start": 650.66, "end": 651.14, "word": " types", "probability": 0.791015625}, {"start": 651.14, "end": 651.46, "word": " of", "probability": 0.96484375}, {"start": 651.46, "end": 651.72, "word": " errors.", "probability": 0.81201171875}, {"start": 651.92, "end": 652.04, "word": " One", "probability": 0.8662109375}, {"start": 652.04, "end": 652.2, "word": " is", "probability": 0.908203125}, {"start": 652.2, "end": 652.4, "word": " called", "probability": 0.78662109375}, {"start": 652.4, "end": 652.8, "word": " coverage", "probability": 0.270751953125}, {"start": 652.8, "end": 653.1, "word": " error.", "probability": 0.8779296875}, {"start": 653.68, "end": 653.82, "word": " In", "probability": 0.9453125}, {"start": 653.82, "end": 654.02, "word": " this", "probability": 0.94873046875}, {"start": 654.02, "end": 654.28, "word": " case,", "probability": 0.91845703125}, {"start": 654.36, "end": 654.42, "word": " you", "probability": 0.92724609375}, {"start": 654.42, "end": 654.58, "word": " have", "probability": 0.94873046875}, {"start": 654.58, "end": 654.94, "word": " problem", "probability": 0.5078125}, {"start": 654.94, "end": 655.38, "word": " with", "probability": 0.91064453125}, {"start": 655.38, "end": 656.84, "word": " the", "probability": 0.8623046875}, {"start": 656.84, "end": 657.18, "word": " frame.", "probability": 0.91357421875}, {"start": 658.2, "end": 658.54, "word": " The", "probability": 0.87109375}, {"start": 658.54, "end": 658.74, "word": " other", "probability": 0.8916015625}, {"start": 658.74, "end": 659.0, "word": " type", "probability": 0.96435546875}, {"start": 659.0, "end": 659.14, "word": " is", "probability": 0.93994140625}, {"start": 659.14, "end": 659.36, "word": " called", "probability": 0.880859375}, {"start": 659.36, "end": 659.58, "word": " non", "probability": 0.89013671875}, {"start": 659.58, "end": 660.02, "word": "-response", "probability": 0.90869140625}, {"start": 660.02, "end": 660.28, "word": " error.", "probability": 0.88525390625}, {"start": 661.26, "end": 661.48, "word": " It", "probability": 0.88232421875}, {"start": 661.48, "end": 661.84, "word": " means", "probability": 0.93212890625}, {"start": 661.84, "end": 662.32, "word": " you", "probability": 0.9267578125}, {"start": 662.32, "end": 662.5, "word": " have", "probability": 0.9501953125}, {"start": 662.5, "end": 662.9, "word": " problem", "probability": 0.8203125}, {"start": 662.9, "end": 663.26, "word": " with", "probability": 0.85888671875}, {"start": 663.26, "end": 663.78, "word": " following", "probability": 0.8935546875}, {"start": 663.78, "end": 664.16, "word": " up.", "probability": 0.953125}, {"start": 665.06, "end": 665.5, "word": " Measurement", "probability": 0.954833984375}, {"start": 665.5, "end": 665.7, "word": " error,", "probability": 0.87890625}, {"start": 665.76, "end": 665.88, "word": " it", "probability": 0.92724609375}, {"start": 665.88, "end": 666.1, "word": " means", "probability": 0.931640625}, {"start": 666.1, "end": 666.28, "word": " you", "probability": 0.955078125}, {"start": 666.28, "end": 666.62, "word": " have", "probability": 0.9501953125}], "temperature": 1.0}, {"id": 26, "seek": 69721, "start": 667.81, "end": 697.21, "text": " Bad questionnaire design, the last type is called semi-error and this one always happens and actually we would like to have this error, I mean this semi-error as small as possible. So these are the steps you have to follow up when you design the questionnaire. 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That's the first type of error, coverage error. So it means there is a problem.", "tokens": [639, 2010, 295, 6713, 8198, 498, 512, 3935, 366, 29486, 490, 264, 3920, 293, 362, 572, 2931, 295, 885, 8209, 13, 663, 311, 264, 700, 2010, 295, 6713, 11, 9645, 6713, 13, 407, 309, 1355, 456, 307, 257, 1154, 13], "avg_logprob": -0.16968369483947754, "compression_ratio": 1.4384615384615385, "no_speech_prob": 0.0, "words": [{"start": 699.15, "end": 699.61, "word": " This", "probability": 0.31396484375}, {"start": 699.61, "end": 700.01, "word": " type", "probability": 0.9541015625}, {"start": 700.01, "end": 700.17, "word": " of", "probability": 0.9716796875}, {"start": 700.17, "end": 700.39, "word": " error", "probability": 0.87158203125}, {"start": 700.39, "end": 700.97, "word": " exists", "probability": 0.830078125}, {"start": 700.97, "end": 701.31, "word": " if", "probability": 0.9404296875}, {"start": 701.31, "end": 701.65, "word": " some", "probability": 0.82763671875}, {"start": 701.65, "end": 702.07, "word": " groups", "probability": 0.94775390625}, {"start": 702.07, "end": 702.33, "word": " are", "probability": 0.94189453125}, {"start": 702.33, "end": 702.89, "word": " excluded", "probability": 0.880859375}, {"start": 702.89, "end": 703.59, "word": " from", "probability": 0.8955078125}, {"start": 703.59, "end": 703.83, "word": " the", "probability": 0.91552734375}, {"start": 703.83, "end": 704.19, "word": " frame", "probability": 0.92236328125}, {"start": 704.19, "end": 704.77, "word": " and", "probability": 0.8046875}, {"start": 704.77, "end": 704.97, "word": " have", "probability": 0.94189453125}, {"start": 704.97, "end": 705.15, "word": " no", "probability": 0.94921875}, {"start": 705.15, "end": 705.53, "word": " chance", "probability": 0.97119140625}, {"start": 705.53, "end": 705.69, "word": " of", "probability": 0.9638671875}, {"start": 705.69, "end": 705.85, "word": " being", "probability": 0.943359375}, {"start": 705.85, "end": 706.35, "word": " selected.", "probability": 0.8916015625}, {"start": 708.43, "end": 708.95, "word": " That's", "probability": 0.805419921875}, {"start": 708.95, "end": 709.09, "word": " the", "probability": 0.90673828125}, {"start": 709.09, "end": 709.35, "word": " first", "probability": 0.8779296875}, {"start": 709.35, "end": 709.63, "word": " type", "probability": 0.98046875}, {"start": 709.63, "end": 709.77, "word": " of", "probability": 0.96484375}, {"start": 709.77, "end": 709.89, "word": " error,", "probability": 0.8828125}, {"start": 710.05, "end": 710.37, "word": " coverage", "probability": 0.456787109375}, {"start": 710.37, "end": 710.63, "word": " error.", "probability": 0.91943359375}, {"start": 711.51, "end": 711.81, "word": " So", "probability": 0.9130859375}, {"start": 711.81, "end": 711.97, "word": " it", "probability": 0.7939453125}, {"start": 711.97, "end": 712.23, "word": " means", "probability": 0.9208984375}, {"start": 712.23, "end": 712.47, "word": " there", "probability": 0.76171875}, {"start": 712.47, "end": 712.63, "word": " is", "probability": 0.7119140625}, {"start": 712.63, "end": 712.75, "word": " a", "probability": 0.99169921875}, {"start": 712.75, "end": 713.11, "word": " problem.", "probability": 0.87353515625}], "temperature": 1.0}, {"id": 28, "seek": 74295, "start": 714.25, "end": 742.95, "text": " on the population frame. Non-response error bias, it means people who don't respond may be different from those who do respond. For example, suppose I have a sample of tennis students. And I got responses from number two, number five,", "tokens": [322, 264, 4415, 3920, 13, 8774, 12, 5667, 3739, 6713, 12577, 11, 309, 1355, 561, 567, 500, 380, 4196, 815, 312, 819, 490, 729, 567, 360, 4196, 13, 1171, 1365, 11, 7297, 286, 362, 257, 6889, 295, 18118, 1731, 13, 400, 286, 658, 13019, 490, 1230, 732, 11, 1230, 1732, 11], "avg_logprob": -0.1849459120287345, "compression_ratio": 1.4968152866242037, "no_speech_prob": 0.0, "words": [{"start": 714.25, "end": 714.57, "word": " on", "probability": 0.337890625}, {"start": 714.57, "end": 714.77, "word": " the", "probability": 0.9111328125}, {"start": 714.77, "end": 715.27, "word": " population", "probability": 0.9365234375}, {"start": 715.27, "end": 715.69, "word": " frame.", "probability": 0.6064453125}, {"start": 716.51, "end": 716.83, "word": " Non", "probability": 0.92724609375}, {"start": 716.83, "end": 717.37, "word": "-response", "probability": 0.8640950520833334}, {"start": 717.37, "end": 717.65, "word": " error", "probability": 0.685546875}, {"start": 717.65, "end": 718.17, "word": " bias,", "probability": 0.9609375}, {"start": 718.33, "end": 719.29, "word": " it", "probability": 0.92236328125}, {"start": 719.29, "end": 719.55, "word": " means", "probability": 0.9345703125}, {"start": 719.55, "end": 719.95, "word": " people", "probability": 0.92431640625}, {"start": 719.95, "end": 720.17, "word": " who", "probability": 0.90380859375}, {"start": 720.17, "end": 720.45, "word": " don't", "probability": 0.971435546875}, {"start": 720.45, "end": 721.05, "word": " respond", "probability": 0.8515625}, {"start": 721.05, "end": 721.41, "word": " may", "probability": 0.69873046875}, {"start": 721.41, "end": 721.51, "word": " be", "probability": 0.95849609375}, {"start": 721.51, "end": 721.93, "word": " different", "probability": 0.9072265625}, {"start": 721.93, "end": 722.27, "word": " from", "probability": 0.87548828125}, {"start": 722.27, "end": 722.75, "word": " those", "probability": 0.88232421875}, {"start": 722.75, "end": 723.01, "word": " who", "probability": 0.904296875}, {"start": 723.01, "end": 723.23, "word": " do", "probability": 0.9169921875}, {"start": 723.23, "end": 723.73, "word": " respond.", "probability": 0.87109375}, {"start": 724.31, "end": 724.63, "word": " For", "probability": 0.94921875}, {"start": 724.63, "end": 724.99, "word": " example,", "probability": 0.9716796875}, {"start": 725.97, "end": 726.45, "word": " suppose", "probability": 0.87939453125}, {"start": 726.45, "end": 727.51, "word": " I", "probability": 0.95263671875}, {"start": 727.51, "end": 727.85, "word": " have", "probability": 0.8603515625}, {"start": 727.85, "end": 728.13, "word": " a", "probability": 0.76220703125}, {"start": 728.13, "end": 728.53, "word": " sample", "probability": 0.89208984375}, {"start": 728.53, "end": 729.73, "word": " of", "probability": 0.9658203125}, {"start": 729.73, "end": 731.03, "word": " tennis", "probability": 0.908203125}, {"start": 731.03, "end": 731.41, "word": " students.", "probability": 0.6796875}, {"start": 735.91, "end": 736.73, "word": " And", "probability": 0.90966796875}, {"start": 736.73, "end": 736.87, "word": " I", "probability": 0.86474609375}, {"start": 736.87, "end": 737.21, "word": " got", "probability": 0.779296875}, {"start": 737.21, "end": 738.87, "word": " responses", "probability": 0.89794921875}, {"start": 738.87, "end": 739.57, "word": " from", "probability": 0.88720703125}, {"start": 739.57, "end": 740.33, "word": " number", "probability": 0.8857421875}, {"start": 740.33, "end": 740.69, "word": " two,", "probability": 0.71435546875}, {"start": 741.31, "end": 742.43, "word": " number", "probability": 0.93017578125}, {"start": 742.43, "end": 742.95, "word": " five,", "probability": 0.8994140625}], "temperature": 1.0}, {"id": 29, "seek": 77152, "start": 744.12, "end": 771.52, "text": " And number 10. So I have these point of views for these three students. Now the other seven students might be they have different opinions. 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The other type, Sample Error, variations from sample to sample will always exist. As I mentioned, here we select six samples, each one has different sample mean. 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So one more time, average error, it means you exclude a group or groups from the frame. So in this case, suppose I excluded these from my frame. So I just select the sample from all of these except this portion, or these two groups.", "tokens": [407, 300, 311, 264, 2010, 295, 8984, 13603, 13, 407, 472, 544, 565, 11, 4274, 6713, 11, 309, 1355, 291, 33536, 257, 1594, 420, 3935, 490, 264, 3920, 13, 407, 294, 341, 1389, 11, 7297, 286, 29486, 613, 490, 452, 3920, 13, 407, 286, 445, 3048, 264, 6889, 490, 439, 295, 613, 3993, 341, 8044, 11, 420, 613, 732, 3935, 13], "avg_logprob": -0.21396169138531532, "compression_ratio": 1.6071428571428572, "no_speech_prob": 0.0, "words": [{"start": 798.22, "end": 798.5, "word": " So", "probability": 0.8505859375}, {"start": 798.5, "end": 798.92, "word": " that's", "probability": 0.880615234375}, {"start": 798.92, "end": 799.2, "word": " the", "probability": 0.90771484375}, {"start": 799.2, "end": 799.74, "word": " type", "probability": 0.75048828125}, {"start": 799.74, "end": 800.64, "word": " of", "probability": 0.92529296875}, {"start": 800.64, "end": 801.46, "word": " survey", "probability": 0.80126953125}, {"start": 801.46, "end": 802.56, "word": " errors.", "probability": 0.70751953125}, {"start": 803.7, "end": 803.94, "word": " So", "probability": 0.94140625}, {"start": 803.94, "end": 804.16, "word": " one", "probability": 0.77978515625}, {"start": 804.16, "end": 804.34, "word": " more", "probability": 0.93310546875}, {"start": 804.34, "end": 804.7, "word": " time,", "probability": 0.87548828125}, {"start": 805.18, "end": 805.6, "word": " average", "probability": 0.322021484375}, {"start": 805.6, "end": 805.98, "word": " error,", "probability": 0.79931640625}, {"start": 806.26, "end": 806.48, "word": " it", "probability": 0.7470703125}, {"start": 806.48, "end": 806.82, "word": " means", "probability": 0.93115234375}, {"start": 806.82, "end": 807.16, "word": " you", "probability": 0.9404296875}, {"start": 807.16, "end": 808.34, "word": " exclude", "probability": 0.86865234375}, {"start": 808.34, "end": 809.54, "word": " a", "probability": 0.381103515625}, {"start": 809.54, "end": 809.84, "word": " group", "probability": 0.96484375}, {"start": 809.84, "end": 810.04, "word": " or", "probability": 0.939453125}, {"start": 810.04, "end": 810.54, "word": " groups", "probability": 0.9208984375}, {"start": 810.54, "end": 812.12, "word": " from", "probability": 0.8623046875}, {"start": 812.12, "end": 812.32, "word": " the", "probability": 0.7353515625}, {"start": 812.32, "end": 812.6, "word": " frame.", "probability": 0.9013671875}, {"start": 813.06, "end": 813.28, "word": " So", "probability": 0.93994140625}, {"start": 813.28, "end": 813.76, "word": " in", "probability": 0.82763671875}, {"start": 813.76, "end": 813.92, "word": " this", "probability": 0.94482421875}, {"start": 813.92, "end": 814.12, "word": " case,", "probability": 0.91455078125}, {"start": 814.16, "end": 814.34, "word": " suppose", "probability": 0.861328125}, {"start": 814.34, "end": 814.54, "word": " I", "probability": 0.97216796875}, {"start": 814.54, "end": 815.08, "word": " excluded", "probability": 0.89013671875}, {"start": 815.08, "end": 815.52, "word": " these", "probability": 0.466064453125}, {"start": 815.52, "end": 816.28, "word": " from", "probability": 0.88037109375}, {"start": 816.28, "end": 816.48, "word": " my", "probability": 0.96630859375}, {"start": 816.48, "end": 816.82, "word": " frame.", "probability": 0.85009765625}, {"start": 817.6, "end": 817.8, "word": " So", "probability": 0.87451171875}, {"start": 817.8, "end": 817.96, "word": " I", "probability": 0.91357421875}, {"start": 817.96, "end": 819.36, "word": " just", "probability": 0.91943359375}, {"start": 819.36, "end": 819.88, "word": " select", "probability": 0.73779296875}, {"start": 819.88, "end": 820.1, "word": " the", "probability": 0.75244140625}, {"start": 820.1, "end": 820.38, "word": " sample", "probability": 0.64208984375}, {"start": 820.38, "end": 820.84, "word": " from", "probability": 0.8798828125}, {"start": 820.84, "end": 821.98, "word": " all", "probability": 0.9482421875}, {"start": 821.98, "end": 822.1, "word": " of", "probability": 0.9658203125}, {"start": 822.1, "end": 822.4, "word": " these", "probability": 0.69873046875}, {"start": 822.4, "end": 823.52, "word": " except", "probability": 0.6435546875}, {"start": 823.52, "end": 824.48, "word": " this", "probability": 0.9375}, {"start": 824.48, "end": 824.94, "word": " portion,", "probability": 0.89697265625}, {"start": 825.4, "end": 825.74, "word": " or", "probability": 0.6298828125}, {"start": 825.74, "end": 825.94, "word": " these", "probability": 0.837890625}, {"start": 825.94, "end": 826.16, "word": " two", "probability": 0.9326171875}, {"start": 826.16, "end": 826.52, "word": " groups.", "probability": 0.931640625}], "temperature": 1.0}, {"id": 32, "seek": 85192, "start": 827.06, "end": 851.92, "text": " Non-response error means you don't have follow-up on non-responses. Sampling error, random sample gives different sample statistics. So it means random differences from sample to sample. Final measurement error, bad or leading questions. This is one of the most important ones that you have to avoid.", "tokens": [8774, 12, 5667, 3739, 6713, 1355, 291, 500, 380, 362, 1524, 12, 1010, 322, 2107, 12, 28930, 279, 13, 4832, 11970, 6713, 11, 4974, 6889, 2709, 819, 6889, 12523, 13, 407, 309, 1355, 4974, 7300, 490, 6889, 281, 6889, 13, 13443, 13160, 6713, 11, 1578, 420, 5775, 1651, 13, 639, 307, 472, 295, 264, 881, 1021, 2306, 300, 291, 362, 281, 5042, 13], "avg_logprob": -0.20654297294095159, "compression_ratio": 1.601063829787234, "no_speech_prob": 0.0, "words": [{"start": 827.06, "end": 827.36, "word": " Non", "probability": 0.90625}, {"start": 827.36, "end": 827.86, "word": "-response", "probability": 0.8229166666666666}, {"start": 827.86, "end": 828.18, "word": " error", "probability": 0.7783203125}, {"start": 828.18, "end": 828.94, "word": " means", "probability": 0.828125}, {"start": 828.94, "end": 829.12, "word": " you", "probability": 0.9345703125}, {"start": 829.12, "end": 829.3, "word": " don't", "probability": 0.902587890625}, {"start": 829.3, "end": 829.5, "word": " have", "probability": 0.9326171875}, {"start": 829.5, "end": 829.68, "word": " follow", "probability": 0.7978515625}, {"start": 829.68, "end": 829.94, "word": "-up", "probability": 0.747314453125}, {"start": 829.94, "end": 830.28, "word": " on", "probability": 0.93408203125}, {"start": 830.28, "end": 830.62, "word": " non", "probability": 0.95947265625}, {"start": 830.62, "end": 831.28, "word": "-responses.", "probability": 0.8904622395833334}, {"start": 832.18, "end": 832.56, "word": " Sampling", "probability": 0.951171875}, {"start": 832.56, "end": 832.92, "word": " error,", "probability": 0.8583984375}, {"start": 834.06, "end": 834.5, "word": " random", "probability": 0.82177734375}, {"start": 834.5, "end": 835.9, "word": " sample", "probability": 0.6494140625}, {"start": 835.9, "end": 837.0, "word": " gives", "probability": 0.84228515625}, {"start": 837.0, "end": 837.56, "word": " different", "probability": 0.86962890625}, {"start": 837.56, "end": 838.0, "word": " sample", "probability": 0.76611328125}, {"start": 838.0, "end": 838.72, "word": " statistics.", "probability": 0.8662109375}, {"start": 839.04, "end": 839.16, "word": " So", "probability": 0.904296875}, {"start": 839.16, "end": 839.26, "word": " it", "probability": 0.82958984375}, {"start": 839.26, "end": 839.44, "word": " means", "probability": 0.9091796875}, {"start": 839.44, "end": 839.86, "word": " random", "probability": 0.84814453125}, {"start": 839.86, "end": 840.42, "word": " differences", "probability": 0.58740234375}, {"start": 840.42, "end": 840.82, "word": " from", "probability": 0.884765625}, {"start": 840.82, "end": 841.18, "word": " sample", "probability": 0.884765625}, {"start": 841.18, "end": 841.4, "word": " to", "probability": 0.9599609375}, {"start": 841.4, "end": 841.66, "word": " sample.", "probability": 0.89404296875}, {"start": 843.12, "end": 843.6, "word": " Final", "probability": 0.71923828125}, {"start": 843.6, "end": 844.0, "word": " measurement", "probability": 0.79150390625}, {"start": 844.0, "end": 844.46, "word": " error,", "probability": 0.88427734375}, {"start": 844.8, "end": 845.06, "word": " bad", "probability": 0.92236328125}, {"start": 845.06, "end": 845.34, "word": " or", "probability": 0.9599609375}, {"start": 845.34, "end": 845.76, "word": " leading", "probability": 0.96044921875}, {"start": 845.76, "end": 846.86, "word": " questions.", "probability": 0.148681640625}, {"start": 847.04, "end": 847.16, "word": " This", "probability": 0.7490234375}, {"start": 847.16, "end": 847.26, "word": " is", "probability": 0.927734375}, {"start": 847.26, "end": 847.5, "word": " one", "probability": 0.720703125}, {"start": 847.5, "end": 847.7, "word": " of", "probability": 0.9111328125}, {"start": 847.7, "end": 847.82, "word": " the", "probability": 0.892578125}, {"start": 847.82, "end": 848.14, "word": " most", "probability": 0.8916015625}, {"start": 848.14, "end": 849.02, "word": " important", "probability": 0.88818359375}, {"start": 849.02, "end": 849.26, "word": " ones", "probability": 0.325927734375}, {"start": 849.26, "end": 849.46, "word": " that", "probability": 0.8857421875}, {"start": 849.46, "end": 849.62, "word": " you", "probability": 0.947265625}, {"start": 849.62, "end": 849.92, "word": " have", "probability": 0.93701171875}, {"start": 849.92, "end": 850.98, "word": " to", "probability": 0.9599609375}, {"start": 850.98, "end": 851.92, "word": " avoid.", "probability": 0.9296875}], "temperature": 1.0}, {"id": 33, "seek": 87889, "start": 852.79, "end": 878.89, "text": " So that's the first part of this chapter, assembling techniques. Do you have any questions? Next, we'll talk about assembling distributions. 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For example, suppose X represents your score in business statistics course. And suppose we know that X is normally distributed with mean of 80, standard deviation of 10.", "tokens": [1171, 1365, 11, 295, 15866, 1783, 5044, 813, 11, 337, 1365, 11, 1614, 13, 1171, 1365, 11, 7297, 1783, 8855, 428, 6175, 294, 1606, 12523, 1164, 13, 400, 7297, 321, 458, 300, 1783, 307, 5646, 12631, 365, 914, 295, 4688, 11, 3832, 25163, 295, 1266, 13], "avg_logprob": -0.22174202127659576, "compression_ratio": 1.4522292993630572, "no_speech_prob": 0.0, "words": [{"start": 879.62, "end": 879.94, "word": " For", "probability": 0.4375}, {"start": 879.94, "end": 880.42, "word": " example,", "probability": 0.9658203125}, {"start": 880.68, "end": 880.84, "word": " of", "probability": 0.4443359375}, {"start": 880.84, "end": 881.5, "word": " computing", "probability": 0.8486328125}, {"start": 881.5, "end": 882.08, "word": " X", "probability": 0.5078125}, {"start": 882.08, "end": 884.0, "word": " greater", "probability": 0.5263671875}, {"start": 884.0, "end": 884.32, "word": " than,", "probability": 0.943359375}, {"start": 884.38, "end": 884.5, "word": " for", "probability": 0.94384765625}, {"start": 884.5, "end": 884.82, "word": " example,", "probability": 0.97314453125}, {"start": 884.96, "end": 885.22, "word": " 7.", "probability": 0.525390625}, {"start": 886.22, "end": 886.58, "word": " For", "probability": 0.92431640625}, {"start": 886.58, "end": 886.8, "word": " example,", "probability": 0.970703125}, {"start": 886.88, "end": 887.32, "word": " suppose", "probability": 0.9091796875}, {"start": 887.32, "end": 888.22, "word": " X", "probability": 0.8916015625}, {"start": 888.22, "end": 889.2, "word": " represents", "probability": 0.85400390625}, {"start": 889.2, "end": 891.32, "word": " your", "probability": 0.888671875}, {"start": 891.32, "end": 892.98, "word": " score", "probability": 0.84814453125}, {"start": 892.98, "end": 893.26, "word": " in", "probability": 0.9375}, {"start": 893.26, "end": 893.76, "word": " business", "probability": 0.69384765625}, {"start": 893.76, "end": 894.42, "word": " statistics", "probability": 0.44384765625}, {"start": 894.42, "end": 895.02, "word": " course.", "probability": 0.927734375}, {"start": 897.68, "end": 898.04, "word": " And", "probability": 0.92138671875}, {"start": 898.04, "end": 898.38, "word": " suppose", "probability": 0.8740234375}, {"start": 898.38, "end": 898.54, "word": " we", "probability": 0.6455078125}, {"start": 898.54, "end": 898.68, "word": " know", "probability": 0.8876953125}, {"start": 898.68, "end": 899.12, "word": " that", "probability": 0.931640625}, {"start": 899.12, "end": 900.04, "word": " X", "probability": 0.96630859375}, {"start": 900.04, "end": 901.52, "word": " is", "probability": 0.94580078125}, {"start": 901.52, "end": 901.94, "word": " normally", "probability": 0.9091796875}, {"start": 901.94, "end": 902.68, "word": " distributed", "probability": 0.89794921875}, {"start": 902.68, "end": 903.52, "word": " with", "probability": 0.84765625}, {"start": 903.52, "end": 903.92, "word": " mean", "probability": 0.966796875}, {"start": 903.92, "end": 905.16, "word": " of", "probability": 0.951171875}, {"start": 905.16, "end": 905.76, "word": " 80,", "probability": 0.8935546875}, {"start": 906.86, "end": 907.32, "word": " standard", "probability": 0.82958984375}, {"start": 907.32, "end": 907.7, "word": " deviation", "probability": 0.89697265625}, {"start": 907.7, "end": 907.94, "word": " of", "probability": 0.95068359375}, {"start": 907.94, "end": 908.2, "word": " 10.", "probability": 0.94677734375}], "temperature": 1.0}, {"id": 35, "seek": 93350, "start": 910.54, "end": 933.5, "text": " My question was, in chapter 6, what's the probability that the student scores more than 70? Suppose we select randomly one student, and the question is, what's the probability that his score, so just for one individual, for one student, his score is above 70?", "tokens": [1222, 1168, 390, 11, 294, 7187, 1386, 11, 437, 311, 264, 8482, 300, 264, 3107, 13444, 544, 813, 5285, 30, 21360, 321, 3048, 16979, 472, 3107, 11, 293, 264, 1168, 307, 11, 437, 311, 264, 8482, 300, 702, 6175, 11, 370, 445, 337, 472, 2609, 11, 337, 472, 3107, 11, 702, 6175, 307, 3673, 5285, 30], "avg_logprob": -0.1640625, "compression_ratio": 1.6774193548387097, "no_speech_prob": 0.0, "words": [{"start": 910.54, "end": 910.86, "word": " My", "probability": 0.78271484375}, {"start": 910.86, "end": 911.3, "word": " question", "probability": 0.9189453125}, {"start": 911.3, "end": 911.76, "word": " was,", "probability": 0.94140625}, {"start": 912.28, "end": 912.62, "word": " in", "probability": 0.822265625}, {"start": 912.62, "end": 912.82, "word": " chapter", "probability": 0.513671875}, {"start": 912.82, "end": 913.32, "word": " 6,", "probability": 0.66162109375}, {"start": 914.4, "end": 914.82, "word": " what's", "probability": 0.810546875}, {"start": 914.82, "end": 914.96, "word": " the", "probability": 0.90771484375}, {"start": 914.96, "end": 915.36, "word": " probability", "probability": 0.9482421875}, {"start": 915.36, "end": 915.82, "word": " that", "probability": 0.9267578125}, {"start": 915.82, "end": 917.06, "word": " the", "probability": 0.84033203125}, {"start": 917.06, "end": 917.58, "word": " student", "probability": 0.94091796875}, {"start": 917.58, "end": 918.54, "word": " scores", "probability": 0.826171875}, {"start": 918.54, "end": 919.92, "word": " more", "probability": 0.93359375}, {"start": 919.92, "end": 920.12, "word": " than", "probability": 0.9541015625}, {"start": 920.12, "end": 920.46, "word": " 70?", "probability": 0.9580078125}, {"start": 922.54, "end": 923.22, "word": " Suppose", "probability": 0.7119140625}, {"start": 923.22, "end": 923.38, "word": " we", "probability": 0.896484375}, {"start": 923.38, "end": 923.74, "word": " select", "probability": 0.85595703125}, {"start": 923.74, "end": 924.28, "word": " randomly", "probability": 0.83154296875}, {"start": 924.28, "end": 924.5, "word": " one", "probability": 0.8857421875}, {"start": 924.5, "end": 924.86, "word": " student,", "probability": 0.96337890625}, {"start": 925.8, "end": 926.06, "word": " and", "probability": 0.9189453125}, {"start": 926.06, "end": 926.18, "word": " the", "probability": 0.921875}, {"start": 926.18, "end": 926.46, "word": " question", "probability": 0.9208984375}, {"start": 926.46, "end": 926.72, "word": " is,", "probability": 0.94921875}, {"start": 926.84, "end": 927.1, "word": " what's", "probability": 0.86328125}, {"start": 927.1, "end": 927.2, "word": " the", "probability": 0.91357421875}, {"start": 927.2, "end": 927.54, "word": " probability", "probability": 0.95361328125}, {"start": 927.54, "end": 928.06, "word": " that", "probability": 0.9365234375}, {"start": 928.06, "end": 928.48, "word": " his", "probability": 0.9375}, {"start": 928.48, "end": 929.04, "word": " score,", "probability": 0.89892578125}, {"start": 929.44, "end": 929.6, "word": " so", "probability": 0.4814453125}, {"start": 929.6, "end": 929.8, "word": " just", "probability": 0.876953125}, {"start": 929.8, "end": 929.98, "word": " for", "probability": 0.9306640625}, {"start": 929.98, "end": 930.16, "word": " one", "probability": 0.92822265625}, {"start": 930.16, "end": 930.62, "word": " individual,", "probability": 0.92138671875}, {"start": 930.72, "end": 930.86, "word": " for", "probability": 0.7998046875}, {"start": 930.86, "end": 931.0, "word": " one", "probability": 0.92626953125}, {"start": 931.0, "end": 931.38, "word": " student,", "probability": 0.9599609375}, {"start": 932.02, "end": 932.3, "word": " his", "probability": 0.94140625}, {"start": 932.3, "end": 932.6, "word": " score", "probability": 0.90087890625}, {"start": 932.6, "end": 932.76, "word": " is", "probability": 0.9423828125}, {"start": 932.76, "end": 933.04, "word": " above", "probability": 0.96826171875}, {"start": 933.04, "end": 933.5, "word": " 70?", "probability": 0.96435546875}], "temperature": 1.0}, {"id": 36, "seek": 95735, "start": 935.67, "end": 957.35, "text": " In that case, if you remember, we transform from normal distribution to standard normal distribution by using this equation, which is x minus the mean divided by sigma. The mean, this one, it means the mean of x. And sigma is also x.", "tokens": [682, 300, 1389, 11, 498, 291, 1604, 11, 321, 4088, 490, 2710, 7316, 281, 3832, 2710, 7316, 538, 1228, 341, 5367, 11, 597, 307, 2031, 3175, 264, 914, 6666, 538, 12771, 13, 440, 914, 11, 341, 472, 11, 309, 1355, 264, 914, 295, 2031, 13, 400, 12771, 307, 611, 2031, 13], "avg_logprob": -0.2579627501276823, "compression_ratio": 1.56, "no_speech_prob": 0.0, "words": [{"start": 935.67, "end": 935.89, "word": " In", "probability": 0.294677734375}, {"start": 935.89, "end": 936.07, "word": " that", "probability": 0.8515625}, {"start": 936.07, "end": 936.29, "word": " case,", "probability": 0.921875}, {"start": 936.39, "end": 936.47, "word": " if", "probability": 0.64990234375}, {"start": 936.47, "end": 936.51, "word": " you", "probability": 0.90380859375}, {"start": 936.51, "end": 936.77, "word": " remember,", "probability": 0.86181640625}, {"start": 936.87, "end": 936.99, "word": " we", "probability": 0.9423828125}, {"start": 936.99, "end": 937.55, "word": " 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which", "probability": 0.7841796875}, {"start": 945.05, "end": 945.19, "word": " is", "probability": 0.94775390625}, {"start": 945.19, "end": 945.63, "word": " x", "probability": 0.56982421875}, {"start": 945.63, "end": 946.93, "word": " minus", "probability": 0.94921875}, {"start": 946.93, "end": 947.17, "word": " the", "probability": 0.80029296875}, {"start": 947.17, "end": 947.43, "word": " mean", "probability": 0.982421875}, {"start": 947.43, "end": 948.17, "word": " divided", "probability": 0.638671875}, {"start": 948.17, "end": 948.49, "word": " by", "probability": 0.978515625}, {"start": 948.49, "end": 948.77, "word": " sigma.", "probability": 0.86181640625}, {"start": 950.45, "end": 951.01, "word": " The", "probability": 0.837890625}, {"start": 951.01, "end": 951.29, "word": " mean,", "probability": 0.9580078125}, {"start": 951.43, "end": 951.61, "word": " this", "probability": 0.896484375}, {"start": 951.61, "end": 951.91, "word": " one,", "probability": 0.9189453125}, {"start": 952.51, "end": 952.79, "word": " it", "probability": 0.77099609375}, {"start": 952.79, "end": 953.01, "word": " means", "probability": 0.91259765625}, {"start": 953.01, "end": 953.17, "word": " the", "probability": 0.84814453125}, {"start": 953.17, "end": 953.27, "word": " mean", "probability": 0.90771484375}, {"start": 953.27, "end": 953.41, "word": " of", "probability": 0.96875}, {"start": 953.41, "end": 953.77, "word": " x.", "probability": 0.95263671875}, {"start": 955.83, "end": 956.09, "word": " And", "probability": 0.9287109375}, {"start": 956.09, "end": 956.39, "word": " sigma", "probability": 0.91064453125}, {"start": 956.39, "end": 956.63, "word": " is", "probability": 0.95556640625}, {"start": 956.63, "end": 956.93, "word": " also", "probability": 0.87451171875}, {"start": 956.93, "end": 957.35, "word": " x.", "probability": 0.53369140625}], "temperature": 1.0}, {"id": 37, "seek": 98726, "start": 959.06, "end": 987.26, "text": " Now suppose instead of saying what's the probability that a selected student scores more than 70 or above 70, suppose we select a random sample of 20 or whatever it is, 20 students from this class, and I'm interested in the probability that the average score of these 20 students is above 70.", "tokens": [823, 7297, 2602, 295, 1566, 437, 311, 264, 8482, 300, 257, 8209, 3107, 13444, 544, 813, 5285, 420, 3673, 5285, 11, 7297, 321, 3048, 257, 4974, 6889, 295, 945, 420, 2035, 309, 307, 11, 945, 1731, 490, 341, 1508, 11, 293, 286, 478, 3102, 294, 264, 8482, 300, 264, 4274, 6175, 295, 613, 945, 1731, 307, 3673, 5285, 13], "avg_logprob": -0.18841145311792692, "compression_ratio": 1.646067415730337, "no_speech_prob": 0.0, "words": [{"start": 959.06, "end": 959.44, "word": " Now", "probability": 0.88720703125}, {"start": 959.44, "end": 960.02, "word": " suppose", "probability": 0.51904296875}, {"start": 960.02, "end": 960.58, "word": " instead", "probability": 0.6455078125}, {"start": 960.58, "end": 960.88, "word": " of", "probability": 0.96923828125}, {"start": 960.88, "end": 961.36, "word": " saying", "probability": 0.70849609375}, {"start": 961.36, "end": 961.8, "word": " what's", "probability": 0.747314453125}, {"start": 961.8, "end": 961.92, "word": " the", "probability": 0.8369140625}, {"start": 961.92, "end": 962.3, "word": " probability", "probability": 0.947265625}, {"start": 962.3, "end": 962.64, "word": " that", "probability": 0.87548828125}, {"start": 962.64, "end": 962.84, "word": " a", "probability": 0.68359375}, {"start": 962.84, "end": 963.2, "word": " selected", "probability": 0.9296875}, {"start": 963.2, "end": 963.82, "word": " student", "probability": 0.94189453125}, {"start": 963.82, "end": 964.48, "word": " scores", "probability": 0.82373046875}, {"start": 964.48, "end": 965.62, "word": " more", "probability": 0.92626953125}, {"start": 965.62, "end": 965.82, "word": " than", "probability": 0.95361328125}, {"start": 965.82, "end": 966.42, "word": " 70", "probability": 0.8740234375}, 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101301, "start": 989.23, "end": 1013.01, "text": " Now look at the difference between two portions. First one, we select a student randomly, and we are asking about what's the probability that this selected student can score above 70. 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So, exactly, if the population is normal, then the shape is also normal, but otherwise, we have to think about it. This is the first question. Now, there are two unknowns in this equation. 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So by sampling distribution we mean that, by sampling distribution, we mean that you have to know the center of distribution,", "tokens": [823, 3909, 11, 3056, 11, 3974, 11, 613, 366, 10891, 11, 613, 10891, 294, 341, 1389, 21179, 7316, 11, 2293, 597, 307, 1219, 21179, 7316, 13, 407, 538, 21179, 7316, 321, 914, 300, 11, 538, 21179, 7316, 11, 321, 914, 300, 291, 362, 281, 458, 264, 3056, 295, 7316, 11], "avg_logprob": -0.3014705929101682, "compression_ratio": 1.993006993006993, "no_speech_prob": 0.0, "words": [{"start": 1178.51, "end": 1178.85, "word": " Now", "probability": 0.74365234375}, {"start": 1178.85, "end": 1179.35, "word": " shape,", "probability": 0.5751953125}, {"start": 1179.85, "end": 1180.15, "word": " center,", "probability": 0.57373046875}, {"start": 1180.45, "end": 1180.95, "word": " spread,", "probability": 0.139892578125}, {"start": 1181.53, "end": 1181.85, "word": " these", "probability": 0.8486328125}, {"start": 1181.85, "end": 1182.17, "word": " are", "probability": 0.93115234375}, {"start": 1182.17, "end": 1183.15, "word": " characteristics,", "probability": 0.861328125}, {"start": 1184.29, "end": 1184.59, "word": " these", "probability": 0.6923828125}, {"start": 1184.59, "end": 1185.31, "word": " characteristics", "probability": 0.88671875}, {"start": 1185.31, "end": 1185.79, "word": " in", "probability": 0.75439453125}, {"start": 1185.79, "end": 1185.99, "word": " this", "probability": 0.95068359375}, {"start": 1185.99, "end": 1186.41, "word": " case", "probability": 0.92138671875}, {"start": 1186.41, "end": 1187.77, "word": " sampling", "probability": 0.2498779296875}, {"start": 1187.77, "end": 1188.23, "word": " distribution,", "probability": 0.7822265625}, {"start": 1188.67, "end": 1189.17, "word": " exactly", "probability": 0.8310546875}, {"start": 1189.17, "end": 1189.75, "word": " which", "probability": 0.482177734375}, {"start": 1189.75, "end": 1189.91, "word": " is", "probability": 0.67529296875}, {"start": 1189.91, "end": 1190.09, "word": " called", "probability": 0.890625}, {"start": 1190.09, "end": 1190.49, "word": " sampling", "probability": 0.94921875}, {"start": 1190.49, "end": 1191.25, "word": " distribution.", "probability": 0.83935546875}, {"start": 1192.97, "end": 1193.85, "word": " So", "probability": 0.87939453125}, {"start": 1193.85, "end": 1194.67, "word": " by", "probability": 0.80078125}, {"start": 1194.67, "end": 1194.99, "word": " sampling", "probability": 0.9052734375}, {"start": 1194.99, "end": 1195.57, "word": " distribution", "probability": 0.86181640625}, {"start": 1195.57, "end": 1195.89, "word": " we", "probability": 0.58251953125}, {"start": 1195.89, "end": 1196.13, "word": " mean", "probability": 0.962890625}, {"start": 1196.13, "end": 1196.61, "word": " that,", "probability": 0.93212890625}, {"start": 1197.05, "end": 1197.79, "word": " by", "probability": 0.921875}, {"start": 1197.79, "end": 1198.13, "word": " sampling", "probability": 0.96142578125}, {"start": 1198.13, "end": 1198.79, "word": " distribution,", "probability": 0.873046875}, {"start": 1199.41, "end": 1199.55, "word": " we", "probability": 0.84130859375}, {"start": 1199.55, "end": 1199.71, "word": " mean", "probability": 0.962890625}, {"start": 1199.71, "end": 1199.97, "word": " that", "probability": 0.9345703125}, {"start": 1199.97, "end": 1200.11, "word": " you", "probability": 0.9326171875}, {"start": 1200.11, "end": 1200.31, "word": " have", "probability": 0.9501953125}, {"start": 1200.31, "end": 1200.43, "word": " to", "probability": 0.9736328125}, {"start": 1200.43, "end": 1200.65, "word": " know", "probability": 0.88671875}, {"start": 1200.65, "end": 1201.87, "word": " the", "probability": 0.6162109375}, {"start": 1201.87, "end": 1202.85, "word": " center", "probability": 0.8896484375}, {"start": 1202.85, "end": 1203.05, "word": " of", "probability": 0.95751953125}, {"start": 1203.05, "end": 1203.63, "word": " distribution,", "probability": 0.76220703125}], "temperature": 1.0}, {"id": 47, "seek": 122940, "start": 1205.46, "end": 1229.4, "text": " I mean the mean of the statistic you are interested in. Second, the spread or the variability of the sample statistic also you are interested in. In addition to that, you have to know the shape of the statistic. So three things we have to know, center, spread and shape.", "tokens": [286, 914, 264, 914, 295, 264, 29588, 291, 366, 3102, 294, 13, 5736, 11, 264, 3974, 420, 264, 35709, 295, 264, 6889, 29588, 611, 291, 366, 3102, 294, 13, 682, 4500, 281, 300, 11, 291, 362, 281, 458, 264, 3909, 295, 264, 29588, 13, 407, 1045, 721, 321, 362, 281, 458, 11, 3056, 11, 3974, 293, 3909, 13], "avg_logprob": -0.17478813963421322, "compression_ratio": 1.8310810810810811, "no_speech_prob": 0.0, "words": [{"start": 1205.46, "end": 1205.7, "word": " I", "probability": 0.77490234375}, {"start": 1205.7, "end": 1205.84, "word": " mean", "probability": 0.96142578125}, {"start": 1205.84, "end": 1206.04, "word": " the", "probability": 0.62744140625}, {"start": 1206.04, "end": 1206.34, "word": " mean", "probability": 0.74560546875}, {"start": 1206.34, "end": 1206.82, "word": " of", "probability": 0.96533203125}, {"start": 1206.82, "end": 1207.02, "word": " the", "probability": 0.91357421875}, {"start": 1207.02, "end": 1207.44, "word": " statistic", "probability": 0.84033203125}, {"start": 1207.44, "end": 1207.68, "word": " you", "probability": 0.943359375}, {"start": 1207.68, "end": 1207.82, "word": " are", "probability": 0.8955078125}, {"start": 1207.82, "end": 1208.32, "word": " interested", "probability": 0.8720703125}, {"start": 1208.32, "end": 1208.76, "word": " in.", "probability": 0.947265625}, {"start": 1209.54, "end": 1209.9, "word": " Second,", "probability": 0.826171875}, {"start": 1210.7, "end": 1211.08, "word": " the", "probability": 0.904296875}, {"start": 1211.08, "end": 1211.56, "word": " spread", "probability": 0.88671875}, {"start": 1211.56, "end": 1212.3, "word": " or", "probability": 0.84033203125}, {"start": 1212.3, "end": 1212.56, "word": " the", "probability": 0.67333984375}, {"start": 1212.56, "end": 1213.22, "word": " variability", "probability": 0.978515625}, {"start": 1213.22, "end": 1214.4, "word": " of", "probability": 0.9580078125}, {"start": 1214.4, "end": 1214.62, "word": " the", "probability": 0.92236328125}, {"start": 1214.62, "end": 1214.88, "word": " sample", "probability": 0.79736328125}, {"start": 1214.88, "end": 1215.48, "word": " statistic", "probability": 0.765625}, {"start": 1215.48, "end": 1215.92, "word": " also", "probability": 0.60302734375}, {"start": 1215.92, "end": 1216.06, "word": " you", "probability": 0.91845703125}, {"start": 1216.06, "end": 1216.16, "word": " are", "probability": 0.8935546875}, {"start": 1216.16, "end": 1216.6, "word": " interested", "probability": 0.86083984375}, {"start": 1216.6, "end": 1216.94, "word": " in.", "probability": 0.94921875}, {"start": 1217.42, "end": 1217.6, "word": " In", "probability": 0.951171875}, {"start": 1217.6, "end": 1217.9, "word": " addition", "probability": 0.9560546875}, {"start": 1217.9, "end": 1218.1, "word": " to", "probability": 0.96533203125}, {"start": 1218.1, "end": 1218.3, "word": " that,", "probability": 0.93994140625}, {"start": 1218.38, "end": 1218.44, "word": " you", "probability": 0.95947265625}, {"start": 1218.44, "end": 1218.62, "word": " have", "probability": 0.943359375}, {"start": 1218.62, "end": 1218.74, "word": " to", "probability": 0.970703125}, {"start": 1218.74, "end": 1218.96, "word": " know", "probability": 0.89013671875}, {"start": 1218.96, "end": 1220.26, "word": " the", "probability": 0.9072265625}, {"start": 1220.26, "end": 1220.94, "word": " shape", "probability": 0.92919921875}, {"start": 1220.94, "end": 1221.24, "word": " of", "probability": 0.9697265625}, {"start": 1221.24, "end": 1221.4, "word": " the", "probability": 0.89306640625}, {"start": 1221.4, "end": 1221.8, "word": " statistic.", "probability": 0.89453125}, {"start": 1222.74, "end": 1223.0, "word": " So", "probability": 0.9560546875}, {"start": 1223.0, "end": 1223.38, "word": " three", "probability": 0.6201171875}, {"start": 1223.38, "end": 1224.46, "word": " things", "probability": 0.857421875}, {"start": 1224.46, "end": 1224.6, "word": " we", "probability": 0.7236328125}, {"start": 1224.6, "end": 1224.76, "word": " have", "probability": 0.94970703125}, {"start": 1224.76, "end": 1224.88, "word": " to", "probability": 0.96923828125}, {"start": 1224.88, "end": 1225.08, "word": " know,", "probability": 0.890625}, {"start": 1225.82, "end": 1226.2, "word": " center,", "probability": 0.62744140625}, {"start": 1227.22, "end": 1227.92, "word": " spread", "probability": 0.9033203125}, {"start": 1227.92, "end": 1229.06, "word": " and", "probability": 0.580078125}, {"start": 1229.06, "end": 1229.4, "word": " shape.", "probability": 0.89892578125}], "temperature": 1.0}, {"id": 48, "seek": 125904, "start": 1230.52, "end": 1259.04, "text": " So that's what we'll talk about now. So now sampling distribution is a distribution of all of the possible values of a sample statistic. This sample statistic could be sample mean, could be sample variance, could be sample proportion, because any population has mainly three characteristics, mean, standard deviation, and proportion.", "tokens": [407, 300, 311, 437, 321, 603, 751, 466, 586, 13, 407, 586, 21179, 7316, 307, 257, 7316, 295, 439, 295, 264, 1944, 4190, 295, 257, 6889, 29588, 13, 639, 6889, 29588, 727, 312, 6889, 914, 11, 727, 312, 6889, 21977, 11, 727, 312, 6889, 16068, 11, 570, 604, 4415, 575, 8704, 1045, 10891, 11, 914, 11, 3832, 25163, 11, 293, 16068, 13], "avg_logprob": -0.1686507941238464, "compression_ratio": 1.8054054054054054, "no_speech_prob": 0.0, "words": [{"start": 1230.52, "end": 1230.78, "word": " So", "probability": 0.74267578125}, {"start": 1230.78, "end": 1231.28, "word": " that's", "probability": 0.814697265625}, {"start": 1231.28, "end": 1231.76, "word": " what", "probability": 0.9404296875}, {"start": 1231.76, "end": 1231.98, "word": " we'll", "probability": 0.806640625}, {"start": 1231.98, 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again, a sampling distribution is a distribution of all of the possible values of a sample statistic or a given size sample selected from a population. For example, suppose you sample 50 students from your college regarding their mean GPA. 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As I mentioned here, I select a sample the same sizes, but we obtain different sample statistics, I mean different sample means. 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So let's focus into these values. So we have again a random sample of 50 sample means. So we have 1, 2, 3, 4, 5, maybe 50, 6, whatever we have. So select a random sample of size 20. Maybe we repeat this sample 10 times. 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Now we have new ten means. Now the question is, what's the center of these values, I mean for the means? What's the spread of the means? And what's the shape of the means? So these are the mainly three questions.", "tokens": [819, 4190, 295, 264, 2199, 1355, 13, 823, 321, 362, 777, 2064, 1355, 13, 823, 264, 1168, 307, 11, 437, 311, 264, 3056, 295, 613, 4190, 11, 286, 914, 337, 264, 1355, 30, 708, 311, 264, 3974, 295, 264, 1355, 30, 400, 437, 311, 264, 3909, 295, 264, 1355, 30, 407, 613, 366, 264, 8704, 1045, 1651, 13], "avg_logprob": -0.21623410966436743, "compression_ratio": 1.7310344827586206, "no_speech_prob": 0.0, "words": [{"start": 1348.01, "end": 1348.59, "word": " different", "probability": 0.423828125}, {"start": 1348.59, "end": 1349.19, "word": " values", "probability": 0.96044921875}, {"start": 1349.19, "end": 1349.47, "word": " of", "probability": 0.94970703125}, {"start": 1349.47, "end": 1349.65, "word": " the", "probability": 0.83837890625}, {"start": 1349.65, "end": 1349.91, "word": " simple", "probability": 0.35791015625}, {"start": 1349.91, "end": 1350.17, "word": " means.", "probability": 0.58740234375}, {"start": 1350.39, "end": 1350.57, "word": " Now", "probability": 0.890625}, {"start": 1350.57, "end": 1350.69, "word": " we", "probability": 0.685546875}, {"start": 1350.69, "end": 1350.93, "word": " have", "probability": 0.951171875}, {"start": 1350.93, "end": 1351.35, "word": " new", "probability": 0.5634765625}, {"start": 1351.35, "end": 1351.65, "word": " ten", "probability": 0.461181640625}, {"start": 1351.65, "end": 1352.19, "word": " means.", "probability": 0.91748046875}, {"start": 1353.21, "end": 1353.47, "word": " Now", "probability": 0.8994140625}, {"start": 1353.47, "end": 1353.65, "word": " the", "probability": 0.8310546875}, {"start": 1353.65, "end": 1354.01, "word": " question", "probability": 0.91748046875}, {"start": 1354.01, "end": 1354.41, "word": " is,", "probability": 0.951171875}, {"start": 1355.55, "end": 1355.79, "word": " what's", "probability": 0.839111328125}, {"start": 1355.79, "end": 1355.95, "word": " the", "probability": 0.92431640625}, {"start": 1355.95, "end": 1356.25, "word": " center", "probability": 0.6943359375}, {"start": 1356.25, "end": 1358.13, "word": " of", "probability": 0.92919921875}, {"start": 1358.13, "end": 1358.43, "word": " these", "probability": 0.8359375}, {"start": 1358.43, "end": 1358.97, "word": " values,", "probability": 0.97705078125}, {"start": 1359.63, "end": 1360.13, "word": " I", "probability": 0.95849609375}, {"start": 1360.13, "end": 1360.27, "word": " mean", "probability": 0.96875}, {"start": 1360.27, "end": 1360.53, "word": " for", "probability": 0.80712890625}, {"start": 1360.53, "end": 1360.71, "word": " the", "probability": 0.91943359375}, {"start": 1360.71, "end": 1361.05, "word": " means?", "probability": 0.9375}, {"start": 1361.81, "end": 1362.41, "word": " What's", "probability": 0.920166015625}, {"start": 1362.41, "end": 1362.59, "word": " the", "probability": 0.9169921875}, {"start": 1362.59, "end": 1362.97, "word": " spread", "probability": 0.89501953125}, {"start": 1362.97, "end": 1363.43, "word": " of", "probability": 0.97216796875}, {"start": 1363.43, "end": 1363.61, "word": " the", "probability": 0.9208984375}, {"start": 1363.61, "end": 1363.93, "word": " means?", "probability": 0.9306640625}, {"start": 1364.85, "end": 1365.11, "word": " And", "probability": 0.9033203125}, {"start": 1365.11, "end": 1365.47, "word": " what's", "probability": 0.93115234375}, {"start": 1365.47, "end": 1365.63, "word": " the", "probability": 0.91748046875}, {"start": 1365.63, "end": 1365.95, "word": " shape", "probability": 0.9130859375}, {"start": 1365.95, "end": 1366.13, "word": " of", "probability": 0.96484375}, {"start": 1366.13, "end": 1366.25, "word": " the", "probability": 0.85302734375}, {"start": 1366.25, "end": 1366.51, "word": " means?", "probability": 0.91015625}, {"start": 1367.11, "end": 1367.35, "word": " So", "probability": 0.88232421875}, {"start": 1367.35, "end": 1367.97, "word": " these", "probability": 0.6708984375}, {"start": 1367.97, "end": 1368.21, "word": " are", "probability": 0.943359375}, {"start": 1368.21, "end": 1368.35, "word": " the", "probability": 0.68798828125}, {"start": 1368.35, "end": 1368.67, "word": " mainly", "probability": 0.95849609375}, {"start": 1368.67, "end": 1369.79, "word": " three", "probability": 0.896484375}, {"start": 1369.79, "end": 1370.31, "word": " questions.", "probability": 0.9521484375}], "temperature": 1.0}, {"id": 53, "seek": 140295, "start": 1373.51, "end": 1402.95, "text": " For example, let's get just simple example and that we have only population of size 4. In the real life, the population size is much bigger than 4, but just for illustration. Because size 4, I mean if the population is 4, it's a small population.", "tokens": [1171, 1365, 11, 718, 311, 483, 445, 2199, 1365, 293, 300, 321, 362, 787, 4415, 295, 2744, 1017, 13, 682, 264, 957, 993, 11, 264, 4415, 2744, 307, 709, 3801, 813, 1017, 11, 457, 445, 337, 22645, 13, 1436, 2744, 1017, 11, 286, 914, 498, 264, 4415, 307, 1017, 11, 309, 311, 257, 1359, 4415, 13], "avg_logprob": -0.23327850458914773, "compression_ratio": 1.5732484076433122, "no_speech_prob": 0.0, "words": [{"start": 1373.51, "end": 1373.83, "word": " For", "probability": 0.70751953125}, {"start": 1373.83, "end": 1374.21, "word": " example,", "probability": 0.951171875}, {"start": 1374.71, "end": 1375.13, "word": " let's", "probability": 0.9130859375}, {"start": 1375.13, "end": 1375.45, "word": " get", "probability": 0.5830078125}, {"start": 1375.45, "end": 1375.79, "word": " just", "probability": 0.798828125}, {"start": 1375.79, "end": 1376.17, "word": " simple", "probability": 0.63037109375}, {"start": 1376.17, "end": 1376.57, "word": " example", "probability": 0.95166015625}, {"start": 1376.57, "end": 1376.81, "word": " and", "probability": 0.3037109375}, {"start": 1376.81, "end": 1376.99, "word": " that", "probability": 0.86279296875}, {"start": 1376.99, "end": 1377.17, "word": " we", "probability": 0.89794921875}, {"start": 1377.17, "end": 1377.39, "word": " have", "probability": 0.92578125}, {"start": 1377.39, "end": 1377.87, "word": " only", "probability": 0.90380859375}, {"start": 1377.87, "end": 1378.79, "word": " population", "probability": 0.873046875}, {"start": 1378.79, "end": 1379.27, "word": " of", "probability": 0.9658203125}, {"start": 1379.27, "end": 1379.63, "word": " size", "probability": 0.828125}, {"start": 1379.63, "end": 1380.01, "word": " 4.", "probability": 0.57421875}, {"start": 1382.45, "end": 1382.71, "word": " In", "probability": 0.91796875}, {"start": 1382.71, "end": 1384.37, "word": " the", "probability": 0.67431640625}, {"start": 1384.37, "end": 1384.73, "word": " real", "probability": 0.8486328125}, {"start": 1384.73, "end": 1385.15, "word": " life,", "probability": 0.9033203125}, {"start": 1386.47, "end": 1386.61, "word": " the", "probability": 0.88037109375}, {"start": 1386.61, "end": 1387.43, "word": " population", "probability": 0.9130859375}, {"start": 1387.43, "end": 1387.91, "word": " size", "probability": 0.84619140625}, {"start": 1387.91, "end": 1388.07, "word": " is", "probability": 0.92578125}, {"start": 1388.07, "end": 1388.39, "word": " much", "probability": 0.89794921875}, {"start": 1388.39, "end": 1389.63, "word": " bigger", "probability": 0.94482421875}, {"start": 1389.63, "end": 1389.95, "word": " than", "probability": 0.94287109375}, {"start": 1389.95, "end": 1390.21, "word": " 4,", "probability": 0.83203125}, {"start": 1390.31, "end": 1390.41, "word": " but", "probability": 0.849609375}, {"start": 1390.41, "end": 1390.69, "word": " just", "probability": 0.7353515625}, {"start": 1390.69, "end": 1390.99, "word": " for", "probability": 0.26025390625}, {"start": 1390.99, "end": 1394.97, "word": " illustration.", "probability": 0.583984375}, {"start": 1397.29, "end": 1397.93, "word": " Because", "probability": 0.8232421875}, {"start": 1397.93, "end": 1398.25, "word": " size", "probability": 0.5849609375}, {"start": 1398.25, "end": 1398.71, "word": " 4,", "probability": 0.876953125}, {"start": 1398.85, "end": 1398.95, "word": " I", "probability": 0.8837890625}, {"start": 1398.95, "end": 1399.07, "word": " mean", "probability": 0.96826171875}, {"start": 1399.07, "end": 1399.21, "word": " if", "probability": 0.734375}, {"start": 1399.21, "end": 1399.33, "word": " the", "probability": 0.77392578125}, {"start": 1399.33, "end": 1399.63, "word": " population", "probability": 0.9482421875}, {"start": 1399.63, "end": 1399.87, "word": " is", "probability": 0.9384765625}, {"start": 1399.87, "end": 1400.19, "word": " 4,", "probability": 0.92578125}, {"start": 1401.49, "end": 1402.21, "word": " it's", "probability": 0.791015625}, {"start": 1402.21, "end": 1402.25, "word": " a", "probability": 0.5556640625}, {"start": 1402.25, "end": 1402.49, "word": " small", "probability": 0.916015625}, {"start": 1402.49, "end": 1402.95, "word": " population.", "probability": 0.92919921875}], "temperature": 1.0}, {"id": 54, "seek": 142985, "start": 1403.41, "end": 1429.85, "text": " So we can take all the values and find the mean and standard deviation. But in reality, we have more than that. So this one just for as example. So let's suppose that we have a population of size 4. So n equals 4. And we are interested in the ages.", "tokens": [407, 321, 393, 747, 439, 264, 4190, 293, 915, 264, 914, 293, 3832, 25163, 13, 583, 294, 4103, 11, 321, 362, 544, 813, 300, 13, 407, 341, 472, 445, 337, 382, 1365, 13, 407, 718, 311, 7297, 300, 321, 362, 257, 4415, 295, 2744, 1017, 13, 407, 297, 6915, 1017, 13, 400, 321, 366, 3102, 294, 264, 12357, 13], "avg_logprob": -0.18750000447034837, "compression_ratio": 1.464705882352941, "no_speech_prob": 0.0, "words": [{"start": 1403.41, "end": 1403.73, "word": " So", "probability": 0.6337890625}, {"start": 1403.73, "end": 1403.83, "word": " we", "probability": 0.462158203125}, {"start": 1403.83, "end": 1403.99, "word": " can", "probability": 0.93212890625}, {"start": 1403.99, "end": 1404.27, "word": " take", "probability": 0.865234375}, {"start": 1404.27, "end": 1404.67, "word": " all", "probability": 0.953125}, {"start": 1404.67, "end": 1404.95, "word": " the", "probability": 0.83203125}, {"start": 1404.95, "end": 1405.91, "word": " values", "probability": 0.95751953125}, {"start": 1405.91, "end": 1406.47, "word": " and", "probability": 0.85498046875}, {"start": 1406.47, "end": 1406.69, "word": " find", "probability": 0.88916015625}, {"start": 1406.69, "end": 1406.85, "word": " the", "probability": 0.8994140625}, {"start": 1406.85, "end": 1406.99, "word": " mean", "probability": 0.87548828125}, {"start": 1406.99, "end": 1407.11, "word": " and", "probability": 0.896484375}, {"start": 1407.11, "end": 1407.25, "word": " standard", "probability": 0.41357421875}, {"start": 1407.25, "end": 1407.61, "word": " deviation.", "probability": 0.9423828125}, {"start": 1408.29, "end": 1408.57, "word": " But", "probability": 0.90185546875}, {"start": 1408.57, "end": 1409.07, "word": " in", "probability": 0.83447265625}, {"start": 1409.07, "end": 1409.45, "word": " reality,", "probability": 0.97509765625}, {"start": 1409.53, "end": 1409.65, "word": " we", "probability": 0.95947265625}, {"start": 1409.65, "end": 1409.91, "word": " have", "probability": 0.94580078125}, {"start": 1409.91, "end": 1410.23, "word": " more", "probability": 0.9384765625}, {"start": 1410.23, "end": 1410.39, "word": " than", "probability": 0.953125}, {"start": 1410.39, "end": 1410.63, "word": " that.", "probability": 0.87451171875}, {"start": 1410.93, "end": 1411.07, "word": " So", "probability": 0.66796875}, {"start": 1411.07, "end": 1411.43, "word": " this", "probability": 0.359375}, {"start": 1411.43, "end": 1412.27, "word": " one", "probability": 0.8671875}, {"start": 1412.27, "end": 1412.47, "word": " just", "probability": 0.41162109375}, {"start": 1412.47, "end": 1412.79, "word": " for", "probability": 0.7998046875}, {"start": 1412.79, "end": 1414.09, "word": " as", "probability": 0.5556640625}, {"start": 1414.09, "end": 1414.43, "word": " example.", "probability": 0.91162109375}, {"start": 1414.99, "end": 1415.25, "word": " So", "probability": 0.94482421875}, {"start": 1415.25, "end": 1415.75, "word": " let's", "probability": 0.953857421875}, {"start": 1415.75, "end": 1416.99, "word": " suppose", "probability": 0.89892578125}, {"start": 1416.99, "end": 1417.23, "word": " that", "probability": 0.9345703125}, {"start": 1417.23, "end": 1417.39, "word": " we", "probability": 0.953125}, {"start": 1417.39, "end": 1417.53, "word": " have", "probability": 0.947265625}, {"start": 1417.53, "end": 1417.67, "word": " a", "probability": 0.9482421875}, {"start": 1417.67, "end": 1418.37, "word": " population", "probability": 0.92919921875}, {"start": 1418.37, "end": 1418.65, "word": " of", "probability": 0.94580078125}, {"start": 1418.65, "end": 1418.91, "word": " size", "probability": 0.83935546875}, {"start": 1418.91, "end": 1419.27, "word": " 4.", "probability": 0.517578125}, {"start": 1421.09, "end": 1421.43, "word": " So", "probability": 0.947265625}, {"start": 1421.43, "end": 1421.63, "word": " n", "probability": 0.662109375}, {"start": 1421.63, "end": 1422.27, "word": " equals", "probability": 0.8369140625}, {"start": 1422.27, "end": 1422.79, "word": " 4.", "probability": 0.9326171875}, {"start": 1426.53, "end": 1427.17, "word": " And", "probability": 0.85302734375}, {"start": 1427.17, "end": 1427.39, "word": " we", "probability": 0.95263671875}, {"start": 1427.39, "end": 1427.73, "word": " are", "probability": 0.93994140625}, {"start": 1427.73, "end": 1428.37, "word": " interested", "probability": 0.869140625}, {"start": 1428.37, "end": 1429.39, "word": " in", "probability": 0.93798828125}, {"start": 1429.39, "end": 1429.53, "word": " the", "probability": 0.86279296875}, {"start": 1429.53, "end": 1429.85, "word": " ages.", "probability": 0.7431640625}], "temperature": 1.0}, {"id": 55, "seek": 145991, "start": 1432.01, "end": 1459.91, "text": " And suppose the values of X, X again represents H, and the values we have. So these are the four values we have. Now simple calculation will give you the mean, the population mean.", "tokens": [400, 7297, 264, 4190, 295, 1783, 11, 1783, 797, 8855, 389, 11, 293, 264, 4190, 321, 362, 13, 407, 613, 366, 264, 1451, 4190, 321, 362, 13, 823, 2199, 17108, 486, 976, 291, 264, 914, 11, 264, 4415, 914, 13], "avg_logprob": -0.2734375, "compression_ratio": 1.4365079365079365, "no_speech_prob": 0.0, "words": [{"start": 1432.01, "end": 1432.33, "word": " And", "probability": 0.76513671875}, {"start": 1432.33, "end": 1432.79, "word": " suppose", "probability": 0.86083984375}, {"start": 1432.79, "end": 1434.03, "word": " the", "probability": 0.7177734375}, {"start": 1434.03, "end": 1434.37, "word": " values", "probability": 0.84619140625}, {"start": 1434.37, "end": 1434.53, "word": " of", "probability": 0.962890625}, {"start": 1434.53, "end": 1434.87, "word": " X,", "probability": 0.429443359375}, {"start": 1435.15, "end": 1435.49, "word": " X", "probability": 0.88232421875}, {"start": 1435.49, "end": 1435.75, "word": " again", "probability": 0.859375}, {"start": 1435.75, "end": 1436.29, "word": " represents", "probability": 0.60595703125}, {"start": 1436.29, "end": 1438.93, "word": " H,", "probability": 0.2822265625}, {"start": 1440.69, "end": 1440.89, "word": " and", "probability": 0.89111328125}, {"start": 1440.89, "end": 1441.03, "word": " the", "probability": 0.8740234375}, {"start": 1441.03, "end": 1441.33, "word": " values", "probability": 0.953125}, {"start": 1441.33, "end": 1441.51, "word": " we", "probability": 0.89697265625}, {"start": 1441.51, "end": 1441.81, "word": " have.", "probability": 0.94580078125}, {"start": 1446.09, "end": 1446.75, "word": " So", "probability": 0.7255859375}, {"start": 1446.75, "end": 1446.99, "word": " these", "probability": 0.7587890625}, {"start": 1446.99, "end": 1447.21, "word": " are", "probability": 0.9482421875}, {"start": 1447.21, "end": 1447.39, "word": " the", "probability": 0.88134765625}, {"start": 1447.39, "end": 1448.11, "word": " four", "probability": 0.828125}, {"start": 1448.11, "end": 1448.47, "word": " values", "probability": 0.97509765625}, {"start": 1448.47, "end": 1448.65, "word": " we", "probability": 0.935546875}, {"start": 1448.65, "end": 1448.93, "word": " have.", "probability": 0.9462890625}, {"start": 1452.05, "end": 1452.71, "word": " Now", "probability": 0.9287109375}, {"start": 1452.71, "end": 1453.15, "word": " simple", "probability": 0.525390625}, {"start": 1453.15, "end": 1453.79, "word": " calculation", "probability": 0.873046875}, {"start": 1453.79, "end": 1456.91, "word": " will", "probability": 0.82373046875}, {"start": 1456.91, "end": 1457.25, "word": " give", "probability": 0.875}, {"start": 1457.25, "end": 1457.47, "word": " you", "probability": 0.953125}, {"start": 1457.47, "end": 1457.73, "word": " the", "probability": 0.91357421875}, {"start": 1457.73, "end": 1457.97, "word": " mean,", "probability": 0.494384765625}, {"start": 1458.89, "end": 1459.07, "word": " the", "probability": 0.90478515625}, {"start": 1459.07, "end": 1459.35, "word": " population", "probability": 0.95068359375}, {"start": 1459.35, "end": 1459.91, "word": " mean.", "probability": 0.94873046875}], "temperature": 1.0}, {"id": 56, "seek": 149509, "start": 1465.93, "end": 1495.09, "text": " Just add these values and divide by the operation size, we'll get 21 years. And sigma, as we mentioned in chapter three, square root of this quantity will give 2.236 years. So simple calculation will give these results. 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The center is 21 of the exact population. The variation is around 2.2. Now, the shape of distribution. Now, 18 represents once. 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In this case, we have something called uniform distribution. In this case, the proportions are the same. So, the mean, not normal, it's uniform distribution. 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Now suppose for example, we select a random sample of size 2 from this population. So we select a sample of size 2. 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And we select a sample of size two. So the first one could be 18 and 18, 18 and 20, 18 and 22. So we have 16 different samples. So number of samples in this case is 16. 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So the rule is number of samples in this case and the volume is million. Because we have four, four squared is sixteen, that's all.", "tokens": [286, 914, 264, 4415, 2744, 307, 1025, 293, 370, 322, 13, 407, 264, 4978, 307, 1230, 295, 10938, 294, 341, 1389, 293, 264, 5523, 307, 2459, 13, 1436, 321, 362, 1451, 11, 1451, 8889, 307, 27847, 11, 300, 311, 439, 13], "avg_logprob": -0.5465029932203747, "compression_ratio": 1.3461538461538463, "no_speech_prob": 0.0, "words": [{"start": 1614.26, "end": 1614.5, "word": " I", "probability": 0.8212890625}, {"start": 1614.5, "end": 1614.62, "word": " mean", "probability": 0.958984375}, {"start": 1614.62, "end": 1614.76, "word": " the", "probability": 0.72705078125}, {"start": 1614.76, "end": 1615.14, "word": " population", "probability": 0.9462890625}, {"start": 1615.14, "end": 1615.46, "word": " size", "probability": 0.81689453125}, {"start": 1615.46, "end": 1615.62, "word": " is", "probability": 0.2607421875}, {"start": 1615.62, "end": 1615.82, "word": " 5", "probability": 0.6025390625}, {"start": 1615.82, "end": 1617.26, "word": " and", "probability": 0.2666015625}, {"start": 1617.26, "end": 1618.62, "word": " so", "probability": 0.83056640625}, {"start": 1618.62, "end": 1618.9, "word": " on.", "probability": 0.93115234375}, {"start": 1619.68, "end": 1619.88, "word": " So", "probability": 0.837890625}, {"start": 1619.88, "end": 1620.22, "word": " the", "probability": 0.7314453125}, {"start": 1620.22, "end": 1620.62, "word": " rule", "probability": 0.67724609375}, {"start": 1620.62, "end": 1621.0, "word": " is", "probability": 0.953125}, {"start": 1621.0, "end": 1626.0, "word": " number", "probability": 0.548828125}, {"start": 1626.0, "end": 1628.1, "word": " of", "probability": 0.96923828125}, {"start": 1628.1, "end": 1628.7, "word": " samples", "probability": 0.8330078125}, {"start": 1628.7, "end": 1630.26, "word": " in", "probability": 0.68505859375}, {"start": 1630.26, "end": 1630.48, "word": " this", "probability": 0.95166015625}, {"start": 1630.48, "end": 1630.84, "word": " case", "probability": 0.91650390625}, {"start": 1630.84, "end": 1631.54, "word": " and", "probability": 0.1317138671875}, {"start": 1631.54, "end": 1631.76, "word": " the", "probability": 0.496826171875}, {"start": 1631.76, "end": 1632.1, "word": " volume", "probability": 0.06903076171875}, {"start": 1632.1, "end": 1632.52, "word": " is", "probability": 0.269287109375}, {"start": 1632.52, "end": 1633.02, "word": " million.", "probability": 0.77685546875}, {"start": 1634.7, "end": 1635.06, "word": " Because", "probability": 0.57763671875}, {"start": 1635.06, "end": 1635.26, "word": " we", "probability": 0.90478515625}, {"start": 1635.26, "end": 1635.6, "word": " have", "probability": 0.93017578125}, {"start": 1635.6, "end": 1636.36, "word": " four,", "probability": 0.42529296875}, {"start": 1636.5, "end": 1637.38, "word": " four", "probability": 0.83837890625}, {"start": 1637.38, "end": 1637.74, "word": " squared", "probability": 0.3466796875}, {"start": 1637.74, "end": 1638.18, "word": " is", "probability": 0.88916015625}, {"start": 1638.18, "end": 1639.14, "word": " sixteen,", "probability": 0.61474609375}, {"start": 1639.44, "end": 1641.0, "word": " that's", "probability": 0.5120849609375}, {"start": 1641.0, "end": 1641.24, "word": " all.", "probability": 0.62353515625}], "temperature": 1.0}, {"id": 62, "seek": 167004, "start": 1642.54, "end": 1670.04, "text": " 5 squared, 25, and so on. Now, we have 16 different samples. For sure, we will have different sample means. Now, for the first sample, 18, 18, the average is also 18. The next one, 18, 20, the average is 19.", "tokens": [1025, 8889, 11, 3552, 11, 293, 370, 322, 13, 823, 11, 321, 362, 3165, 819, 10938, 13, 1171, 988, 11, 321, 486, 362, 819, 6889, 1355, 13, 823, 11, 337, 264, 700, 6889, 11, 2443, 11, 2443, 11, 264, 4274, 307, 611, 2443, 13, 440, 958, 472, 11, 2443, 11, 945, 11, 264, 4274, 307, 1294, 13], "avg_logprob": -0.2064924599795506, "compression_ratio": 1.4964028776978417, "no_speech_prob": 0.0, "words": [{"start": 1642.54, "end": 1643.1, "word": " 5", "probability": 0.453369140625}, {"start": 1643.1, "end": 1643.44, "word": " squared,", "probability": 0.5146484375}, {"start": 1643.58, "end": 1644.04, "word": " 25,", "probability": 0.90869140625}, {"start": 1644.46, "end": 1644.6, "word": " and", "probability": 0.77197265625}, {"start": 1644.6, "end": 1644.8, "word": " so", "probability": 0.95361328125}, {"start": 1644.8, "end": 1645.06, "word": " on.", "probability": 0.94189453125}, {"start": 1646.1, "end": 1646.36, "word": " Now,", "probability": 0.90966796875}, {"start": 1646.44, "end": 1646.66, "word": " we", "probability": 0.92822265625}, {"start": 1646.66, "end": 1646.94, "word": " have", "probability": 0.94580078125}, {"start": 1646.94, "end": 1647.7, "word": " 16", "probability": 0.8662109375}, {"start": 1647.7, "end": 1648.2, "word": " different", "probability": 0.89892578125}, {"start": 1648.2, "end": 1648.7, "word": " samples.", "probability": 0.86328125}, {"start": 1649.46, "end": 1650.1, "word": " For", "probability": 0.927734375}, {"start": 1650.1, "end": 1650.54, "word": " sure,", "probability": 0.91796875}, {"start": 1650.66, "end": 1650.88, "word": " we", "probability": 0.9130859375}, {"start": 1650.88, "end": 1651.14, "word": " will", "probability": 0.638671875}, {"start": 1651.14, "end": 1651.74, "word": " have", "probability": 0.9462890625}, {"start": 1651.74, "end": 1653.68, "word": " different", "probability": 0.88671875}, {"start": 1653.68, "end": 1654.26, "word": " sample", "probability": 0.87744140625}, {"start": 1654.26, "end": 1654.68, "word": " means.", "probability": 0.9287109375}, {"start": 1656.4, "end": 1656.68, "word": " Now,", "probability": 0.9326171875}, {"start": 1656.74, "end": 1656.92, "word": " for", "probability": 0.95068359375}, {"start": 1656.92, "end": 1657.08, "word": " the", "probability": 0.92041015625}, {"start": 1657.08, "end": 1657.4, "word": " first", "probability": 0.830078125}, {"start": 1657.4, "end": 1657.94, "word": " sample,", "probability": 0.892578125}, {"start": 1659.56, "end": 1659.92, "word": " 18,", "probability": 0.94482421875}, {"start": 1660.02, "end": 1660.3, "word": " 18,", "probability": 0.76318359375}, {"start": 1660.42, "end": 1660.56, "word": " the", "probability": 0.89501953125}, {"start": 1660.56, "end": 1660.88, "word": " average", "probability": 0.7978515625}, {"start": 1660.88, "end": 1662.58, "word": " is", "probability": 0.8564453125}, {"start": 1662.58, "end": 1662.94, "word": " also", "probability": 0.87255859375}, {"start": 1662.94, "end": 1663.28, "word": " 18.", "probability": 0.91650390625}, {"start": 1664.98, "end": 1665.66, "word": " The", "probability": 0.875}, {"start": 1665.66, "end": 1665.86, "word": " next", "probability": 0.94921875}, {"start": 1665.86, "end": 1666.14, "word": " one,", "probability": 0.94189453125}, {"start": 1666.8, "end": 1667.2, "word": " 18,", "probability": 0.98681640625}, {"start": 1667.28, "end": 1667.62, "word": " 20,", "probability": 0.93701171875}, {"start": 1668.06, "end": 1669.3, "word": " the", "probability": 0.8876953125}, {"start": 1669.3, "end": 1669.56, "word": " average", "probability": 0.796875}, {"start": 1669.56, "end": 1669.72, "word": " is", "probability": 0.86328125}, {"start": 1669.72, "end": 1670.04, "word": " 19.", "probability": 0.9658203125}], "temperature": 1.0}, {"id": 63, "seek": 170403, "start": 1674.79, "end": 1704.03, "text": " 20, 18, 24, the average is 21, and so on. So now we have 16 sample means. Now this is my new values. It's my sample. This sample has different sample means. Now let's take these values and compute average, sigma, and the shape of the distribution.", "tokens": [945, 11, 2443, 11, 4022, 11, 264, 4274, 307, 5080, 11, 293, 370, 322, 13, 407, 586, 321, 362, 3165, 6889, 1355, 13, 823, 341, 307, 452, 777, 4190, 13, 467, 311, 452, 6889, 13, 639, 6889, 575, 819, 6889, 1355, 13, 823, 718, 311, 747, 613, 4190, 293, 14722, 4274, 11, 12771, 11, 293, 264, 3909, 295, 264, 7316, 13], "avg_logprob": -0.21018145762143597, "compression_ratio": 1.4939759036144578, "no_speech_prob": 0.0, "words": [{"start": 1674.79, "end": 1675.13, "word": " 20,", "probability": 0.1297607421875}, {"start": 1675.63, "end": 1676.13, "word": " 18,", "probability": 0.8681640625}, {"start": 1676.25, "end": 1676.79, "word": " 24,", "probability": 0.90869140625}, {"start": 1676.95, "end": 1677.01, "word": " the", "probability": 0.58740234375}, {"start": 1677.01, "end": 1677.21, "word": " average", "probability": 0.77294921875}, {"start": 1677.21, "end": 1677.35, "word": " is", 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{"start": 1684.29, "end": 1684.71, "word": " this", "probability": 0.537109375}, {"start": 1684.71, "end": 1684.87, "word": " is", "probability": 0.94873046875}, {"start": 1684.87, "end": 1685.11, "word": " my", "probability": 0.97265625}, {"start": 1685.11, "end": 1685.45, "word": " new", "probability": 0.91162109375}, {"start": 1685.45, "end": 1686.21, "word": " values.", "probability": 0.79150390625}, {"start": 1686.83, "end": 1687.15, "word": " It's", "probability": 0.778564453125}, {"start": 1687.15, "end": 1687.37, "word": " my", "probability": 0.97119140625}, {"start": 1687.37, "end": 1687.77, "word": " sample.", "probability": 0.72216796875}, {"start": 1688.39, "end": 1688.71, "word": " This", "probability": 0.88623046875}, {"start": 1688.71, "end": 1689.01, "word": " sample", "probability": 0.876953125}, {"start": 1689.01, "end": 1689.47, "word": " has", "probability": 0.93603515625}, {"start": 1689.47, "end": 1690.51, "word": " different", "probability": 0.87841796875}, {"start": 1690.51, "end": 1691.07, "word": " sample", "probability": 0.8427734375}, {"start": 1691.07, "end": 1691.45, "word": " means.", "probability": 0.8662109375}, {"start": 1692.27, "end": 1692.63, "word": " Now", "probability": 0.89306640625}, {"start": 1692.63, "end": 1693.17, "word": " let's", "probability": 0.874267578125}, {"start": 1693.17, "end": 1693.57, "word": " take", "probability": 0.869140625}, {"start": 1693.57, "end": 1694.25, "word": " these", "probability": 0.8173828125}, {"start": 1694.25, "end": 1694.85, "word": " values", "probability": 0.9658203125}, {"start": 1694.85, "end": 1696.05, "word": " and", "probability": 0.87109375}, {"start": 1696.05, "end": 1696.83, "word": " compute", "probability": 0.93408203125}, {"start": 1696.83, "end": 1698.31, "word": " average,", "probability": 0.70068359375}, {"start": 1699.63, "end": 1700.23, "word": " sigma,", "probability": 0.8203125}, {"start": 1700.71, "end": 1701.45, "word": " and", "probability": 0.93896484375}, {"start": 1701.45, "end": 1701.81, "word": " the", "probability": 0.9189453125}, {"start": 1701.81, "end": 1702.51, "word": " shape", "probability": 0.943359375}, {"start": 1702.51, "end": 1702.95, "word": " of", "probability": 0.96728515625}, {"start": 1702.95, "end": 1703.27, "word": " the", "probability": 0.91796875}, {"start": 1703.27, "end": 1704.03, "word": " distribution.", "probability": 0.85009765625}], "temperature": 1.0}, {"id": 64, "seek": 171248, "start": 1706.12, "end": 1712.48, "text": " So again, we have a population of size 4, we select a random cell bone.", "tokens": [407, 797, 11, 321, 362, 257, 4415, 295, 2744, 1017, 11, 321, 3048, 257, 4974, 2815, 9026, 13], "avg_logprob": -0.3511513032411274, "compression_ratio": 0.9863013698630136, "no_speech_prob": 0.0, "words": [{"start": 1706.1200000000001, "end": 1706.74, "word": " So", "probability": 0.270751953125}, {"start": 1706.74, "end": 1707.04, "word": " again,", "probability": 0.7578125}, {"start": 1707.74, "end": 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Might be two of them are the same. I mean, we have 18 just repeated once, but 19 repeated twice, 23 times, 24 times, and so on. 22 three times, 23 twice, 24 once. So it depends on", "tokens": [295, 2744, 568, 490, 300, 4415, 11, 321, 917, 365, 3165, 4974, 10938, 11, 293, 436, 362, 819, 6889, 1355, 13, 23964, 312, 732, 295, 552, 366, 264, 912, 13, 286, 914, 11, 321, 362, 2443, 445, 10477, 1564, 11, 457, 1294, 10477, 6091, 11, 6673, 1413, 11, 4022, 1413, 11, 293, 370, 322, 13, 5853, 1045, 1413, 11, 6673, 6091, 11, 4022, 1564, 13, 407, 309, 5946, 322], "avg_logprob": -0.24107142984867097, "compression_ratio": 1.53551912568306, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1714.3, "end": 1714.58, "word": " of", "probability": 0.344970703125}, {"start": 1714.58, "end": 1714.94, "word": " size", "probability": 0.78369140625}, {"start": 1714.94, "end": 1715.24, "word": " 2", "probability": 0.62841796875}, {"start": 1715.24, "end": 1715.54, "word": " from", "probability": 0.798828125}, {"start": 1715.54, "end": 1715.74, "word": " that", "probability": 0.86083984375}, {"start": 1715.74, "end": 1716.3, "word": " population,", "probability": 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So we have actually different samples. For example, let's look at 24 and 22. What's the average of these two values? N divided by 2 will give 22.", "tokens": [440, 6889, 1355, 291, 362, 13, 407, 321, 362, 767, 819, 10938, 13, 1171, 1365, 11, 718, 311, 574, 412, 4022, 293, 5853, 13, 708, 311, 264, 4274, 295, 613, 732, 4190, 30, 426, 6666, 538, 568, 486, 976, 5853, 13], "avg_logprob": -0.21819196712403072, "compression_ratio": 1.2627737226277371, "no_speech_prob": 1.7285346984863281e-06, "words": [{"start": 1743.05, "end": 1743.51, "word": " The", "probability": 0.2095947265625}, {"start": 1743.51, "end": 1743.97, "word": " sample", "probability": 0.703125}, {"start": 1743.97, "end": 1744.27, "word": " means", "probability": 0.728515625}, {"start": 1744.27, "end": 1744.45, "word": " you", "probability": 0.83837890625}, {"start": 1744.45, "end": 1744.69, "word": " have.", "probability": 0.92919921875}, {"start": 1744.89, "end": 1745.03, "word": " So", "probability": 0.93408203125}, {"start": 1745.03, "end": 1745.15, "word": " we", "probability": 0.5166015625}, {"start": 1745.15, "end": 1745.35, "word": " have", "probability": 0.92138671875}, {"start": 1745.35, "end": 1745.79, "word": " actually", "probability": 0.849609375}, {"start": 1745.79, "end": 1746.35, "word": " different", "probability": 0.87451171875}, {"start": 1746.35, "end": 1747.21, "word": " samples.", "probability": 0.51025390625}, {"start": 1754.79, "end": 1755.39, "word": " For", "probability": 0.83935546875}, {"start": 1755.39, "end": 1755.75, "word": " example,", "probability": 0.974609375}, {"start": 1756.03, "end": 1756.39, "word": " let's", "probability": 0.963623046875}, {"start": 1756.39, "end": 1756.63, "word": " look", "probability": 0.96533203125}, {"start": 1756.63, "end": 1756.81, "word": " at", "probability": 0.9658203125}, {"start": 1756.81, "end": 1757.25, "word": " 24", "probability": 0.9521484375}, {"start": 1757.25, "end": 1757.45, "word": " and", "probability": 0.7412109375}, {"start": 1757.45, "end": 1757.81, "word": " 22.", "probability": 0.96728515625}, {"start": 1758.55, "end": 1758.85, "word": " What's", "probability": 0.91748046875}, {"start": 1758.85, "end": 1758.97, "word": " the", "probability": 0.92431640625}, {"start": 1758.97, "end": 1759.23, "word": " average", "probability": 0.818359375}, {"start": 1759.23, "end": 1759.37, "word": " of", "probability": 0.951171875}, {"start": 1759.37, "end": 1759.59, "word": " these", "probability": 0.86279296875}, {"start": 1759.59, "end": 1759.79, "word": " two", "probability": 0.90869140625}, {"start": 1759.79, "end": 1760.17, "word": " values?", "probability": 0.9208984375}, {"start": 1761.43, "end": 1761.73, "word": " N", "probability": 0.281494140625}, {"start": 1761.73, "end": 1761.99, "word": " divided", "probability": 0.681640625}, {"start": 1761.99, "end": 1762.19, "word": " by", "probability": 0.9755859375}, {"start": 1762.19, "end": 1762.49, "word": " 2", "probability": 0.7890625}, {"start": 1762.49, "end": 1762.79, "word": " will", "probability": 0.80859375}, {"start": 1762.79, "end": 1763.07, "word": " give", "probability": 0.87109375}, {"start": 1763.07, "end": 1764.29, "word": " 22.", "probability": 0.9052734375}], "temperature": 1.0}, {"id": 67, "seek": 179795, "start": 1773.39, "end": 1797.95, "text": " So again, we have 16 sample means. Now look first at the shape of the distribution. 18, as I mentioned, repeated once. 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We have to add the values of X bar, the sample mean, then divide by the total number of size, which is 16. 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The mu of x bar is the same as the population mean mu. The second one, the split sigma of x bar by using the same equation we have, sum of x bar in this case minus the mean of x bar squared, then divide this quantity by the capital I which is 16 in this case.", "tokens": [407, 341, 307, 264, 700, 9841, 13075, 13, 440, 2992, 295, 2031, 2159, 307, 264, 912, 382, 264, 4415, 914, 2992, 13, 440, 1150, 472, 11, 264, 7472, 12771, 295, 2031, 2159, 538, 1228, 264, 912, 5367, 321, 362, 11, 2408, 295, 2031, 2159, 294, 341, 1389, 3175, 264, 914, 295, 2031, 2159, 8889, 11, 550, 9845, 341, 11275, 538, 264, 4238, 286, 597, 307, 3165, 294, 341, 1389, 13], "avg_logprob": -0.23195423080887592, "compression_ratio": 1.694915254237288, "no_speech_prob": 0.0, "words": [{"start": 1854.75, "end": 1855.09, "word": " So", "probability": 0.71435546875}, {"start": 1855.09, "end": 1855.37, "word": " this", "probability": 0.7265625}, {"start": 1855.37, "end": 1855.51, "word": " is", "probability": 0.9345703125}, {"start": 1855.51, "end": 1855.63, "word": " the", 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"seek": 191105, "start": 1885.17, "end": 1911.05, "text": " So we will end with 1.58. Now let's compare population standard deviation and the sample standard deviation. First of all, you see that these two values are not the same. The population standard deviation was 2.2, around 2.2.", "tokens": [407, 321, 486, 917, 365, 502, 13, 20419, 13, 823, 718, 311, 6794, 4415, 3832, 25163, 293, 264, 6889, 3832, 25163, 13, 2386, 295, 439, 11, 291, 536, 300, 613, 732, 4190, 366, 406, 264, 912, 13, 440, 4415, 3832, 25163, 390, 568, 13, 17, 11, 926, 568, 13, 17, 13], "avg_logprob": -0.12575119762466505, "compression_ratio": 1.5804195804195804, "no_speech_prob": 0.0, "words": [{"start": 1885.17, "end": 1885.55, "word": " So", "probability": 0.73828125}, {"start": 1885.55, "end": 1885.81, "word": " we", "probability": 0.7099609375}, {"start": 1885.81, "end": 1886.01, "word": " will", "probability": 0.88623046875}, {"start": 1886.01, "end": 1886.27, "word": " end", "probability": 0.8984375}, {"start": 1886.27, "end": 1886.63, "word": " with", "probability": 0.90087890625}, {"start": 1886.63, "end": 1887.73, "word": " 1", "probability": 0.95458984375}, {"start": 1887.73, "end": 1888.51, "word": ".58.", "probability": 0.97412109375}, {"start": 1891.27, "end": 1891.59, "word": " Now", "probability": 0.9208984375}, {"start": 1891.59, "end": 1891.89, "word": " let's", "probability": 0.834228515625}, {"start": 1891.89, "end": 1892.41, "word": " compare", "probability": 0.9560546875}, {"start": 1892.41, "end": 1895.39, "word": " population", "probability": 0.84326171875}, {"start": 1895.39, "end": 1895.77, "word": " standard", "probability": 0.92626953125}, {"start": 1895.77, "end": 1896.17, "word": " deviation", "probability": 0.9052734375}, {"start": 1896.17, "end": 1897.73, "word": " and", "probability": 0.8466796875}, {"start": 1897.73, "end": 1897.99, "word": " the", "probability": 0.74755859375}, {"start": 1897.99, "end": 1898.29, "word": " sample", "probability": 0.916015625}, {"start": 1898.29, "end": 1898.95, "word": " standard", "probability": 0.947265625}, {"start": 1898.95, "end": 1899.97, "word": " deviation.", "probability": 0.8974609375}, {"start": 1901.23, "end": 1901.87, "word": " First", "probability": 0.900390625}, {"start": 1901.87, "end": 1902.05, "word": " of", "probability": 0.96728515625}, {"start": 1902.05, "end": 1902.21, "word": " all,", "probability": 0.94970703125}, {"start": 1902.25, "end": 1902.31, "word": " you", "probability": 0.93896484375}, {"start": 1902.31, "end": 1902.57, "word": " see", "probability": 0.438720703125}, {"start": 1902.57, "end": 1902.91, "word": " that", "probability": 0.89990234375}, {"start": 1902.91, "end": 1903.79, "word": " these", "probability": 0.84423828125}, {"start": 1903.79, "end": 1903.99, "word": " two", "probability": 0.90625}, {"start": 1903.99, "end": 1904.33, "word": " values", "probability": 0.9013671875}, {"start": 1904.33, "end": 1904.51, "word": " are", "probability": 0.94189453125}, {"start": 1904.51, "end": 1904.65, "word": " not", "probability": 0.94189453125}, {"start": 1904.65, "end": 1904.81, "word": " the", "probability": 0.91796875}, {"start": 1904.81, "end": 1905.05, "word": " same.", "probability": 0.908203125}, {"start": 1907.53, "end": 1907.99, "word": " The", "probability": 0.8837890625}, {"start": 1907.99, "end": 1908.51, "word": " population", "probability": 0.94482421875}, {"start": 1908.51, "end": 1908.87, "word": " standard", "probability": 0.94091796875}, {"start": 1908.87, "end": 1909.23, "word": " deviation", "probability": 0.888671875}, {"start": 1909.23, "end": 1909.55, "word": " was", "probability": 0.9482421875}, {"start": 1909.55, "end": 1909.75, "word": " 2", "probability": 0.79736328125}, {"start": 1909.75, "end": 1910.13, "word": ".2,", "probability": 0.994873046875}, {"start": 1910.19, "end": 1910.37, "word": " around", "probability": 0.9267578125}, {"start": 1910.37, "end": 1910.61, "word": " 2", "probability": 0.99462890625}, {"start": 1910.61, "end": 1911.05, "word": ".2.", "probability": 0.99853515625}], "temperature": 1.0}, {"id": 72, "seek": 193577, "start": 1913.05, "end": 1935.77, "text": " But for the sample, for the sample mean, it's 1.58, so that means sigma of X bar is smaller than sigma of X. It means exactly, the variation of X bar is always smaller than the variation of X, always.", "tokens": [583, 337, 264, 6889, 11, 337, 264, 6889, 914, 11, 309, 311, 502, 13, 20419, 11, 370, 300, 1355, 12771, 295, 1783, 2159, 307, 4356, 813, 12771, 295, 1783, 13, 467, 1355, 2293, 11, 264, 12990, 295, 1783, 2159, 307, 1009, 4356, 813, 264, 12990, 295, 1783, 11, 1009, 13], "avg_logprob": -0.18841912056885513, "compression_ratio": 1.6611570247933884, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1913.05, "end": 1913.37, "word": " But", "probability": 0.578125}, {"start": 1913.37, "end": 1913.57, "word": " for", "probability": 0.84912109375}, {"start": 1913.57, "end": 1913.79, "word": " the", "probability": 0.9013671875}, {"start": 1913.79, "end": 1914.11, "word": " sample,", "probability": 0.66552734375}, {"start": 1915.55, "end": 1915.81, "word": " for", "probability": 0.69775390625}, {"start": 1915.81, "end": 1915.97, "word": " the", "probability": 0.91650390625}, {"start": 1915.97, "end": 1916.37, "word": " sample", "probability": 0.86669921875}, {"start": 1916.37, "end": 1916.75, "word": " mean,", "probability": 0.7490234375}, {"start": 1916.93, "end": 1917.31, "word": " it's", "probability": 0.914794921875}, {"start": 1917.31, "end": 1917.57, "word": " 1", "probability": 0.90283203125}, {"start": 1917.57, "end": 1918.55, "word": ".58,", "probability": 0.973876953125}, {"start": 1919.33, "end": 1919.57, "word": " so", "probability": 0.92333984375}, {"start": 1919.57, "end": 1919.79, "word": " that", "probability": 0.93310546875}, {"start": 1919.79, "end": 1920.19, "word": " means", "probability": 0.93603515625}, {"start": 1920.19, "end": 1920.97, "word": " sigma", "probability": 0.5859375}, {"start": 1920.97, "end": 1921.13, "word": " of", "probability": 0.78662109375}, {"start": 1921.13, "end": 1921.29, "word": " X", "probability": 0.482421875}, {"start": 1921.29, "end": 1921.59, "word": " bar", "probability": 0.90087890625}, {"start": 1921.59, "end": 1921.89, "word": " is", "probability": 0.94970703125}, {"start": 1921.89, "end": 1922.25, "word": " smaller", "probability": 0.85693359375}, {"start": 1922.25, "end": 1922.69, "word": " than", "probability": 0.94775390625}, {"start": 1922.69, "end": 1923.29, "word": " sigma", "probability": 0.9208984375}, {"start": 1923.29, "end": 1923.45, "word": " of", "probability": 0.94384765625}, {"start": 1923.45, "end": 1923.71, "word": " X.", "probability": 0.990234375}, {"start": 1927.27, "end": 1927.71, "word": " It", "probability": 0.76318359375}, {"start": 1927.71, "end": 1927.99, "word": " means", "probability": 0.91357421875}, {"start": 1927.99, "end": 1928.37, "word": " exactly,", "probability": 0.87451171875}, {"start": 1928.47, "end": 1928.55, "word": " the", "probability": 0.9091796875}, {"start": 1928.55, "end": 1928.99, "word": " variation", "probability": 0.884765625}, {"start": 1928.99, "end": 1930.37, "word": " of", "probability": 0.96142578125}, {"start": 1930.37, "end": 1930.67, "word": " X", "probability": 0.98876953125}, {"start": 1930.67, "end": 1931.05, "word": " bar", "probability": 0.951171875}, {"start": 1931.05, "end": 1931.43, "word": " is", "probability": 0.9453125}, {"start": 1931.43, "end": 1932.01, "word": " always", "probability": 0.91162109375}, {"start": 1932.01, "end": 1933.05, "word": " smaller", "probability": 0.8486328125}, {"start": 1933.05, "end": 1933.31, "word": " than", "probability": 0.9443359375}, {"start": 1933.31, "end": 1933.47, "word": " the", "probability": 0.9033203125}, {"start": 1933.47, "end": 1933.75, "word": " variation", "probability": 0.82080078125}, {"start": 1933.75, "end": 1933.95, "word": " of", "probability": 0.95947265625}, {"start": 1933.95, "end": 1934.23, "word": " X,", "probability": 0.9921875}, {"start": 1934.51, "end": 1935.77, "word": " always.", "probability": 0.9091796875}], "temperature": 1.0}, {"id": 73, "seek": 196806, "start": 1940.42, "end": 1968.06, "text": " So here is the comparison. The distribution was uniform. It's no longer uniform. It looks like a bell shape. The mean of X is 21, which is the same as the mean of X bar. But the standard deviation of the population is larger than the standard deviation of the sample mean or the average.", "tokens": [407, 510, 307, 264, 9660, 13, 440, 7316, 390, 9452, 13, 467, 311, 572, 2854, 9452, 13, 467, 1542, 411, 257, 4549, 3909, 13, 440, 914, 295, 1783, 307, 5080, 11, 597, 307, 264, 912, 382, 264, 914, 295, 1783, 2159, 13, 583, 264, 3832, 25163, 295, 264, 4415, 307, 4833, 813, 264, 3832, 25163, 295, 264, 6889, 914, 420, 264, 4274, 13], "avg_logprob": -0.1955566427204758, "compression_ratio": 1.6842105263157894, "no_speech_prob": 0.0, "words": [{"start": 1940.4199999999998, "end": 1941.08, "word": " So", "probability": 0.849609375}, {"start": 1941.08, "end": 1941.74, "word": " here", "probability": 0.57861328125}, {"start": 1941.74, "end": 1942.1, "word": " is", "probability": 0.72265625}, {"start": 1942.1, "end": 1942.32, "word": " the", "probability": 0.8857421875}, {"start": 1942.32, "end": 1942.72, "word": " comparison.", "probability": 0.86083984375}, 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We know that. If we have a population and from that population, so we have this big population, from this population suppose we selected 10 samples, sample 1 with size 50.", "tokens": [20825, 10938, 295, 264, 912, 6889, 2744, 490, 264, 912, 4415, 486, 11257, 819, 6889, 1355, 13, 492, 458, 300, 13, 759, 321, 362, 257, 4415, 293, 490, 300, 4415, 11, 370, 321, 362, 341, 955, 4415, 11, 490, 341, 4415, 7297, 321, 8209, 1266, 10938, 11, 6889, 502, 365, 2744, 2625, 13], "avg_logprob": -0.20833333278143848, "compression_ratio": 1.7908496732026145, "no_speech_prob": 0.0, "words": [{"start": 1973.83, "end": 1974.37, "word": " Different", "probability": 0.37890625}, {"start": 1974.37, "end": 1974.99, "word": " samples", "probability": 0.8251953125}, {"start": 1974.99, "end": 1975.21, "word": " of", "probability": 0.87841796875}, {"start": 1975.21, "end": 1975.39, "word": " the", "probability": 0.84619140625}, {"start": 1975.39, "end": 1975.67, "word": " same", "probability": 0.85986328125}, {"start": 1975.67, "end": 1976.07, "word": " sample", "probability": 0.869140625}, {"start": 1976.07, "end": 1976.59, "word": " size", "probability": 0.8115234375}, {"start": 1976.59, "end": 1977.85, "word": " from", "probability": 0.69970703125}, {"start": 1977.85, "end": 1978.09, "word": " the", "probability": 0.91748046875}, {"start": 1978.09, "end": 1978.31, "word": " same", "probability": 0.896484375}, {"start": 1978.31, "end": 1978.87, "word": " population", "probability": 0.94140625}, {"start": 1978.87, "end": 1979.35, "word": " will", "probability": 0.82080078125}, {"start": 1979.35, "end": 1979.63, "word": " yield", "probability": 0.92578125}, {"start": 1979.63, "end": 1980.11, "word": " different", "probability": 0.8798828125}, {"start": 1980.11, "end": 1980.49, "word": " sample", "probability": 0.7880859375}, {"start": 1980.49, "end": 1980.79, "word": " means.", "probability": 0.7236328125}, {"start": 1981.45, "end": 1981.59, "word": " We", "probability": 0.75244140625}, {"start": 1981.59, "end": 1981.69, "word": " know", "probability": 0.87890625}, {"start": 1981.69, "end": 1981.93, "word": " that.", "probability": 0.9375}, {"start": 1982.93, "end": 1983.31, "word": " If", "probability": 0.9033203125}, {"start": 1983.31, "end": 1983.41, "word": " we", "probability": 0.9306640625}, {"start": 1983.41, "end": 1983.51, "word": " have", "probability": 0.94873046875}, {"start": 1983.51, "end": 1983.61, "word": " a", "probability": 0.95556640625}, {"start": 1983.61, "end": 1984.03, "word": " population", "probability": 0.93701171875}, {"start": 1984.03, "end": 1985.75, "word": " and", "probability": 0.53857421875}, {"start": 1985.75, "end": 1986.05, "word": " from", "probability": 0.8681640625}, {"start": 1986.05, "end": 1986.33, "word": " that", "probability": 0.93505859375}, {"start": 1986.33, "end": 1986.93, "word": " population,", "probability": 0.92822265625}, {"start": 1987.23, "end": 1987.39, "word": " so", "probability": 0.8193359375}, {"start": 1987.39, "end": 1987.53, "word": " we", "probability": 0.88525390625}, {"start": 1987.53, "end": 1987.65, "word": " have", "probability": 0.94873046875}, {"start": 1987.65, "end": 1987.89, "word": " this", "probability": 0.94873046875}, {"start": 1987.89, "end": 1988.11, "word": " big", "probability": 0.89990234375}, {"start": 1988.11, "end": 1988.57, "word": " population,", "probability": 0.93212890625}, {"start": 1990.25, "end": 1990.53, "word": " from", "probability": 0.732421875}, {"start": 1990.53, "end": 1990.81, "word": " this", "probability": 0.94091796875}, {"start": 1990.81, "end": 1991.29, "word": " population", "probability": 0.9267578125}, {"start": 1991.29, "end": 1991.71, "word": " suppose", "probability": 0.63330078125}, {"start": 1991.71, "end": 1992.21, "word": " we", "probability": 0.8681640625}, {"start": 1992.21, "end": 1992.91, "word": " selected", "probability": 0.87890625}, {"start": 1992.91, "end": 1995.01, "word": " 10", "probability": 0.60595703125}, {"start": 1995.01, "end": 1995.71, "word": " samples,", "probability": 0.86328125}, {"start": 1995.91, "end": 1996.23, "word": " sample", "probability": 0.8955078125}, {"start": 1996.23, "end": 1996.55, "word": " 1", "probability": 0.72021484375}, {"start": 1996.55, "end": 1997.85, "word": " with", "probability": 0.7685546875}, {"start": 1997.85, "end": 1998.47, "word": " size", "probability": 0.849609375}, {"start": 1998.47, "end": 1999.85, "word": " 50.", "probability": 0.91552734375}], "temperature": 1.0}, {"id": 75, "seek": 202852, "start": 2001.54, "end": 2028.52, "text": " Another sample, sample 2 with the same size. All the way, suppose we select 10 samples, sample 10, also with the same sample size. Each one will have different average, different sample. Maybe the first one has 70, 68, suppose the last one has 71.", "tokens": [3996, 6889, 11, 6889, 568, 365, 264, 912, 2744, 13, 1057, 264, 636, 11, 7297, 321, 3048, 1266, 10938, 11, 6889, 1266, 11, 611, 365, 264, 912, 6889, 2744, 13, 6947, 472, 486, 362, 819, 4274, 11, 819, 6889, 13, 2704, 264, 700, 472, 575, 5285, 11, 23317, 11, 7297, 264, 1036, 472, 575, 30942, 13], "avg_logprob": -0.2197094298245614, "compression_ratio": 1.6423841059602649, "no_speech_prob": 0.0, "words": [{"start": 2001.54, "end": 2001.92, "word": " Another", "probability": 0.501953125}, {"start": 2001.92, "end": 2002.38, "word": " sample,", "probability": 0.71435546875}, {"start": 2002.5, "end": 2002.7, "word": " sample", "probability": 0.78173828125}, {"start": 2002.7, "end": 2003.02, "word": " 2", "probability": 0.6171875}, {"start": 2003.02, "end": 2003.24, "word": " with", "probability": 0.58740234375}, {"start": 2003.24, "end": 2003.38, "word": " the", "probability": 0.869140625}, {"start": 2003.38, "end": 2003.58, "word": " same", "probability": 0.9013671875}, {"start": 2003.58, "end": 2004.02, "word": " size.", "probability": 0.83203125}, {"start": 2006.06, "end": 2006.4, "word": " All", "probability": 0.89892578125}, {"start": 2006.4, "end": 2006.56, "word": " the", "probability": 0.9150390625}, {"start": 2006.56, "end": 2006.78, "word": " way,", "probability": 0.96142578125}, {"start": 2007.0, "end": 2007.26, "word": " suppose", "probability": 0.8388671875}, {"start": 2007.26, "end": 2007.54, "word": " we", "probability": 0.8525390625}, {"start": 2007.54, "end": 2007.96, "word": " select", "probability": 0.85400390625}, {"start": 2007.96, "end": 2008.46, "word": " 10", "probability": 0.74365234375}, {"start": 2008.46, "end": 2009.04, "word": " samples,", "probability": 0.8388671875}, {"start": 2009.32, "end": 2009.6, "word": " sample", "probability": 0.81591796875}, {"start": 2009.6, "end": 2009.98, "word": " 10,", "probability": 0.9560546875}, {"start": 2010.86, "end": 2011.36, "word": " also", "probability": 0.86181640625}, {"start": 2011.36, "end": 2011.84, "word": " with", "probability": 0.8955078125}, {"start": 2011.84, "end": 2012.0, "word": " the", "probability": 0.91162109375}, {"start": 2012.0, "end": 2012.8, "word": " same", "probability": 0.89501953125}, {"start": 2012.8, "end": 2013.68, "word": " sample", "probability": 0.888671875}, {"start": 2013.68, "end": 2014.16, "word": " size.", "probability": 0.83740234375}, {"start": 2015.42, "end": 2016.08, "word": " Each", "probability": 0.876953125}, {"start": 2016.08, "end": 2016.4, "word": " one", "probability": 0.93603515625}, {"start": 2016.4, "end": 2018.02, "word": " will", "probability": 0.8701171875}, {"start": 2018.02, "end": 2018.46, "word": " have", "probability": 0.9453125}, {"start": 2018.46, "end": 2021.06, "word": " different", "probability": 0.76513671875}, {"start": 2021.06, "end": 2021.46, "word": " average,", "probability": 0.52294921875}, {"start": 2021.62, "end": 2021.9, "word": " different", "probability": 0.77978515625}, {"start": 2021.9, "end": 2022.22, "word": " sample.", "probability": 0.435302734375}, {"start": 2022.34, "end": 2022.66, "word": " Maybe", "probability": 0.90966796875}, {"start": 2022.66, "end": 2022.96, "word": " the", "probability": 0.8984375}, {"start": 2022.96, "end": 2023.2, "word": " first", "probability": 0.88916015625}, {"start": 2023.2, "end": 2023.4, "word": " one", "probability": 0.93359375}, {"start": 2023.4, "end": 2023.62, "word": " has", "probability": 0.8681640625}, {"start": 2023.62, "end": 2024.12, "word": " 70,", "probability": 0.96484375}, {"start": 2024.64, "end": 2025.48, "word": " 68,", "probability": 0.95703125}, {"start": 2026.72, "end": 2027.02, "word": " suppose", "probability": 0.728515625}, {"start": 2027.02, "end": 2027.2, "word": " the", "probability": 0.9150390625}, {"start": 2027.2, "end": 2027.44, "word": " last", "probability": 0.88427734375}, {"start": 2027.44, "end": 2027.68, "word": " one", "probability": 0.92626953125}, {"start": 2027.68, "end": 2028.06, "word": " has", "probability": 0.94580078125}, {"start": 2028.06, "end": 2028.52, "word": " 71.", "probability": 0.9755859375}], "temperature": 1.0}, {"id": 76, "seek": 205164, "start": 2029.88, "end": 2051.64, "text": " So again, different samples of the same size, I got size of 15, from the same population will yield different sample means. This is one fact. Now, a measure of the variability, which means sigma.", "tokens": [407, 797, 11, 819, 10938, 295, 264, 912, 2744, 11, 286, 658, 2744, 295, 2119, 11, 490, 264, 912, 4415, 486, 11257, 819, 6889, 1355, 13, 639, 307, 472, 1186, 13, 823, 11, 257, 3481, 295, 264, 35709, 11, 597, 1355, 12771, 13], "avg_logprob": -0.20259232785214076, "compression_ratio": 1.410071942446043, "no_speech_prob": 0.0, "words": [{"start": 2029.88, "end": 2030.16, "word": " So", "probability": 0.80029296875}, {"start": 2030.16, "end": 2030.46, "word": " again,", "probability": 0.75537109375}, {"start": 2030.72, "end": 2030.98, "word": " different", "probability": 0.87451171875}, {"start": 2030.98, "end": 2031.62, "word": " samples", "probability": 0.87109375}, {"start": 2031.62, "end": 2034.04, "word": " of", "probability": 0.90966796875}, {"start": 2034.04, "end": 2034.26, "word": " the", "probability": 0.9130859375}, {"start": 2034.26, "end": 2034.54, "word": " same", "probability": 0.91015625}, {"start": 2034.54, "end": 2035.12, "word": " size,", "probability": 0.81494140625}, {"start": 2035.42, "end": 2036.04, "word": " I", "probability": 0.387451171875}, {"start": 2036.04, "end": 2036.2, "word": " got", "probability": 0.908203125}, {"start": 2036.2, "end": 2036.48, "word": " size", "probability": 0.62109375}, {"start": 2036.48, "end": 2036.66, "word": " of", "probability": 0.76904296875}, {"start": 2036.66, "end": 2037.06, "word": " 15,", "probability": 0.85595703125}, {"start": 2037.72, "end": 2038.12, "word": " from", "probability": 0.861328125}, {"start": 2038.12, "end": 2038.34, "word": " the", "probability": 0.92041015625}, {"start": 2038.34, "end": 2038.58, "word": " same", "probability": 0.90478515625}, {"start": 2038.58, "end": 2039.22, "word": " population", "probability": 0.93603515625}, {"start": 2039.22, "end": 2040.46, "word": " will", "probability": 0.6533203125}, {"start": 2040.46, "end": 2040.72, "word": " yield", "probability": 0.923828125}, {"start": 2040.72, "end": 2041.14, "word": " different", "probability": 0.8876953125}, {"start": 2041.14, "end": 2041.52, "word": " sample", "probability": 0.8125}, {"start": 2041.52, "end": 2041.86, "word": " means.", "probability": 0.8291015625}, {"start": 2043.12, "end": 2043.28, "word": " This", "probability": 0.7568359375}, {"start": 2043.28, "end": 2043.4, "word": " is", "probability": 0.94384765625}, {"start": 2043.4, "end": 2043.68, "word": " one", "probability": 0.921875}, {"start": 2043.68, "end": 2044.94, "word": " fact.", "probability": 0.89697265625}, {"start": 2045.9, "end": 2046.26, "word": " Now,", "probability": 0.94482421875}, {"start": 2046.66, "end": 2046.82, "word": " a", "probability": 0.81103515625}, {"start": 2046.82, "end": 2047.0, "word": " measure", "probability": 0.87939453125}, {"start": 2047.0, "end": 2047.38, "word": " of", "probability": 0.96826171875}, {"start": 2047.38, "end": 2047.54, "word": " the", "probability": 0.62451171875}, {"start": 2047.54, "end": 2048.08, "word": " variability,", "probability": 0.97509765625}, {"start": 2049.48, "end": 2049.92, "word": " which", "probability": 0.95166015625}, {"start": 2049.92, "end": 2050.44, "word": " means", "probability": 0.94384765625}, {"start": 2050.44, "end": 2051.64, "word": " sigma.", "probability": 0.76123046875}], "temperature": 1.0}, {"id": 77, "seek": 208188, "start": 2053.18, "end": 2081.88, "text": " and I'm interested in x bar. So a measure of variability in the mean from sample to sample is given by something called, instead of saying standard deviation of the sample mean, we have this expression, standard error of the mean. So this one is called standard error of the mean, or sigma of x bar. 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So it's better to distinguish between population standard deviation sigma and sigma of x bar which is the standard error of the mean. So we have sigma", "tokens": [6713, 295, 264, 914, 420, 2935, 445, 584, 3832, 6713, 13, 407, 309, 311, 1101, 281, 20206, 1296, 4415, 3832, 25163, 12771, 293, 12771, 295, 2031, 2159, 597, 307, 264, 3832, 6713, 295, 264, 914, 13, 407, 321, 362, 12771], "avg_logprob": -0.17701981998071437, "compression_ratio": 1.5813953488372092, "no_speech_prob": 2.384185791015625e-07, "words": [{"start": 2083.59, "end": 2083.93, "word": " error", "probability": 0.46875}, {"start": 2083.93, "end": 2084.15, "word": " of", "probability": 0.947265625}, {"start": 2084.15, "end": 2084.29, "word": " the", "probability": 0.87744140625}, {"start": 2084.29, "end": 2084.47, "word": " mean", "probability": 0.95751953125}, {"start": 2084.47, "end": 2084.87, "word": " or", "probability": 0.54345703125}, {"start": 2084.87, "end": 2085.25, "word": " simply", "probability": 0.8818359375}, {"start": 2085.25, "end": 2085.53, "word": " just", "probability": 0.8681640625}, {"start": 2085.53, "end": 2085.91, "word": " say", "probability": 0.93505859375}, {"start": 2085.91, "end": 2086.59, "word": " standard", "probability": 0.8486328125}, {"start": 2086.59, "end": 2086.89, "word": " error.", "probability": 0.8935546875}, {"start": 2088.33, "end": 2088.63, "word": " So", "probability": 0.85009765625}, {"start": 2088.63, "end": 2088.81, "word": " it's", "probability": 0.75537109375}, {"start": 2088.81, "end": 2089.01, "word": " better", "probability": 0.91259765625}, {"start": 2089.01, "end": 2089.61, "word": " to", "probability": 0.94970703125}, {"start": 2089.61, "end": 2090.25, "word": " distinguish", "probability": 0.88916015625}, {"start": 2090.25, "end": 2090.85, "word": " between", "probability": 0.853515625}, {"start": 2090.85, "end": 2092.29, "word": " population", "probability": 0.81640625}, {"start": 2092.29, "end": 2092.69, "word": " standard", "probability": 0.7353515625}, {"start": 2092.69, "end": 2093.15, "word": " deviation", "probability": 0.908203125}, {"start": 2093.15, "end": 2093.61, "word": " sigma", "probability": 0.454833984375}, {"start": 2093.61, "end": 2096.61, "word": " and", "probability": 0.82275390625}, {"start": 2096.61, "end": 2097.05, "word": " sigma", "probability": 0.90576171875}, {"start": 2097.05, "end": 2097.25, "word": " of", "probability": 0.90966796875}, {"start": 2097.25, "end": 2097.51, "word": " x", "probability": 0.8447265625}, {"start": 2097.51, "end": 2097.85, "word": " bar", "probability": 0.85205078125}, {"start": 2097.85, "end": 2098.17, "word": " which", "probability": 0.84033203125}, {"start": 2098.17, "end": 2098.45, "word": " is", "probability": 0.95068359375}, {"start": 2098.45, "end": 2098.71, "word": " the", "probability": 0.916015625}, {"start": 2098.71, "end": 2099.21, "word": " standard", "probability": 0.9375}, {"start": 2099.21, "end": 2099.61, "word": " error", "probability": 0.87255859375}, {"start": 2099.61, "end": 2100.53, "word": " of", "probability": 0.96337890625}, {"start": 2100.53, "end": 2100.67, "word": " the", "probability": 0.908203125}, {"start": 2100.67, "end": 2100.81, "word": " mean.", "probability": 0.96923828125}, {"start": 2101.17, "end": 2101.43, "word": " So", "probability": 0.92919921875}, {"start": 2101.43, "end": 2101.53, "word": " we", "probability": 0.87890625}, {"start": 2101.53, "end": 2101.67, "word": " have", "probability": 0.9501953125}, {"start": 2101.67, "end": 2102.07, "word": " sigma", "probability": 0.9306640625}], "temperature": 1.0}, {"id": 79, "seek": 212960, "start": 2104.02, "end": 2129.6, "text": " And sigma of x bar. This one is standard error of x bar. And always sigma of x bar is smaller than sigma, unless n equals one. Later we'll see why if n is one, then the two quantities are the same. Now, sigma of x bar", "tokens": [400, 12771, 295, 2031, 2159, 13, 639, 472, 307, 3832, 6713, 295, 2031, 2159, 13, 400, 1009, 12771, 295, 2031, 2159, 307, 4356, 813, 12771, 11, 5969, 297, 6915, 472, 13, 11965, 321, 603, 536, 983, 498, 297, 307, 472, 11, 550, 264, 732, 22927, 366, 264, 912, 13, 823, 11, 12771, 295, 2031, 2159], "avg_logprob": -0.2053571372692074, "compression_ratio": 1.5571428571428572, "no_speech_prob": 0.0, "words": [{"start": 2104.02, "end": 2104.42, "word": " And", "probability": 0.52587890625}, {"start": 2104.42, "end": 2105.08, "word": " sigma", "probability": 0.58642578125}, {"start": 2105.08, "end": 2105.24, "word": " of", "probability": 0.88330078125}, {"start": 2105.24, "end": 2105.36, "word": " x", "probability": 0.81591796875}, {"start": 2105.36, "end": 2105.54, "word": " bar.", "probability": 0.93310546875}, {"start": 2105.84, "end": 2106.2, "word": " This", "probability": 0.876953125}, {"start": 2106.2, "end": 2106.5, "word": " one", "probability": 0.916015625}, {"start": 2106.5, "end": 2106.9, "word": " is", "probability": 0.947265625}, {"start": 2106.9, "end": 2107.46, "word": " standard", "probability": 0.85595703125}, {"start": 2107.46, "end": 2107.86, "word": " error", "probability": 0.88330078125}, {"start": 2107.86, "end": 2108.46, "word": " of", "probability": 0.96142578125}, {"start": 2108.46, "end": 2108.98, "word": " x", "probability": 0.98046875}, {"start": 2108.98, "end": 2109.24, "word": " bar.", "probability": 0.9306640625}, {"start": 2109.98, "end": 2110.2, "word": " And", "probability": 0.93408203125}, {"start": 2110.2, "end": 2110.66, "word": " always", "probability": 0.85498046875}, {"start": 2110.66, "end": 2111.88, "word": " sigma", "probability": 0.5888671875}, {"start": 2111.88, "end": 2112.04, "word": " of", "probability": 0.9052734375}, {"start": 2112.04, "end": 2112.18, "word": " x", "probability": 0.99609375}, {"start": 2112.18, "end": 2112.38, "word": " bar", "probability": 0.9501953125}, {"start": 2112.38, "end": 2112.54, "word": " is", "probability": 0.94921875}, {"start": 2112.54, "end": 2112.86, "word": " smaller", "probability": 0.87158203125}, {"start": 2112.86, "end": 2114.16, "word": " than", "probability": 0.9130859375}, {"start": 2114.16, "end": 2114.6, "word": " sigma,", "probability": 0.88916015625}, {"start": 2114.94, "end": 2115.48, "word": " unless", "probability": 0.83349609375}, {"start": 2115.48, "end": 2115.76, "word": " n", "probability": 0.8544921875}, {"start": 2115.76, "end": 2116.06, "word": " equals", "probability": 0.787109375}, {"start": 2116.06, "end": 2116.3, "word": " one.", "probability": 0.5341796875}, {"start": 2116.96, "end": 2117.3, "word": " Later", "probability": 0.796875}, {"start": 2117.3, "end": 2117.5, "word": " we'll", "probability": 0.5167236328125}, {"start": 2117.5, "end": 2117.64, "word": " see", "probability": 0.9296875}, {"start": 2117.64, "end": 2118.08, "word": " why", "probability": 0.91455078125}, {"start": 2118.08, "end": 2118.66, "word": " if", "probability": 0.78466796875}, {"start": 2118.66, "end": 2118.82, "word": " n", "probability": 0.9375}, {"start": 2118.82, "end": 2118.96, "word": " is", "probability": 0.916015625}, {"start": 2118.96, "end": 2119.22, "word": " one,", "probability": 0.892578125}, {"start": 2119.34, "end": 2119.56, "word": " then", "probability": 0.841796875}, {"start": 2119.56, "end": 2120.84, "word": " the", "probability": 0.90283203125}, {"start": 2120.84, "end": 2121.08, "word": " two", "probability": 0.9384765625}, {"start": 2121.08, "end": 2121.64, "word": " quantities", "probability": 0.98095703125}, {"start": 2121.64, "end": 2122.8, "word": " are", "probability": 0.9169921875}, {"start": 2122.8, "end": 2122.98, "word": " the", "probability": 0.90283203125}, {"start": 2122.98, "end": 2123.18, "word": " same.", "probability": 0.9150390625}, {"start": 2125.76, "end": 2126.3, "word": " Now,", "probability": 0.94775390625}, {"start": 2127.84, "end": 2128.84, "word": " sigma", "probability": 0.84716796875}, {"start": 2128.84, "end": 2129.04, "word": " of", "probability": 0.96142578125}, {"start": 2129.04, "end": 2129.26, "word": " x", "probability": 0.99560546875}, {"start": 2129.26, "end": 2129.6, "word": " bar", "probability": 0.962890625}], "temperature": 1.0}, {"id": 80, "seek": 215982, "start": 2132.34, "end": 2159.82, "text": " In this case, it's 158 equals sigma over root n. I mean, for this specific example, if we divide sigma, which is 2.236 divided by n, and n 2, you will get 1.58. So we got mu x bar equal mu.", "tokens": [682, 341, 1389, 11, 309, 311, 2119, 23, 6915, 12771, 670, 5593, 297, 13, 286, 914, 11, 337, 341, 2685, 1365, 11, 498, 321, 9845, 12771, 11, 597, 307, 568, 13, 9356, 21, 6666, 538, 297, 11, 293, 297, 568, 11, 291, 486, 483, 502, 13, 20419, 13, 407, 321, 658, 2992, 2031, 2159, 2681, 2992, 13], "avg_logprob": -0.21093750077074971, "compression_ratio": 1.3013698630136987, "no_speech_prob": 0.0, "words": [{"start": 2132.34, "end": 2132.54, "word": " In", "probability": 0.2919921875}, {"start": 2132.54, "end": 2132.78, "word": " this", "probability": 0.947265625}, {"start": 2132.78, "end": 2133.12, "word": " case,", "probability": 0.9150390625}, {"start": 2133.34, "end": 2133.46, "word": " it's", "probability": 0.76025390625}, {"start": 2133.46, "end": 2134.26, "word": " 158", "probability": 0.8798828125}, {"start": 2134.26, "end": 2135.12, "word": " equals", "probability": 0.712890625}, {"start": 2135.12, "end": 2135.58, "word": " sigma", "probability": 0.833984375}, {"start": 2135.58, "end": 2135.84, "word": " over", "probability": 0.85693359375}, {"start": 2135.84, "end": 2136.1, "word": " root", "probability": 0.90380859375}, {"start": 2136.1, "end": 2136.28, "word": " n.", "probability": 0.56982421875}, {"start": 2137.6, "end": 2137.82, "word": " I", "probability": 0.947265625}, {"start": 2137.82, "end": 2138.02, "word": " mean,", "probability": 0.9619140625}, {"start": 2138.18, "end": 2138.42, "word": " for", "probability": 0.94921875}, {"start": 2138.42, "end": 2138.68, "word": " this", "probability": 0.94775390625}, {"start": 2138.68, "end": 2139.34, "word": " specific", "probability": 0.90478515625}, {"start": 2139.34, "end": 2140.6, "word": " example,", "probability": 0.97216796875}, {"start": 2140.78, "end": 2140.86, "word": " if", "probability": 0.91552734375}, {"start": 2140.86, "end": 2141.16, "word": " we", "probability": 0.95751953125}, {"start": 2141.16, "end": 2142.48, "word": " divide", "probability": 0.9169921875}, {"start": 2142.48, "end": 2143.66, "word": " sigma,", "probability": 0.88525390625}, {"start": 2143.82, "end": 2143.9, "word": " which", "probability": 0.94873046875}, {"start": 2143.9, "end": 2144.06, "word": " is", "probability": 0.9482421875}, {"start": 2144.06, "end": 2144.26, "word": " 2", "probability": 0.98388671875}, {"start": 2144.26, "end": 2145.22, "word": ".236", "probability": 0.9466145833333334}, {"start": 2145.22, "end": 2145.56, "word": " divided", "probability": 0.3740234375}, {"start": 2145.56, "end": 2145.84, "word": " by", "probability": 0.97119140625}, {"start": 2145.84, "end": 2146.16, "word": " n,", "probability": 0.92529296875}, {"start": 2146.82, "end": 2147.7, "word": " and", "probability": 0.91796875}, {"start": 2147.7, "end": 2147.98, "word": " n", "probability": 0.80810546875}, {"start": 2147.98, "end": 2150.16, "word": " 2,", "probability": 0.369140625}, {"start": 2150.4, "end": 2150.62, "word": " you", "probability": 0.71435546875}, {"start": 2150.62, "end": 2150.8, "word": " will", "probability": 0.763671875}, {"start": 2150.8, "end": 2151.14, "word": " get", "probability": 0.94189453125}, {"start": 2151.14, "end": 2152.72, "word": " 1", "probability": 0.98974609375}, {"start": 2152.72, "end": 2153.44, "word": ".58.", "probability": 0.984130859375}, {"start": 2157.62, "end": 2158.16, "word": " So", "probability": 0.95263671875}, {"start": 2158.16, "end": 2158.3, "word": " we", "probability": 0.8173828125}, {"start": 2158.3, "end": 2158.52, "word": " got", "probability": 0.830078125}, {"start": 2158.52, "end": 2158.74, "word": " mu", "probability": 0.6611328125}, {"start": 2158.74, "end": 2159.02, "word": " x", "probability": 0.904296875}, {"start": 2159.02, "end": 2159.28, "word": " bar", "probability": 0.77099609375}, {"start": 2159.28, "end": 2159.48, "word": " equal", "probability": 0.6669921875}, {"start": 2159.48, "end": 2159.82, "word": " mu.", "probability": 0.64990234375}], "temperature": 1.0}, {"id": 81, "seek": 218917, "start": 2162.14, "end": 2189.18, "text": " The spread is sigma over root. Now, if you compare sigma x bar and sigma, always sigma of x bar is smaller than sigma, unless m equals 1. And in reality, we don't have a sample of size 1. So always the sample size is greater than 1. So always sigma of x bar is smaller than sigma of the standard deviation of normalization.", "tokens": [440, 3974, 307, 12771, 670, 5593, 13, 823, 11, 498, 291, 6794, 12771, 2031, 2159, 293, 12771, 11, 1009, 12771, 295, 2031, 2159, 307, 4356, 813, 12771, 11, 5969, 275, 6915, 502, 13, 400, 294, 4103, 11, 321, 500, 380, 362, 257, 6889, 295, 2744, 502, 13, 407, 1009, 264, 6889, 2744, 307, 5044, 813, 502, 13, 407, 1009, 12771, 295, 2031, 2159, 307, 4356, 813, 12771, 295, 264, 3832, 25163, 295, 2710, 2144, 13], "avg_logprob": -0.2732318973070697, "compression_ratio": 1.7704918032786885, "no_speech_prob": 0.0, "words": [{"start": 2162.14, "end": 2162.42, "word": " The", "probability": 0.404296875}, {"start": 2162.42, "end": 2162.96, "word": " spread", "probability": 0.87451171875}, {"start": 2162.96, "end": 2163.32, "word": " is", "probability": 0.92822265625}, {"start": 2163.32, "end": 2163.64, "word": " sigma", "probability": 0.83642578125}, {"start": 2163.64, "end": 2163.86, "word": " 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{"start": 2173.68, "end": 2173.8, "word": " in", "probability": 0.4189453125}, {"start": 2173.8, "end": 2174.1, "word": " reality,", "probability": 0.9580078125}, {"start": 2174.22, "end": 2174.3, "word": " we", "probability": 0.7919921875}, {"start": 2174.3, "end": 2174.46, "word": " don't", "probability": 0.8291015625}, {"start": 2174.46, "end": 2174.64, "word": " have", "probability": 0.94482421875}, {"start": 2174.64, "end": 2174.8, "word": " a", "probability": 0.9384765625}, {"start": 2174.8, "end": 2175.0, "word": " sample", "probability": 0.87158203125}, {"start": 2175.0, "end": 2175.16, "word": " of", "probability": 0.495361328125}, {"start": 2175.16, "end": 2175.34, "word": " size", "probability": 0.8642578125}, {"start": 2175.34, "end": 2175.58, "word": " 1.", "probability": 0.84814453125}, {"start": 2176.18, "end": 2176.6, "word": " So", "probability": 0.95751953125}, {"start": 2176.6, "end": 2176.92, "word": " always", "probability": 0.54248046875}, {"start": 2176.92, 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standard error of X bar and the sample size, we'll see that as the sample size increases, sigma of X bar decreases. 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So as n increases, sigma of x bar goes down. So there is inverse relationship between the standard error of the mean and the sample size. So now we answered the three questions. 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So now, let's talk about sampling distribution of the sample mean if the population is normal.", "tokens": [498, 321, 3048, 527, 6889, 490, 2710, 4415, 365, 914, 6915, 264, 4415, 914, 293, 3832, 25163, 295, 3832, 6713, 6915, 12771, 670, 3732, 5593, 295, 300, 13, 407, 586, 11, 718, 311, 751, 466, 21179, 7316, 295, 264, 6889, 914, 498, 264, 4415, 307, 2710, 13], "avg_logprob": -0.21647135571887097, "compression_ratio": 1.6818181818181819, "no_speech_prob": 0.0, "words": [{"start": 2247.19, "end": 2247.59, "word": " if", "probability": 0.43896484375}, {"start": 2247.59, "end": 2248.03, "word": " we", "probability": 0.9482421875}, {"start": 2248.03, "end": 2249.79, "word": " select", "probability": 0.802734375}, {"start": 2249.79, "end": 2250.13, "word": " our", "probability": 0.904296875}, {"start": 2250.13, "end": 2250.47, "word": " sample", "probability": 0.87744140625}, {"start": 2250.47, "end": 2250.81, "word": " from", "probability": 0.873046875}, {"start": 2250.81, "end": 2251.29, "word": " normal", "probability": 0.75146484375}, {"start": 2251.29, "end": 2251.73, "word": " population", "probability": 0.96533203125}, {"start": 2251.73, "end": 2253.41, "word": " with", "probability": 0.7060546875}, {"start": 2253.41, "end": 2253.85, "word": " mean", "probability": 0.904296875}, {"start": 2253.85, "end": 2256.03, "word": " equals", "probability": 0.80712890625}, {"start": 2256.03, "end": 2256.45, "word": " the", "probability": 0.7255859375}, {"start": 2256.45, "end": 2257.43, "word": " population", "probability": 0.91162109375}, {"start": 2257.43, "end": 2257.85, "word": " mean", "probability": 0.95556640625}, {"start": 2257.85, "end": 2258.53, "word": " and", "probability": 0.72021484375}, {"start": 2258.53, "end": 2258.89, "word": " standard", "probability": 0.865234375}, {"start": 2258.89, "end": 2259.27, "word": " deviation", "probability": 0.91064453125}, {"start": 2259.27, "end": 2259.51, "word": " of", "probability": 0.43505859375}, {"start": 2259.51, "end": 2259.79, "word": " standard", "probability": 0.85205078125}, {"start": 2259.79, "end": 2260.09, "word": " error", "probability": 0.71240234375}, {"start": 2260.09, "end": 2260.53, "word": " equals", "probability": 0.94384765625}, {"start": 2260.53, "end": 2261.37, "word": " sigma", "probability": 0.79833984375}, {"start": 2261.37, "end": 2261.83, "word": " over", "probability": 0.90625}, {"start": 2261.83, "end": 2262.99, "word": " square", "probability": 0.7978515625}, {"start": 2262.99, "end": 2263.23, "word": " root", "probability": 0.92138671875}, {"start": 2263.23, "end": 2263.39, "word": " of", "probability": 0.76708984375}, {"start": 2263.39, "end": 2263.59, "word": " that.", "probability": 0.258544921875}, {"start": 2265.95, "end": 2266.27, "word": " So", "probability": 0.83447265625}, {"start": 2266.27, "end": 2266.51, "word": " now,", "probability": 0.7001953125}, {"start": 2266.99, "end": 2267.93, "word": " let's", "probability": 0.93310546875}, {"start": 2267.93, "end": 2268.17, "word": " talk", "probability": 0.90185546875}, {"start": 2268.17, "end": 2268.85, "word": " about", "probability": 0.90966796875}, {"start": 2268.85, "end": 2269.89, "word": " sampling", "probability": 0.95947265625}, {"start": 2269.89, "end": 2270.97, "word": " distribution", "probability": 0.5751953125}, {"start": 2270.97, "end": 2272.05, "word": " of", "probability": 0.96484375}, {"start": 2272.05, "end": 2272.25, "word": " the", "probability": 0.89892578125}, {"start": 2272.25, "end": 2272.55, "word": " sample", "probability": 0.91259765625}, {"start": 2272.55, "end": 2272.91, "word": " mean", "probability": 0.95361328125}, {"start": 2272.91, "end": 2273.73, "word": " if", "probability": 0.81591796875}, {"start": 2273.73, "end": 2273.95, "word": " the", "probability": 0.9150390625}, {"start": 2273.95, "end": 2274.41, "word": " population", "probability": 0.94140625}, {"start": 2274.41, "end": 2274.89, "word": " is", "probability": 0.9501953125}, {"start": 2274.89, "end": 2275.25, "word": " normal.", "probability": 0.8701171875}], "temperature": 1.0}, {"id": 85, "seek": 230087, "start": 2276.47, "end": 2300.87, "text": " So now, my population is normally distributed, and we are interested in the sampling distribution of the sample mean of X bar. 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So that's the shape. 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So now let's go back to the z-score we discussed before. 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And we know that Z has standard normal distribution with mean zero and variance one. In this case, we are looking for the semi-distribution of X bar. 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So the same equation, but different statistic. In the first one, we have x, for example, represents the score. Here, my sample statistic is the sample mean, which represents the average of the score. 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So x bar minus the mean of x bar divided by sigma of x bar. By using that mu of x bar equals mu, and sigma of x bar equals sigma over root n, we will end with this mu z square.", "tokens": [3175, 1080, 914, 11, 286, 914, 264, 914, 295, 2031, 2159, 11, 6666, 538, 1080, 3832, 6713, 13, 407, 2031, 2159, 3175, 264, 914, 295, 2031, 2159, 6666, 538, 12771, 295, 2031, 2159, 13, 3146, 1228, 300, 2992, 295, 2031, 2159, 6915, 2992, 11, 293, 12771, 295, 2031, 2159, 6915, 12771, 670, 5593, 297, 11, 321, 486, 917, 365, 341, 2992, 710, 3732, 13], "avg_logprob": -0.19771634615384615, "compression_ratio": 1.7241379310344827, "no_speech_prob": 0.0, "words": [{"start": 2426.34, "end": 2426.94, "word": " minus", "probability": 0.45849609375}, {"start": 2426.94, "end": 2427.54, "word": " its", "probability": 0.6201171875}, {"start": 2427.54, "end": 2427.94, "word": " mean,", "probability": 0.9619140625}, {"start": 2428.58, "end": 2428.78, "word": " I", "probability": 0.92822265625}, {"start": 2428.78, "end": 2428.9, "word": " mean", "probability": 0.966796875}, 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So z square equals sigma, I'm sorry, z equals x bar minus the mean divided by sigma bar, where x bar the sample mean, mu the population mean, sigma population standard deviation, and n is the sample size. So that's the difference between chapter six,", "tokens": [407, 341, 5367, 486, 312, 1143, 2602, 295, 1228, 264, 3894, 472, 13, 407, 710, 3732, 6915, 12771, 11, 286, 478, 2597, 11, 710, 6915, 2031, 2159, 3175, 264, 914, 6666, 538, 12771, 2159, 11, 689, 2031, 2159, 264, 6889, 914, 11, 2992, 264, 4415, 914, 11, 12771, 4415, 3832, 25163, 11, 293, 297, 307, 264, 6889, 2744, 13, 407, 300, 311, 264, 2649, 1296, 7187, 2309, 11], "avg_logprob": -0.2549818702366041, "compression_ratio": 1.6544502617801047, "no_speech_prob": 0.0, "words": [{"start": 2456.31, "end": 2456.63, "word": " So", "probability": 0.779296875}, {"start": 2456.63, "end": 2457.09, "word": " this", "probability": 0.7392578125}, {"start": 2457.09, "end": 2457.65, "word": " equation", "probability": 0.9697265625}, {"start": 2457.65, "end": 2457.93, "word": " will", "probability": 0.75244140625}, {"start": 2457.93, "end": 2458.09, "word": " be", "probability": 0.9482421875}, {"start": 2458.09, "end": 2458.47, "word": " used", 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Here we are interested in x bar minus the mean of x bar which is mu. And sigma of x bar equals sigma of r. 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When we are saying mean of X bar equals mu, it means the expected value of X bar equals mu. In other words, the expected of X bar equals mu. 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So this is a new definition, unbiased estimator", "tokens": [307, 364, 517, 5614, 1937, 8017, 1639, 295, 2992, 13, 407, 341, 307, 257, 777, 7123, 11, 517, 5614, 1937, 8017, 1639], "avg_logprob": -0.2749660429747208, "compression_ratio": 1.1940298507462686, "no_speech_prob": 0.0, "words": [{"start": 2545.54, "end": 2546.0, "word": " is", "probability": 0.37744140625}, {"start": 2546.0, "end": 2547.2, "word": " an", "probability": 0.85546875}, {"start": 2547.2, "end": 2547.9, "word": " unbiased", "probability": 0.93212890625}, {"start": 2547.9, "end": 2551.42, "word": " estimator", "probability": 0.926025390625}, {"start": 2551.42, "end": 2555.58, "word": " of", "probability": 0.9384765625}, {"start": 2555.58, "end": 2555.82, "word": " mu.", "probability": 0.32470703125}, {"start": 2557.54, "end": 2558.52, "word": " So", "probability": 0.68359375}, {"start": 2558.52, "end": 2558.72, "word": " this", "probability": 0.495361328125}, {"start": 2558.72, "end": 2558.84, "word": " is", "probability": 0.80859375}, {"start": 2558.84, "end": 2558.9, "word": " a", "probability": 0.83251953125}, {"start": 2558.9, "end": 2559.06, "word": " new", "probability": 0.92333984375}, {"start": 2559.06, "end": 2559.66, "word": " definition,", "probability": 0.91845703125}, {"start": 2560.06, "end": 2560.62, "word": " unbiased", "probability": 0.8986002604166666}, {"start": 2560.62, "end": 2561.54, "word": " estimator", "probability": 0.94140625}], "temperature": 1.0}, {"id": 96, "seek": 258244, "start": 2562.53, "end": 2582.45, "text": " X bar is called unbiased estimator if this condition is satisfied. I mean, if the mean of X bar or if the expected value of X bar equals the population mean, in this case, we say that X bar is good estimator of Mu. Because on average,", "tokens": [1783, 2159, 307, 1219, 517, 5614, 1937, 8017, 1639, 498, 341, 4188, 307, 11239, 13, 286, 914, 11, 498, 264, 914, 295, 1783, 2159, 420, 498, 264, 5176, 2158, 295, 1783, 2159, 6915, 264, 4415, 914, 11, 294, 341, 1389, 11, 321, 584, 300, 1783, 2159, 307, 665, 8017, 1639, 295, 15601, 13, 1436, 322, 4274, 11], "avg_logprob": -0.17268318991208897, "compression_ratio": 1.5771812080536913, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2562.53, "end": 2562.89, "word": " X", "probability": 0.51513671875}, {"start": 2562.89, "end": 2563.07, "word": " bar", "probability": 0.7744140625}, {"start": 2563.07, "end": 2563.27, "word": " is", "probability": 0.93212890625}, {"start": 2563.27, "end": 2563.63, "word": " called", "probability": 0.88916015625}, {"start": 2563.63, "end": 2564.31, "word": " unbiased", "probability": 0.93603515625}, {"start": 2564.31, "end": 2564.81, "word": " estimator", "probability": 0.949951171875}, {"start": 2564.81, "end": 2565.49, "word": " if", "probability": 0.8291015625}, {"start": 2565.49, "end": 2565.97, "word": " this", "probability": 0.82373046875}, {"start": 2565.97, "end": 2566.35, "word": " condition", "probability": 0.943359375}, {"start": 2566.35, "end": 2566.55, "word": " is", "probability": 0.9541015625}, {"start": 2566.55, "end": 2567.09, "word": " satisfied.", "probability": 0.86083984375}, {"start": 2567.87, "end": 2568.01, "word": " I", "probability": 0.9296875}, {"start": 2568.01, "end": 2568.27, "word": " mean,", "probability": 0.962890625}, {"start": 2568.83, "end": 2569.03, "word": " if", "probability": 0.947265625}, {"start": 2569.03, "end": 2569.25, "word": " the", "probability": 0.916015625}, {"start": 2569.25, "end": 2569.41, "word": " mean", "probability": 0.97607421875}, {"start": 2569.41, "end": 2569.53, "word": " of", "probability": 0.97021484375}, {"start": 2569.53, "end": 2569.75, "word": " X", "probability": 0.73828125}, {"start": 2569.75, "end": 2570.11, "word": " bar", "probability": 0.95751953125}, {"start": 2570.11, "end": 2571.39, "word": " or", "probability": 0.69287109375}, {"start": 2571.39, "end": 2571.73, "word": " if", "probability": 0.912109375}, {"start": 2571.73, "end": 2571.93, "word": " the", "probability": 0.90673828125}, {"start": 2571.93, "end": 2572.49, "word": " expected", "probability": 0.8720703125}, {"start": 2572.49, "end": 2572.89, "word": " value", "probability": 0.97509765625}, {"start": 2572.89, "end": 2573.09, "word": " of", "probability": 0.9638671875}, {"start": 2573.09, "end": 2573.27, "word": " X", "probability": 0.9794921875}, {"start": 2573.27, "end": 2573.63, "word": " bar", "probability": 0.96533203125}, {"start": 2573.63, "end": 2574.45, "word": " equals", "probability": 0.916015625}, {"start": 2574.45, "end": 2574.73, "word": " the", "probability": 0.87939453125}, {"start": 2574.73, "end": 2575.13, "word": " population", "probability": 0.95947265625}, {"start": 2575.13, "end": 2575.53, "word": " mean,", "probability": 0.96923828125}, {"start": 2575.99, "end": 2576.15, "word": " in", "probability": 0.923828125}, {"start": 2576.15, "end": 2576.43, "word": " this", "probability": 0.94580078125}, {"start": 2576.43, "end": 2576.75, "word": " case,", "probability": 0.91259765625}, {"start": 2576.81, "end": 2576.93, "word": " we", "probability": 0.943359375}, {"start": 2576.93, "end": 2577.15, "word": " say", "probability": 0.9150390625}, {"start": 2577.15, "end": 2577.47, "word": " that", "probability": 0.9345703125}, {"start": 2577.47, "end": 2577.79, "word": " X", "probability": 0.9619140625}, {"start": 2577.79, "end": 2578.11, "word": " bar", "probability": 0.953125}, {"start": 2578.11, "end": 2579.09, "word": " is", "probability": 0.955078125}, {"start": 2579.09, "end": 2579.33, "word": " good", "probability": 0.56591796875}, {"start": 2579.33, "end": 2579.89, "word": " estimator", "probability": 0.965087890625}, {"start": 2579.89, "end": 2580.09, "word": " of", "probability": 0.9716796875}, {"start": 2580.09, "end": 2580.25, "word": " Mu.", "probability": 0.41943359375}, {"start": 2581.33, "end": 2581.81, "word": " Because", "probability": 0.89501953125}, {"start": 2581.81, "end": 2581.97, "word": " on", "probability": 0.72607421875}, {"start": 2581.97, "end": 2582.45, "word": " average,", "probability": 0.7607421875}], "temperature": 1.0}, {"id": 97, "seek": 261055, "start": 2585.43, "end": 2610.55, "text": " Expected value of X bar equals the population mean, so in this case X bar is L by estimator of Mu. Now if you compare the two distributions, normal distribution here with population mean Mu and standard deviation for example sigma.", "tokens": [2111, 10729, 2158, 295, 1783, 2159, 6915, 264, 4415, 914, 11, 370, 294, 341, 1389, 1783, 2159, 307, 441, 538, 8017, 1639, 295, 15601, 13, 823, 498, 291, 6794, 264, 732, 37870, 11, 2710, 7316, 510, 365, 4415, 914, 15601, 293, 3832, 25163, 337, 1365, 12771, 13], "avg_logprob": -0.30371095053851604, "compression_ratio": 1.4871794871794872, "no_speech_prob": 0.0, "words": [{"start": 2585.43, "end": 2585.97, "word": " Expected", "probability": 0.55670166015625}, {"start": 2585.97, "end": 2586.27, "word": " value", "probability": 0.73193359375}, {"start": 2586.27, "end": 2586.41, "word": " of", "probability": 0.8388671875}, {"start": 2586.41, "end": 2586.57, "word": " X", "probability": 0.65966796875}, {"start": 2586.57, "end": 2586.79, "word": " bar", "probability": 0.796875}, {"start": 2586.79, "end": 2587.27, "word": " equals", "probability": 0.7646484375}, {"start": 2587.27, "end": 2587.85, "word": " the", "probability": 0.74169921875}, {"start": 2587.85, "end": 2588.23, "word": " population", "probability": 0.94677734375}, {"start": 2588.23, "end": 2589.65, "word": " mean,", "probability": 0.8974609375}, {"start": 2589.99, "end": 2590.13, "word": " so", "probability": 0.603515625}, {"start": 2590.13, "end": 2590.25, "word": " in", "probability": 0.87548828125}, {"start": 2590.25, "end": 2590.41, "word": " this", "probability": 0.951171875}, {"start": 2590.41, "end": 2590.69, "word": " case", "probability": 0.912109375}, {"start": 2590.69, "end": 2591.05, "word": " X", "probability": 0.69140625}, {"start": 2591.05, "end": 2591.41, "word": " bar", "probability": 0.93017578125}, {"start": 2591.41, "end": 2592.25, "word": " is", "probability": 0.8837890625}, {"start": 2592.25, "end": 2592.83, "word": " L", "probability": 0.28662109375}, {"start": 2592.83, "end": 2593.05, "word": " by", "probability": 0.9033203125}, {"start": 2593.05, "end": 2593.91, "word": " estimator", "probability": 0.743408203125}, {"start": 2593.91, "end": 2594.97, "word": " of", "probability": 0.70556640625}, {"start": 2594.97, "end": 2595.21, "word": " Mu.", "probability": 0.44873046875}, {"start": 2596.29, "end": 2596.57, "word": " Now", "probability": 0.89501953125}, {"start": 2596.57, "end": 2596.75, "word": " if", "probability": 0.72802734375}, {"start": 2596.75, "end": 2596.89, "word": " you", "probability": 0.82373046875}, {"start": 2596.89, "end": 2597.47, "word": " compare", "probability": 0.93896484375}, {"start": 2597.47, "end": 2598.25, "word": " the", "probability": 0.875}, {"start": 2598.25, "end": 2598.73, "word": " two", "probability": 0.89599609375}, {"start": 2598.73, "end": 2600.41, "word": " distributions,", "probability": 0.86376953125}, {"start": 2602.03, "end": 2603.69, "word": " normal", "probability": 0.8017578125}, {"start": 2603.69, "end": 2604.33, "word": " distribution", "probability": 0.82763671875}, {"start": 2604.33, "end": 2604.73, "word": " here", "probability": 0.8134765625}, {"start": 2604.73, "end": 2605.99, "word": " with", "probability": 0.708984375}, {"start": 2605.99, "end": 2606.61, "word": " population", "probability": 0.94580078125}, {"start": 2606.61, "end": 2607.17, "word": " mean", "probability": 0.927734375}, {"start": 2607.17, "end": 2607.51, "word": " Mu", "probability": 0.9052734375}, {"start": 2607.51, "end": 2608.31, "word": " and", "probability": 0.8193359375}, {"start": 2608.31, "end": 2608.77, "word": " standard", "probability": 0.84765625}, {"start": 2608.77, "end": 2609.23, "word": " deviation", "probability": 0.947265625}, {"start": 2609.23, "end": 2609.53, "word": " for", "probability": 0.71484375}, {"start": 2609.53, "end": 2610.03, "word": " example", "probability": 0.97314453125}, {"start": 2610.03, "end": 2610.55, "word": " sigma.", "probability": 0.43701171875}], "temperature": 1.0}, {"id": 98, "seek": 264057, "start": 2613.19, "end": 2640.57, "text": " That's for the scores, the scores. Now instead of the scores above, we have x bar, the sample mean. Again, the mean of x bar is the same as the population mean. Both means are the same, mu of x bar equals mu. 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So again, to compare or to figure out the relationship between sigma of x bar and the sample size. Suppose we have this blue normal distribution with sample size say 10 or 30, for example.", "tokens": [407, 300, 311, 264, 9660, 1296, 264, 732, 12822, 13, 407, 797, 11, 281, 6794, 420, 281, 2573, 484, 264, 2480, 1296, 12771, 295, 2031, 2159, 293, 264, 6889, 2744, 13, 21360, 321, 362, 341, 3344, 2710, 7316, 365, 6889, 2744, 584, 1266, 420, 2217, 11, 337, 1365, 13], "avg_logprob": -0.19453124850988388, "compression_ratio": 1.51875, "no_speech_prob": 0.0, "words": [{"start": 2641.19, "end": 2641.51, "word": " So", "probability": 0.86083984375}, {"start": 2641.51, "end": 2641.77, "word": " that's", "probability": 0.865234375}, {"start": 2641.77, "end": 2641.93, "word": " the", "probability": 0.90771484375}, {"start": 2641.93, "end": 2642.33, "word": " comparison", "probability": 0.87353515625}, {"start": 2642.33, "end": 2642.83, "word": " between", "probability": 0.87939453125}, {"start": 2642.83, "end": 2643.35, "word": " the", "probability": 0.89453125}, {"start": 2643.35, "end": 2643.73, "word": " two", "probability": 0.91650390625}, {"start": 2643.73, "end": 2645.53, "word": " populations.", "probability": 0.931640625}, {"start": 2647.05, "end": 2647.31, "word": " So", "probability": 0.9384765625}, {"start": 2647.31, "end": 2647.65, "word": " again,", "probability": 0.857421875}, {"start": 2648.81, "end": 2649.07, "word": " to", "probability": 0.947265625}, {"start": 2649.07, "end": 2649.53, "word": " compare", "probability": 0.9560546875}, {"start": 2649.53, "end": 2652.53, "word": " or", "probability": 0.67919921875}, {"start": 2652.53, "end": 2652.75, "word": " to", "probability": 0.90771484375}, {"start": 2652.75, "end": 2652.95, "word": " figure", "probability": 0.9697265625}, {"start": 2652.95, "end": 2653.21, "word": " out", "probability": 0.89306640625}, {"start": 2653.21, "end": 2653.39, "word": " the", "probability": 0.92138671875}, {"start": 2653.39, "end": 2653.87, "word": " relationship", "probability": 0.90673828125}, {"start": 2653.87, "end": 2654.37, "word": " between", "probability": 0.8740234375}, {"start": 2654.37, "end": 2655.29, "word": " sigma", "probability": 0.69580078125}, {"start": 2655.29, "end": 2655.47, "word": " of", "probability": 0.501953125}, {"start": 2655.47, "end": 2655.65, "word": " x", "probability": 0.5810546875}, {"start": 2655.65, "end": 2656.03, "word": " bar", "probability": 0.8388671875}, {"start": 2656.03, "end": 2657.51, "word": " and", "probability": 0.90625}, {"start": 2657.51, "end": 2657.71, "word": " the", "probability": 0.8369140625}, {"start": 2657.71, "end": 2657.91, "word": " sample", "probability": 0.87744140625}, {"start": 2657.91, "end": 2658.33, "word": " size.", "probability": 0.87255859375}, {"start": 2659.49, "end": 2660.05, "word": " Suppose", "probability": 0.80859375}, {"start": 2660.05, "end": 2660.25, "word": " we", "probability": 0.91552734375}, {"start": 2660.25, "end": 2660.43, "word": " have", "probability": 0.94482421875}, {"start": 2660.43, "end": 2660.75, "word": " this", "probability": 0.93798828125}, {"start": 2660.75, "end": 2661.27, "word": " blue", "probability": 0.6201171875}, {"start": 2661.27, "end": 2662.11, "word": " normal", "probability": 0.75537109375}, {"start": 2662.11, "end": 2662.77, "word": " distribution", "probability": 0.83935546875}, {"start": 2662.77, "end": 2664.31, "word": " with", "probability": 0.83349609375}, {"start": 2664.31, "end": 2664.71, "word": " sample", "probability": 0.8740234375}, {"start": 2664.71, "end": 2665.15, "word": " size", "probability": 0.87841796875}, {"start": 2665.15, "end": 2665.63, "word": " say", "probability": 0.59423828125}, {"start": 2665.63, "end": 2666.45, "word": " 10", "probability": 0.64599609375}, {"start": 2666.45, "end": 2667.27, "word": " or", "probability": 0.77294921875}, {"start": 2667.27, "end": 2668.01, "word": " 30,", "probability": 0.75244140625}, {"start": 2668.31, "end": 2668.59, "word": " for", "probability": 0.951171875}, {"start": 2668.59, "end": 2668.87, "word": " example.", "probability": 0.97314453125}], "temperature": 1.0}, {"id": 100, "seek": 270062, "start": 2672.22, "end": 2700.62, "text": " As n gets bigger and bigger, sigma of x bar becomes smaller and smaller. If you look at the red one, maybe if the red one has n equal 100, we'll get this spread. But for the other one, we have larger spread. So as n increases, sigma of x bar decreases. So this, the blue one for smaller sample size.", "tokens": [1018, 297, 2170, 3801, 293, 3801, 11, 12771, 295, 2031, 2159, 3643, 4356, 293, 4356, 13, 759, 291, 574, 412, 264, 2182, 472, 11, 1310, 498, 264, 2182, 472, 575, 297, 2681, 2319, 11, 321, 603, 483, 341, 3974, 13, 583, 337, 264, 661, 472, 11, 321, 362, 4833, 3974, 13, 407, 382, 297, 8637, 11, 12771, 295, 2031, 2159, 24108, 13, 407, 341, 11, 264, 3344, 472, 337, 4356, 6889, 2744, 13], "avg_logprob": -0.15825591115532694, "compression_ratio": 1.6574585635359116, "no_speech_prob": 0.0, "words": [{"start": 2672.22, "end": 2672.6, "word": " As", "probability": 0.86669921875}, {"start": 2672.6, "end": 2672.84, "word": " n", "probability": 0.552734375}, {"start": 2672.84, "end": 2673.18, "word": " gets", "probability": 0.87158203125}, {"start": 2673.18, "end": 2673.58, "word": " bigger", "probability": 0.94677734375}, {"start": 2673.58, "end": 2673.78, "word": " and", "probability": 0.93701171875}, {"start": 2673.78, "end": 2674.06, 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So again, as n increases, sigma of x bar goes down four degrees. Next, let's use this fact to figure out", "tokens": [440, 2182, 472, 337, 4833, 6889, 2744, 13, 407, 797, 11, 382, 297, 8637, 11, 12771, 295, 2031, 2159, 1709, 760, 1451, 5310, 13, 3087, 11, 718, 311, 764, 341, 1186, 281, 2573, 484], "avg_logprob": -0.24732141835348948, "compression_ratio": 1.236842105263158, "no_speech_prob": 0.0, "words": [{"start": 2701.58, "end": 2701.88, "word": " The", "probability": 0.3125}, {"start": 2701.88, "end": 2702.18, "word": " red", "probability": 0.90380859375}, {"start": 2702.18, "end": 2702.54, "word": " one", "probability": 0.91650390625}, {"start": 2702.54, "end": 2703.02, "word": " for", "probability": 0.7919921875}, {"start": 2703.02, "end": 2704.18, "word": " larger", "probability": 0.701171875}, {"start": 2704.18, "end": 2705.86, "word": " sample", "probability": 0.7138671875}, {"start": 2705.86, "end": 2706.24, "word": " size.", "probability": 0.763671875}, {"start": 2706.84, "end": 2707.56, "word": " So", "probability": 0.9560546875}, 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So in this case, we are looking for the estimation of the sample mean. And we have this information,", "tokens": [663, 486, 4090, 13420, 4, 295, 264, 6889, 1355, 562, 2992, 6915, 8652, 23, 11, 12771, 307, 2119, 11, 293, 428, 6889, 2744, 307, 3552, 13, 407, 294, 341, 1389, 11, 321, 366, 1237, 337, 264, 35701, 295, 264, 6889, 914, 13, 400, 321, 362, 341, 1589, 11], "avg_logprob": -0.2514349587109624, "compression_ratio": 1.3877551020408163, "no_speech_prob": 0.0, "words": [{"start": 2758.79, "end": 2759.17, "word": " That", "probability": 0.307861328125}, {"start": 2759.17, "end": 2759.47, "word": " will", "probability": 0.8671875}, {"start": 2759.47, "end": 2760.39, "word": " include", "probability": 0.84228515625}, {"start": 2760.39, "end": 2760.97, "word": " 95", "probability": 0.943359375}, {"start": 2760.97, "end": 2761.53, "word": "%", "probability": 0.85888671875}, {"start": 2761.53, "end": 2762.21, "word": " of", "probability": 0.96142578125}, {"start": 2762.21, "end": 2762.43, "word": " the", "probability": 0.87744140625}, {"start": 2762.43, "end": 2762.73, "word": " sample", "probability": 0.8369140625}, {"start": 2762.73, "end": 2763.19, "word": " means", "probability": 0.84716796875}, {"start": 2763.19, "end": 2763.91, "word": " when", "probability": 0.587890625}, {"start": 2763.91, "end": 2764.13, "word": " mu", "probability": 0.429931640625}, {"start": 2764.13, "end": 2764.51, "word": " equals", "probability": 0.537109375}, {"start": 2764.51, "end": 2765.39, "word": " 368,", "probability": 0.84765625}, {"start": 2765.81, "end": 2766.41, "word": " sigma", "probability": 0.6611328125}, {"start": 2766.41, "end": 2766.63, "word": " is", "probability": 0.8623046875}, {"start": 2766.63, "end": 2767.13, "word": " 15,", "probability": 0.95751953125}, {"start": 2767.65, "end": 2767.99, "word": " and", "probability": 0.9228515625}, {"start": 2767.99, "end": 2768.27, "word": " your", "probability": 0.8466796875}, {"start": 2768.27, "end": 2768.61, "word": " sample", "probability": 0.904296875}, {"start": 2768.61, "end": 2769.03, "word": " size", "probability": 0.8603515625}, {"start": 2769.03, "end": 2769.17, "word": " is", "probability": 0.382568359375}, {"start": 2769.17, "end": 2769.63, "word": " 25.", "probability": 0.9619140625}, {"start": 2770.37, "end": 2771.03, "word": " So", "probability": 0.9482421875}, {"start": 2771.03, "end": 2771.17, "word": " in", "probability": 0.75048828125}, {"start": 2771.17, "end": 2771.31, "word": " this", "probability": 0.9462890625}, {"start": 2771.31, "end": 2771.57, "word": " case,", "probability": 0.919921875}, {"start": 2771.67, "end": 2771.79, "word": " we", "probability": 0.9580078125}, {"start": 2771.79, "end": 2772.05, "word": " are", "probability": 0.923828125}, {"start": 2772.05, "end": 2773.37, "word": " looking", "probability": 0.90380859375}, {"start": 2773.37, "end": 2773.83, "word": " for", "probability": 0.95263671875}, {"start": 2773.83, "end": 2777.15, "word": " the", "probability": 0.5869140625}, {"start": 2777.15, "end": 2777.75, "word": " estimation", "probability": 0.951171875}, {"start": 2777.75, "end": 2778.35, "word": " of", "probability": 0.96875}, {"start": 2778.35, "end": 2778.51, "word": " the", "probability": 0.89306640625}, {"start": 2778.51, "end": 2778.77, "word": " sample", "probability": 0.7236328125}, {"start": 2778.77, "end": 2779.11, "word": " mean.", "probability": 0.88916015625}, {"start": 2783.13, "end": 2783.97, "word": " And", "probability": 0.86474609375}, {"start": 2783.97, "end": 2784.11, "word": " we", "probability": 0.9013671875}, {"start": 2784.11, "end": 2784.27, "word": " have", "probability": 0.94677734375}, {"start": 2784.27, "end": 2784.45, "word": " this", "probability": 0.9384765625}, {"start": 2784.45, "end": 2784.97, "word": " information,", "probability": 0.83642578125}], "temperature": 1.0}, {"id": 104, "seek": 281649, "start": 2788.91, "end": 2816.49, "text": " Sigma is 15 and N is 25. The problem mentioned there, we have symmetric distribution and this area is 95% bisymmetric and we have only 5% out. So that means half to the right and half to the left.", "tokens": [36595, 307, 2119, 293, 426, 307, 3552, 13, 440, 1154, 2835, 456, 11, 321, 362, 32330, 7316, 293, 341, 1859, 307, 13420, 4, 7393, 32497, 17475, 293, 321, 362, 787, 1025, 4, 484, 13, 407, 300, 1355, 1922, 281, 264, 558, 293, 1922, 281, 264, 1411, 13], "avg_logprob": -0.20052083861082792, "compression_ratio": 1.4172661870503598, "no_speech_prob": 0.0, "words": [{"start": 2788.91, "end": 2789.29, "word": " Sigma", "probability": 0.54345703125}, {"start": 2789.29, "end": 2789.47, "word": " is", "probability": 0.81982421875}, {"start": 2789.47, "end": 2789.97, "word": " 15", "probability": 0.86962890625}, {"start": 2789.97, "end": 2791.09, "word": " and", "probability": 0.7099609375}, {"start": 2791.09, "end": 2791.29, "word": " N", "probability": 0.65380859375}, {"start": 2791.29, "end": 2791.43, "word": " is", "probability": 0.92724609375}, {"start": 2791.43, "end": 2791.75, "word": " 25.", "probability": 0.90625}, {"start": 2795.65, "end": 2796.33, "word": " The", "probability": 0.83447265625}, {"start": 2796.33, "end": 2796.67, "word": " problem", "probability": 0.86279296875}, {"start": 2796.67, "end": 2797.13, "word": " mentioned", "probability": 0.8359375}, {"start": 2797.13, "end": 2797.49, "word": " there,", "probability": 0.52099609375}, {"start": 2798.01, "end": 2798.29, "word": " we", "probability": 0.921875}, {"start": 2798.29, "end": 2798.47, "word": " have", "probability": 0.94970703125}, {"start": 2798.47, "end": 2798.89, "word": " symmetric", "probability": 0.77978515625}, {"start": 2798.89, "end": 2799.47, "word": " distribution", "probability": 0.673828125}, {"start": 2799.47, "end": 2801.45, "word": " and", "probability": 0.489990234375}, {"start": 2801.45, "end": 2801.75, "word": " this", "probability": 0.935546875}, {"start": 2801.75, "end": 2802.19, "word": " area", "probability": 0.89501953125}, {"start": 2802.19, "end": 2803.41, "word": " is", "probability": 0.94384765625}, {"start": 2803.41, "end": 2803.79, "word": " 95", "probability": 0.974609375}, {"start": 2803.79, "end": 2804.45, "word": "%", "probability": 0.68212890625}, {"start": 2804.45, "end": 2806.41, "word": " bisymmetric", "probability": 0.7611490885416666}, {"start": 2806.41, "end": 2808.49, "word": " and", "probability": 0.6591796875}, {"start": 2808.49, "end": 2808.63, "word": " we", "probability": 0.93505859375}, {"start": 2808.63, "end": 2808.77, "word": " have", "probability": 0.89208984375}, {"start": 2808.77, "end": 2808.97, "word": " only", "probability": 0.9052734375}, {"start": 2808.97, "end": 2809.25, "word": " 5", "probability": 0.98095703125}, {"start": 2809.25, "end": 2809.67, "word": "%", "probability": 0.98388671875}, {"start": 2809.67, "end": 2810.17, "word": " out.", "probability": 0.8798828125}, {"start": 2811.33, "end": 2811.57, "word": " So", "probability": 0.90771484375}, {"start": 2811.57, "end": 2811.79, "word": " that", "probability": 0.81396484375}, {"start": 2811.79, "end": 2812.09, "word": " means", "probability": 0.93408203125}, {"start": 2812.09, "end": 2812.53, "word": " half", "probability": 0.74462890625}, {"start": 2812.53, "end": 2812.75, "word": " to", "probability": 0.95654296875}, {"start": 2812.75, "end": 2812.89, "word": " the", "probability": 0.91259765625}, {"start": 2812.89, "end": 2813.17, "word": " right", "probability": 0.91015625}, {"start": 2813.17, "end": 2815.69, "word": " and", "probability": 0.8896484375}, {"start": 2815.69, "end": 2815.95, "word": " half", "probability": 0.8642578125}, {"start": 2815.95, "end": 2816.13, "word": " to", "probability": 0.958984375}, {"start": 2816.13, "end": 2816.27, "word": " the", "probability": 0.9111328125}, {"start": 2816.27, "end": 2816.49, "word": " left.", "probability": 0.947265625}], "temperature": 1.0}, {"id": 105, "seek": 284718, "start": 2819.74, "end": 2847.18, "text": " And let's see how can we compute these two values. The problem says that the average T68 for this data and the standard deviation sigma of 15. He asked about what are the values of x bar.", "tokens": [400, 718, 311, 536, 577, 393, 321, 14722, 613, 732, 4190, 13, 440, 1154, 1619, 300, 264, 4274, 314, 27102, 337, 341, 1412, 293, 264, 3832, 25163, 12771, 295, 2119, 13, 634, 2351, 466, 437, 366, 264, 4190, 295, 2031, 2159, 13], "avg_logprob": -0.22183866071146588, "compression_ratio": 1.3055555555555556, "no_speech_prob": 0.0, "words": [{"start": 2819.74, "end": 2819.98, "word": " And", "probability": 0.7568359375}, {"start": 2819.98, "end": 2820.26, "word": " let's", "probability": 0.945068359375}, {"start": 2820.26, "end": 2820.38, "word": " see", "probability": 0.90087890625}, {"start": 2820.38, "end": 2820.52, "word": " how", "probability": 0.88037109375}, {"start": 2820.52, "end": 2820.68, "word": " can", "probability": 0.779296875}, {"start": 2820.68, "end": 2820.82, "word": " we", "probability": 0.947265625}, {"start": 2820.82, "end": 2821.36, "word": " compute", "probability": 0.9150390625}, {"start": 2821.36, "end": 2822.06, "word": " these", "probability": 0.853515625}, {"start": 2822.06, "end": 2822.28, "word": " two", "probability": 0.91796875}, {"start": 2822.28, "end": 2822.64, "word": " values.", "probability": 0.927734375}, {"start": 2823.82, "end": 2824.2, "word": " The", "probability": 0.728515625}, {"start": 2824.2, "end": 2824.6, "word": " problem", "probability": 0.8818359375}, {"start": 2824.6, "end": 2825.0, "word": " says", "probability": 0.90966796875}, {"start": 2825.0, "end": 2825.46, "word": " that", "probability": 0.9150390625}, {"start": 2825.46, "end": 2826.94, "word": " the", "probability": 0.81298828125}, {"start": 2826.94, "end": 2827.5, "word": " average", "probability": 0.75732421875}, {"start": 2827.5, "end": 2831.44, "word": " T68", "probability": 0.6187744140625}, {"start": 2831.44, "end": 2833.38, "word": " for", "probability": 0.478759765625}, {"start": 2833.38, "end": 2833.6, "word": " this", "probability": 0.9404296875}, {"start": 2833.6, "end": 2833.96, "word": " data", "probability": 0.9384765625}, {"start": 2833.96, "end": 2835.46, "word": " and", "probability": 0.6669921875}, {"start": 2835.46, "end": 2835.82, "word": " the", "probability": 0.6865234375}, {"start": 2835.82, "end": 2836.08, "word": " standard", "probability": 0.92529296875}, {"start": 2836.08, "end": 2836.54, "word": " deviation", "probability": 0.92919921875}, {"start": 2836.54, "end": 2837.64, "word": " sigma", "probability": 0.6484375}, {"start": 2837.64, "end": 2838.66, "word": " of", "probability": 0.8916015625}, {"start": 2838.66, "end": 2839.08, "word": " 15.", "probability": 0.5634765625}, {"start": 2841.6, "end": 2842.02, "word": " He", "probability": 0.60693359375}, {"start": 2842.02, "end": 2842.18, "word": " asked", "probability": 0.49609375}, {"start": 2842.18, "end": 2842.48, "word": " about", "probability": 0.85498046875}, {"start": 2842.48, "end": 2842.82, "word": " what", "probability": 0.890625}, {"start": 2842.82, "end": 2843.28, "word": " are", "probability": 0.84765625}, {"start": 2843.28, "end": 2844.26, "word": " the", "probability": 0.9208984375}, {"start": 2844.26, "end": 2844.76, "word": " values", "probability": 0.9619140625}, {"start": 2844.76, "end": 2846.66, "word": " of", "probability": 0.958984375}, {"start": 2846.66, "end": 2846.9, "word": " x", "probability": 0.529296875}, {"start": 2846.9, "end": 2847.18, "word": " bar.", "probability": 0.849609375}], "temperature": 1.0}, {"id": 106, "seek": 287621, "start": 2848.31, "end": 2876.21, "text": " I mean, we have to find the interval of x bar. Let's see. If you remember last time, z score was x minus mu divided by sigma. But now we have x bar. So your z score should be minus mu divided by sigma over root n. Now cross multiplication, you will get x bar minus mu equals z sigma over root n.", "tokens": [286, 914, 11, 321, 362, 281, 915, 264, 15035, 295, 2031, 2159, 13, 961, 311, 536, 13, 759, 291, 1604, 1036, 565, 11, 710, 6175, 390, 2031, 3175, 2992, 6666, 538, 12771, 13, 583, 586, 321, 362, 2031, 2159, 13, 407, 428, 710, 6175, 820, 312, 3175, 2992, 6666, 538, 12771, 670, 5593, 297, 13, 823, 3278, 27290, 11, 291, 486, 483, 2031, 2159, 3175, 2992, 6915, 710, 12771, 670, 5593, 297, 13], "avg_logprob": -0.17567568171668696, "compression_ratio": 1.6444444444444444, "no_speech_prob": 0.0, "words": [{"start": 2848.31, "end": 2848.51, "word": " I", "probability": 0.7646484375}, {"start": 2848.51, "end": 2848.69, "word": " mean,", "probability": 0.96533203125}, {"start": 2848.77, "end": 2848.87, "word": " we", "probability": 0.94482421875}, {"start": 2848.87, "end": 2849.37, "word": " have", "probability": 0.908203125}, {"start": 2849.37, "end": 2849.49, "word": " to", "probability": 0.96875}, 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"probability": 0.98876953125}, {"start": 2871.93, "end": 2872.33, "word": " bar", "probability": 0.91650390625}, {"start": 2872.33, "end": 2874.13, "word": " minus", "probability": 0.95947265625}, {"start": 2874.13, "end": 2874.41, "word": " mu", "probability": 0.94921875}, {"start": 2874.41, "end": 2874.79, "word": " equals", "probability": 0.9228515625}, {"start": 2874.79, "end": 2875.03, "word": " z", "probability": 0.92724609375}, {"start": 2875.03, "end": 2875.57, "word": " sigma", "probability": 0.83349609375}, {"start": 2875.57, "end": 2875.77, "word": " over", "probability": 0.79736328125}, {"start": 2875.77, "end": 2875.97, "word": " root", "probability": 0.93017578125}, {"start": 2875.97, "end": 2876.21, "word": " n.", "probability": 0.97265625}], "temperature": 1.0}, {"id": 107, "seek": 290558, "start": 2877.24, "end": 2905.58, "text": " That means x bar equals mu plus z sigma over root n. Exactly the same equation we got in chapter six, but there, in that one we have x equals mu plus z sigma. Now we have x bar equals mu plus z sigma over root n, because we have different statistics. It's x bar instead of x. Now we are looking for these two values.", "tokens": [663, 1355, 2031, 2159, 6915, 2992, 1804, 710, 12771, 670, 5593, 297, 13, 7587, 264, 912, 5367, 321, 658, 294, 7187, 2309, 11, 457, 456, 11, 294, 300, 472, 321, 362, 2031, 6915, 2992, 1804, 710, 12771, 13, 823, 321, 362, 2031, 2159, 6915, 2992, 1804, 710, 12771, 670, 5593, 297, 11, 570, 321, 362, 819, 12523, 13, 467, 311, 2031, 2159, 2602, 295, 2031, 13, 823, 321, 366, 1237, 337, 613, 732, 4190, 13], "avg_logprob": -0.1942845453557215, "compression_ratio": 1.770949720670391, "no_speech_prob": 0.0, "words": [{"start": 2877.24, "end": 2877.56, "word": " That", "probability": 0.6884765625}, {"start": 2877.56, "end": 2877.88, "word": " means", "probability": 0.91259765625}, {"start": 2877.88, "end": 2878.14, "word": " x", "probability": 0.66064453125}, {"start": 2878.14, "end": 2878.34, "word": " bar", "probability": 0.7822265625}, {"start": 2878.34, "end": 2878.56, "word": " equals", "probability": 0.226806640625}, {"start": 2878.56, 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293663, "start": 2907.95, "end": 2936.63, "text": " Now let's compute z-score. The z-score for this point, which has area of 2.5% below it, is the same as the z-score, but in the opposite direction. If you remember, we got this value, 1.96. So my z-score is negative 1.96 to the left.", "tokens": [823, 718, 311, 14722, 710, 12, 4417, 418, 13, 440, 710, 12, 4417, 418, 337, 341, 935, 11, 597, 575, 1859, 295, 568, 13, 20, 4, 2507, 309, 11, 307, 264, 912, 382, 264, 710, 12, 4417, 418, 11, 457, 294, 264, 6182, 3513, 13, 759, 291, 1604, 11, 321, 658, 341, 2158, 11, 502, 13, 22962, 13, 407, 452, 710, 12, 4417, 418, 307, 3671, 502, 13, 22962, 281, 264, 1411, 13], "avg_logprob": -0.16575168898782214, "compression_ratio": 1.3952095808383234, "no_speech_prob": 0.0, "words": [{"start": 2907.95, "end": 2908.21, "word": " Now", "probability": 0.8642578125}, {"start": 2908.21, "end": 2908.51, "word": " let's", "probability": 0.801025390625}, {"start": 2908.51, "end": 2908.75, "word": " compute", "probability": 0.7353515625}, {"start": 2908.75, "end": 2909.09, "word": " z", "probability": 0.3720703125}, {"start": 2909.09, "end": 2909.41, "word": "-score.", "probability": 0.737548828125}, {"start": 2912.45, "end": 2913.01, "word": " The", 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"start": 2967.16, "end": 2996.44, "text": " Divide by root, 25. So that's the value of the sample mean in the lower limit, or lower bound. On the other hand, expand our limit to our hand equals 316 plus 1.96 sigma over root. Simple calculation will give this result.", "tokens": [9886, 482, 538, 5593, 11, 3552, 13, 407, 300, 311, 264, 2158, 295, 264, 6889, 914, 294, 264, 3126, 4948, 11, 420, 3126, 5472, 13, 1282, 264, 661, 1011, 11, 5268, 527, 4948, 281, 527, 1011, 6915, 805, 6866, 1804, 502, 13, 22962, 12771, 670, 5593, 13, 21532, 17108, 486, 976, 341, 1874, 13], "avg_logprob": -0.3667613690549677, "compression_ratio": 1.39375, "no_speech_prob": 0.0, "words": [{"start": 2967.16, "end": 2967.62, "word": " Divide", "probability": 0.57696533203125}, {"start": 2967.62, "end": 2967.82, "word": " by", "probability": 0.95361328125}, {"start": 2967.82, "end": 2968.24, "word": " root,", "probability": 0.783203125}, {"start": 2969.08, "end": 2969.72, "word": " 25.", "probability": 0.91357421875}, {"start": 2970.34, "end": 2971.12, "word": " So", "probability": 0.9599609375}, {"start": 2971.12, "end": 2971.58, "word": " that's", "probability": 0.900390625}, {"start": 2971.58, "end": 2971.8, "word": " the", "probability": 0.92138671875}, {"start": 2971.8, "end": 2972.22, "word": " value", "probability": 0.97314453125}, {"start": 2972.22, "end": 2973.16, "word": " of", "probability": 0.95166015625}, {"start": 2973.16, "end": 2973.32, "word": " the", "probability": 0.86572265625}, {"start": 2973.32, "end": 2973.58, "word": " sample", "probability": 0.201171875}, {"start": 2973.58, "end": 2973.94, "word": " mean", "probability": 0.91357421875}, {"start": 2973.94, "end": 2974.84, "word": " in", "probability": 0.70068359375}, {"start": 2974.84, "end": 2974.98, "word": " the", "probability": 0.91455078125}, {"start": 2974.98, "end": 2975.22, "word": " lower", "probability": 0.85009765625}, {"start": 2975.22, "end": 2975.52, "word": " limit,", "probability": 0.57861328125}, {"start": 2976.02, "end": 2976.22, "word": " or", "probability": 0.313232421875}, {"start": 2976.22, "end": 2976.46, "word": " lower", "probability": 0.82568359375}, {"start": 2976.46, "end": 2976.78, "word": " bound.", "probability": 0.85107421875}, {"start": 2978.16, "end": 2978.9, "word": " On", "probability": 0.94873046875}, {"start": 2978.9, "end": 2979.04, "word": " the", "probability": 0.92138671875}, {"start": 2979.04, "end": 2979.26, "word": " other", "probability": 0.88427734375}, {"start": 2979.26, "end": 2979.74, "word": " hand,", "probability": 0.92138671875}, {"start": 2982.32, "end": 2982.7, "word": " expand", "probability": 0.1112060546875}, {"start": 2982.7, "end": 2983.0, "word": " our", "probability": 0.50244140625}, {"start": 2983.0, "end": 2983.4, "word": " limit", "probability": 0.9248046875}, {"start": 2983.4, "end": 2983.98, "word": " to", "probability": 0.57373046875}, {"start": 2983.98, "end": 2984.28, "word": " our", "probability": 0.62939453125}, {"start": 2984.28, "end": 2984.66, "word": " hand", "probability": 0.70703125}, {"start": 2984.66, "end": 2985.58, "word": " equals", "probability": 0.62841796875}, {"start": 2985.58, "end": 2987.5, "word": " 316", "probability": 0.66357421875}, {"start": 2987.5, "end": 2988.54, "word": " plus", "probability": 0.833984375}, {"start": 2988.54, "end": 2988.94, "word": " 1", "probability": 0.9755859375}, {"start": 2988.94, "end": 2989.72, "word": ".96", "probability": 0.9892578125}, {"start": 2989.72, "end": 2991.26, "word": " sigma", "probability": 0.50244140625}, {"start": 2991.26, "end": 2991.52, "word": " over", "probability": 0.68115234375}, {"start": 2991.52, "end": 2991.82, "word": " root.", "probability": 0.1087646484375}, {"start": 2994.1, "end": 2994.9, "word": " Simple", "probability": 0.39892578125}, {"start": 2994.9, "end": 2995.44, "word": " calculation", "probability": 0.88720703125}, {"start": 2995.44, "end": 2995.7, "word": " will", "probability": 0.86181640625}, {"start": 2995.7, "end": 2995.9, "word": " give", "probability": 0.87255859375}, {"start": 2995.9, "end": 2996.1, "word": " this", "probability": 0.91357421875}, {"start": 2996.1, "end": 2996.44, "word": " result.", "probability": 0.92138671875}], "temperature": 1.0}, {"id": 111, "seek": 302767, "start": 2999.77, "end": 3027.67, "text": " The first X bar for the lower limit is 362.12, the other 373.1. So again for this data, for this example, the mean was, the population mean was 368, the population has non-degradation of 15, we select a random sample of size 25,", "tokens": [440, 700, 1783, 2159, 337, 264, 3126, 4948, 307, 8652, 17, 13, 4762, 11, 264, 661, 13435, 18, 13, 16, 13, 407, 797, 337, 341, 1412, 11, 337, 341, 1365, 11, 264, 914, 390, 11, 264, 4415, 914, 390, 8652, 23, 11, 264, 4415, 575, 2107, 12, 1479, 7165, 399, 295, 2119, 11, 321, 3048, 257, 4974, 6889, 295, 2744, 3552, 11], "avg_logprob": -0.3025793698098924, "compression_ratio": 1.506578947368421, "no_speech_prob": 0.0, "words": [{"start": 2999.77, "end": 3000.21, "word": " The", "probability": 0.50390625}, {"start": 3000.21, "end": 3000.71, "word": " first", "probability": 0.8349609375}, {"start": 3000.71, "end": 3001.29, "word": " X", "probability": 0.60498046875}, {"start": 3001.29, "end": 3001.63, "word": " bar", "probability": 0.59619140625}, {"start": 3001.63, "end": 3001.99, "word": " for", "probability": 0.81591796875}, {"start": 3001.99, "end": 3002.43, "word": " the", "probability": 0.8759765625}, {"start": 3002.43, "end": 3002.87, "word": " lower", "probability": 0.8095703125}, {"start": 3002.87, "end": 3003.15, "word": " limit", "probability": 0.76318359375}, {"start": 3003.15, "end": 3003.35, "word": " is", "probability": 0.67919921875}, {"start": 3003.35, "end": 3005.19, "word": " 362", "probability": 0.69873046875}, {"start": 3005.19, "end": 3005.87, "word": ".12,", "probability": 0.944580078125}, {"start": 3006.73, "end": 3006.87, "word": " the", "probability": 0.4892578125}, {"start": 3006.87, "end": 3007.11, "word": " other", "probability": 0.85498046875}, {"start": 3007.11, "end": 3008.37, "word": " 373", "probability": 0.849853515625}, {"start": 3008.37, "end": 3010.05, "word": ".1.", "probability": 0.53369140625}, {"start": 3011.45, "end": 3012.21, "word": " So", "probability": 0.89013671875}, {"start": 3012.21, "end": 3012.53, "word": " again", "probability": 0.81005859375}, {"start": 3012.53, "end": 3012.73, "word": " for", "probability": 0.611328125}, {"start": 3012.73, "end": 3012.93, "word": " this", "probability": 0.9462890625}, {"start": 3012.93, "end": 3013.27, "word": " data,", "probability": 0.85498046875}, {"start": 3014.71, "end": 3015.35, "word": " for", "probability": 0.8798828125}, {"start": 3015.35, "end": 3015.53, "word": " this", "probability": 0.94677734375}, {"start": 3015.53, "end": 3015.91, "word": " example,", "probability": 0.9765625}, {"start": 3016.75, "end": 3016.99, "word": " the", "probability": 0.91064453125}, {"start": 3016.99, "end": 3017.17, "word": " mean", "probability": 0.86279296875}, {"start": 3017.17, "end": 3017.53, "word": " was,", "probability": 0.93798828125}, {"start": 3017.63, "end": 3017.79, "word": " the", "probability": 0.916015625}, {"start": 3017.79, "end": 3018.03, "word": " population", "probability": 0.953125}, {"start": 3018.03, "end": 3018.45, "word": " mean", "probability": 0.95556640625}, {"start": 3018.45, "end": 3020.03, "word": " was", "probability": 0.70703125}, {"start": 3020.03, "end": 3020.99, "word": " 368,", "probability": 0.9716796875}, {"start": 3022.23, "end": 3022.65, "word": " the", "probability": 0.85986328125}, {"start": 3022.65, "end": 3023.03, "word": " population", "probability": 0.947265625}, {"start": 3023.03, "end": 3023.35, "word": " has", "probability": 0.8642578125}, {"start": 3023.35, "end": 3023.59, "word": " non", "probability": 0.11077880859375}, {"start": 3023.59, "end": 3023.99, "word": "-degradation", "probability": 0.7181396484375}, {"start": 3023.99, "end": 3024.11, "word": " of", "probability": 0.8857421875}, {"start": 3024.11, "end": 3024.55, "word": " 15,", "probability": 0.9697265625}, {"start": 3025.49, "end": 3025.67, "word": " we", "probability": 0.78857421875}, {"start": 3025.67, "end": 3025.97, "word": " select", "probability": 0.841796875}, {"start": 3025.97, "end": 3026.11, "word": " a", "probability": 0.986328125}, {"start": 3026.11, "end": 3026.31, "word": " random", "probability": 0.8681640625}, {"start": 3026.31, "end": 3026.77, "word": " sample", "probability": 0.87353515625}, {"start": 3026.77, "end": 3026.97, "word": " of", "probability": 0.9306640625}, {"start": 3026.97, "end": 3027.21, "word": " size", "probability": 0.869140625}, {"start": 3027.21, "end": 3027.67, "word": " 25,", "probability": 0.947265625}], "temperature": 1.0}, {"id": 112, "seek": 305379, "start": 3029.57, "end": 3053.79, "text": " Then we end with this result that 95% of all sample means of sample size 25 are between these two values. It means that we have this big population and this population is symmetric, is normal. And we know that", "tokens": [1396, 321, 917, 365, 341, 1874, 300, 13420, 4, 295, 439, 6889, 1355, 295, 6889, 2744, 3552, 366, 1296, 613, 732, 4190, 13, 467, 1355, 300, 321, 362, 341, 955, 4415, 293, 341, 4415, 307, 32330, 11, 307, 2710, 13, 400, 321, 458, 300], "avg_logprob": -0.19809027645323013, "compression_ratio": 1.4189189189189189, "no_speech_prob": 0.0, "words": [{"start": 3029.57, "end": 3029.91, "word": " Then", "probability": 0.6064453125}, {"start": 3029.91, "end": 3030.09, "word": " we", "probability": 0.83544921875}, {"start": 3030.09, "end": 3030.31, "word": " end", "probability": 0.8974609375}, {"start": 3030.31, "end": 3030.47, "word": " with", "probability": 0.89208984375}, {"start": 3030.47, "end": 3030.69, "word": " this", "probability": 0.93017578125}, {"start": 3030.69, "end": 3031.07, "word": " result", "probability": 0.92919921875}, {"start": 3031.07, "end": 3031.55, "word": " that", "probability": 0.53857421875}, {"start": 3031.55, "end": 3033.75, "word": " 95", "probability": 0.9306640625}, {"start": 3033.75, "end": 3034.49, "word": "%", "probability": 0.84619140625}, {"start": 3034.49, "end": 3036.59, "word": " of", "probability": 0.96630859375}, {"start": 3036.59, "end": 3036.95, "word": " all", "probability": 0.927734375}, {"start": 3036.95, "end": 3037.45, "word": " sample", "probability": 0.80029296875}, {"start": 3037.45, "end": 3037.87, "word": " means", "probability": 0.84130859375}, {"start": 3037.87, "end": 3038.83, "word": " of", "probability": 0.56005859375}, {"start": 3038.83, "end": 3039.21, "word": " sample", "probability": 0.8544921875}, {"start": 3039.21, "end": 3039.61, "word": " size", "probability": 0.814453125}, {"start": 3039.61, "end": 3040.15, "word": " 25", "probability": 0.87646484375}, {"start": 3040.15, "end": 3041.11, "word": " are", "probability": 0.85693359375}, {"start": 3041.11, "end": 3041.41, "word": " between", "probability": 0.83056640625}, {"start": 3041.41, "end": 3041.71, "word": " these", "probability": 0.83837890625}, {"start": 3041.71, "end": 3041.87, "word": " two", "probability": 0.84375}, {"start": 3041.87, "end": 3042.15, "word": " values.", "probability": 0.82373046875}, {"start": 3042.27, "end": 3042.39, "word": " It", "probability": 0.74267578125}, {"start": 3042.39, "end": 3042.63, "word": " means", "probability": 0.92724609375}, {"start": 3042.63, "end": 3042.93, "word": " that", "probability": 0.9326171875}, {"start": 3042.93, "end": 3044.55, "word": " we", "probability": 0.849609375}, {"start": 3044.55, "end": 3044.81, "word": " have", "probability": 0.9482421875}, {"start": 3044.81, "end": 3045.21, "word": " this", "probability": 0.94873046875}, {"start": 3045.21, "end": 3045.67, "word": " big", "probability": 0.908203125}, {"start": 3045.67, "end": 3046.19, "word": " population", "probability": 0.9384765625}, {"start": 3046.19, "end": 3048.63, "word": " and", "probability": 0.43310546875}, {"start": 3048.63, "end": 3048.81, "word": " this", "probability": 0.94580078125}, {"start": 3048.81, "end": 3049.23, "word": " population", "probability": 0.9287109375}, {"start": 3049.23, "end": 3049.53, "word": " is", "probability": 0.95458984375}, {"start": 3049.53, "end": 3049.91, "word": " symmetric,", "probability": 0.65478515625}, {"start": 3050.21, "end": 3050.37, "word": " is", "probability": 0.8173828125}, {"start": 3050.37, "end": 3050.75, "word": " normal.", "probability": 0.8759765625}, {"start": 3052.47, "end": 3053.11, "word": " And", "probability": 0.93017578125}, {"start": 3053.11, "end": 3053.33, "word": " we", "probability": 0.94873046875}, {"start": 3053.33, "end": 3053.55, "word": " know", "probability": 0.8876953125}, {"start": 3053.55, "end": 3053.79, "word": " that", "probability": 0.8798828125}], "temperature": 1.0}, {"id": 113, "seek": 308180, "start": 3054.54, "end": 3081.8, "text": " The mean of this population is 368 with sigma of 15. We select from this population many samples. Each one has size of 25. Suppose, for example, we select 100 samples, 100 random samples.", "tokens": [440, 914, 295, 341, 4415, 307, 8652, 23, 365, 12771, 295, 2119, 13, 492, 3048, 490, 341, 4415, 867, 10938, 13, 6947, 472, 575, 2744, 295, 3552, 13, 21360, 11, 337, 1365, 11, 321, 3048, 2319, 10938, 11, 2319, 4974, 10938, 13], "avg_logprob": -0.18595566513926484, "compression_ratio": 1.4029850746268657, "no_speech_prob": 0.0, "words": [{"start": 3054.54, "end": 3054.88, "word": " The", "probability": 0.7861328125}, {"start": 3054.88, "end": 3055.1, "word": " mean", "probability": 0.96142578125}, {"start": 3055.1, "end": 3055.24, "word": " of", "probability": 0.96630859375}, {"start": 3055.24, "end": 3055.44, "word": " this", "probability": 0.93310546875}, {"start": 3055.44, "end": 3055.9, "word": " population", "probability": 0.96484375}, {"start": 3055.9, "end": 3056.1, "word": " is", "probability": 0.7578125}, {"start": 3056.1, "end": 3057.32, "word": " 368", "probability": 0.94775390625}, {"start": 3057.32, "end": 3058.34, "word": " with", "probability": 0.6416015625}, {"start": 3058.34, "end": 3058.74, "word": " sigma", "probability": 0.615234375}, {"start": 3058.74, "end": 3059.26, "word": " of", "probability": 0.66015625}, {"start": 3059.26, "end": 3060.68, "word": " 15.", "probability": 0.94580078125}, {"start": 3062.28, "end": 3063.06, "word": " We", "probability": 0.94921875}, {"start": 3063.06, "end": 3063.48, "word": " select", "probability": 0.66650390625}, {"start": 3063.48, "end": 3063.74, "word": " from", "probability": 0.87158203125}, {"start": 3063.74, "end": 3063.98, "word": " this", "probability": 0.94482421875}, {"start": 3063.98, "end": 3064.6, "word": " population", "probability": 0.94482421875}, {"start": 3064.6, "end": 3065.82, "word": " many", "probability": 0.7734375}, {"start": 3065.82, "end": 3066.32, "word": " samples.", "probability": 0.9072265625}, {"start": 3067.86, "end": 3068.32, "word": " Each", "probability": 0.88671875}, {"start": 3068.32, "end": 3068.72, "word": " one", "probability": 0.939453125}, {"start": 3068.72, "end": 3070.28, "word": " has", "probability": 0.92724609375}, {"start": 3070.28, "end": 3070.82, "word": " size", "probability": 0.71533203125}, {"start": 3070.82, "end": 3071.08, "word": " of", "probability": 0.96337890625}, {"start": 3071.08, "end": 3071.6, "word": " 25.", "probability": 0.92431640625}, {"start": 3075.88, "end": 3076.48, "word": " Suppose,", "probability": 0.7841796875}, {"start": 3076.6, "end": 3076.72, "word": " for", "probability": 0.9521484375}, {"start": 3076.72, "end": 3077.1, "word": " example,", "probability": 0.97509765625}, {"start": 3078.0, "end": 3078.28, "word": " we", "probability": 0.9404296875}, {"start": 3078.28, "end": 3078.84, "word": " select", "probability": 0.8486328125}, {"start": 3078.84, "end": 3079.36, "word": " 100", "probability": 0.7138671875}, {"start": 3079.36, "end": 3080.02, "word": " samples,", "probability": 0.7958984375}, {"start": 3080.68, "end": 3080.94, "word": " 100", "probability": 0.87939453125}, {"start": 3080.94, "end": 3081.28, "word": " random", "probability": 0.84033203125}, {"start": 3081.28, "end": 3081.8, "word": " samples.", "probability": 0.8525390625}], "temperature": 1.0}, {"id": 114, "seek": 311066, "start": 3082.5, "end": 3110.66, "text": " So we end with different sample means. So we have 100 new sample means. In this case, you can say that 95 out of these, 95 out of 100, it means 95, one of these sample means.", "tokens": [407, 321, 917, 365, 819, 6889, 1355, 13, 407, 321, 362, 2319, 777, 6889, 1355, 13, 682, 341, 1389, 11, 291, 393, 584, 300, 13420, 484, 295, 613, 11, 13420, 484, 295, 2319, 11, 309, 1355, 13420, 11, 472, 295, 613, 6889, 1355, 13], "avg_logprob": -0.19270832803514268, "compression_ratio": 1.5086206896551724, "no_speech_prob": 0.0, "words": [{"start": 3082.5, "end": 3082.78, "word": " So", "probability": 0.66455078125}, {"start": 3082.78, "end": 3082.98, "word": " we", "probability": 0.76513671875}, {"start": 3082.98, "end": 3083.22, "word": " end", "probability": 0.890625}, {"start": 3083.22, "end": 3083.6, "word": " with", "probability": 0.8984375}, {"start": 3083.6, "end": 3085.86, "word": " different", "probability": 0.86083984375}, {"start": 3085.86, "end": 3087.26, "word": " sample", "probability": 0.57421875}, {"start": 3087.26, "end": 3087.62, "word": " means.", "probability": 0.89501953125}, {"start": 3093.72, "end": 3094.44, "word": " So", "probability": 0.8798828125}, {"start": 3094.44, "end": 3094.56, "word": " we", "probability": 0.865234375}, {"start": 3094.56, "end": 3094.76, "word": " have", "probability": 0.95556640625}, {"start": 3094.76, "end": 3095.56, "word": " 100", "probability": 0.818359375}, {"start": 3095.56, "end": 3096.28, "word": " new", "probability": 0.83642578125}, {"start": 3096.28, "end": 3097.24, "word": " sample", "probability": 0.88134765625}, {"start": 3097.24, "end": 3098.06, "word": " means.", "probability": 0.94580078125}, {"start": 3098.9, "end": 3099.2, "word": " In", "probability": 0.9326171875}, {"start": 3099.2, "end": 3099.4, "word": " this", "probability": 0.94677734375}, {"start": 3099.4, "end": 3099.66, "word": " case,", "probability": 0.923828125}, {"start": 3099.72, "end": 3099.82, "word": " you", "probability": 0.947265625}, {"start": 3099.82, "end": 3100.02, "word": " can", "probability": 0.94775390625}, {"start": 3100.02, "end": 3100.24, "word": " say", "probability": 0.873046875}, {"start": 3100.24, "end": 3100.56, "word": " that", "probability": 0.91015625}, {"start": 3100.56, "end": 3101.76, "word": " 95", "probability": 0.9423828125}, {"start": 3101.76, "end": 3102.78, "word": " out", "probability": 0.89013671875}, {"start": 3102.78, "end": 3102.96, "word": " of", "probability": 0.9736328125}, {"start": 3102.96, "end": 3103.3, "word": " these,", "probability": 0.666015625}, {"start": 3103.86, "end": 3104.4, "word": " 95", "probability": 0.958984375}, {"start": 3104.4, "end": 3105.04, "word": " out", "probability": 0.8828125}, {"start": 3105.04, "end": 3105.18, "word": " of", "probability": 0.966796875}, {"start": 3105.18, "end": 3105.54, "word": " 100,", "probability": 0.93408203125}, {"start": 3106.12, "end": 3106.32, "word": " it", "probability": 0.8388671875}, {"start": 3106.32, "end": 3106.54, "word": " means", "probability": 0.9306640625}, {"start": 3106.54, "end": 3107.4, "word": " 95,", "probability": 0.96044921875}, {"start": 3109.12, "end": 3109.48, "word": " one", "probability": 0.8271484375}, {"start": 3109.48, "end": 3109.66, "word": " of", "probability": 0.966796875}, {"start": 3109.66, "end": 3109.88, "word": " these", "probability": 0.83203125}, {"start": 3109.88, "end": 3110.24, "word": " sample", "probability": 0.884765625}, {"start": 3110.24, "end": 3110.66, "word": " means.", "probability": 0.94384765625}], "temperature": 1.0}, {"id": 115, "seek": 313772, "start": 3111.6, "end": 3137.72, "text": " have values between 362.12 and 373.5. And what's remaining? Just five of these sample means would be out of this interval either below 362 or above the upper limit. So you are 95% sure that", "tokens": [362, 4190, 1296, 8652, 17, 13, 4762, 293, 13435, 18, 13, 20, 13, 400, 437, 311, 8877, 30, 1449, 1732, 295, 613, 6889, 1355, 576, 312, 484, 295, 341, 15035, 2139, 2507, 8652, 17, 420, 3673, 264, 6597, 4948, 13, 407, 291, 366, 13420, 4, 988, 300], "avg_logprob": -0.18815104477107525, "compression_ratio": 1.2666666666666666, "no_speech_prob": 0.0, "words": [{"start": 3111.6, "end": 3111.98, "word": " have", "probability": 0.493896484375}, {"start": 3111.98, "end": 3112.56, "word": " values", "probability": 0.958984375}, {"start": 3112.56, "end": 3113.24, "word": " between", "probability": 0.8916015625}, {"start": 3113.24, "end": 3115.7, "word": " 362", "probability": 0.920654296875}, {"start": 3115.7, "end": 3116.38, "word": ".12", "probability": 0.965087890625}, {"start": 3116.38, "end": 3116.92, "word": " and", "probability": 0.9248046875}, {"start": 3116.92, "end": 3117.7, "word": " 373", "probability": 0.9482421875}, {"start": 3117.7, "end": 3118.0, "word": ".5.", "probability": 0.54412841796875}, {"start": 3119.44, "end": 3119.98, "word": " And", "probability": 0.92529296875}, {"start": 3119.98, "end": 3121.4, "word": " what's", "probability": 0.885009765625}, {"start": 3121.4, "end": 3121.72, "word": " remaining?", "probability": 0.8466796875}, {"start": 3123.0, "end": 3123.96, "word": " Just", "probability": 0.8740234375}, {"start": 3123.96, "end": 3124.5, "word": " five", "probability": 0.76806640625}, {"start": 3124.5, "end": 3124.9, "word": " of", "probability": 0.96875}, {"start": 3124.9, "end": 3125.14, "word": " these", "probability": 0.83740234375}, {"start": 3125.14, "end": 3125.48, "word": " sample", "probability": 0.86962890625}, {"start": 3125.48, "end": 3125.86, "word": " means", "probability": 0.75439453125}, {"start": 3125.86, "end": 3126.4, "word": " would", "probability": 0.560546875}, {"start": 3126.4, "end": 3126.52, "word": " be", "probability": 0.9541015625}, {"start": 3126.52, "end": 3126.9, "word": " out", "probability": 0.89404296875}, {"start": 3126.9, "end": 3127.94, "word": " of", "probability": 0.95458984375}, {"start": 3127.94, "end": 3128.18, "word": " this", "probability": 0.94091796875}, {"start": 3128.18, "end": 3128.56, "word": " interval", "probability": 0.966796875}, {"start": 3128.56, "end": 3129.04, "word": " either", "probability": 0.6337890625}, {"start": 3129.04, "end": 3130.2, "word": " below", "probability": 0.85791015625}, {"start": 3130.2, "end": 3131.8, "word": " 362", "probability": 0.959716796875}, {"start": 3131.8, "end": 3132.38, "word": " or", "probability": 0.6328125}, {"start": 3132.38, "end": 3132.8, "word": " above", "probability": 0.9716796875}, {"start": 3132.8, "end": 3133.02, "word": " the", "probability": 0.9228515625}, {"start": 3133.02, "end": 3133.22, "word": " upper", "probability": 0.82373046875}, {"start": 3133.22, "end": 3133.52, "word": " limit.", "probability": 0.94091796875}, {"start": 3134.98, "end": 3135.28, "word": " So", "probability": 0.95361328125}, {"start": 3135.28, "end": 3135.44, "word": " you", "probability": 0.8173828125}, {"start": 3135.44, "end": 3135.74, "word": " are", "probability": 0.9404296875}, {"start": 3135.74, "end": 3136.44, "word": " 95", "probability": 0.95849609375}, {"start": 3136.44, "end": 3136.82, "word": "%", "probability": 0.7705078125}, {"start": 3136.82, "end": 3137.36, "word": " sure", "probability": 0.90966796875}, {"start": 3137.36, "end": 3137.72, "word": " that", "probability": 0.80322265625}], "temperature": 1.0}, {"id": 116, "seek": 317051, "start": 3141.23, "end": 3170.51, "text": " The sample means lies between these two points. So, 5% of the sample means will be out. Make sense? Imagine that I have selected 200 samples. Now, how many X bar will be between these two values? 95% of these 200.", "tokens": [440, 6889, 1355, 9134, 1296, 613, 732, 2793, 13, 407, 11, 1025, 4, 295, 264, 6889, 1355, 486, 312, 484, 13, 4387, 2020, 30, 11739, 300, 286, 362, 8209, 2331, 10938, 13, 823, 11, 577, 867, 1783, 2159, 486, 312, 1296, 613, 732, 4190, 30, 13420, 4, 295, 613, 2331, 13], "avg_logprob": -0.2029747607616278, "compression_ratio": 1.4657534246575343, "no_speech_prob": 0.0, "words": [{"start": 3141.23, "end": 3141.63, "word": " The", "probability": 0.5654296875}, {"start": 3141.63, "end": 3141.99, "word": " sample", "probability": 0.303466796875}, {"start": 3141.99, "end": 3142.35, "word": " means", "probability": 0.806640625}, {"start": 3142.35, "end": 3142.85, "word": " lies", "probability": 0.8662109375}, {"start": 3142.85, "end": 3143.59, "word": " between", "probability": 0.859375}, {"start": 3143.59, "end": 3143.83, "word": " these", "probability": 0.8486328125}, {"start": 3143.83, "end": 3143.99, "word": " two", "probability": 0.888671875}, {"start": 3143.99, "end": 3144.35, "word": " points.", "probability": 0.9150390625}, {"start": 3145.41, "end": 3145.55, "word": " So,", "probability": 0.904296875}, {"start": 3145.79, "end": 3145.85, "word": " 5", "probability": 0.6494140625}, {"start": 3145.85, "end": 3146.11, "word": "%", "probability": 0.857421875}, {"start": 3146.11, "end": 3146.43, "word": " of", "probability": 0.94970703125}, {"start": 3146.43, "end": 3146.55, "word": " the", "probability": 0.611328125}, {"start": 3146.55, "end": 3146.77, "word": " sample", "probability": 0.87744140625}, {"start": 3146.77, "end": 3146.99, "word": " means", "probability": 0.837890625}, {"start": 3146.99, "end": 3147.15, "word": " will", "probability": 0.85107421875}, {"start": 3147.15, "end": 3147.31, "word": " be", "probability": 0.95361328125}, {"start": 3147.31, "end": 3147.65, "word": " out.", "probability": 0.8310546875}, {"start": 3149.23, "end": 3149.47, "word": " Make", "probability": 0.8154296875}, {"start": 3149.47, "end": 3149.77, "word": " sense?", "probability": 0.8271484375}, {"start": 3151.81, "end": 3152.51, "word": " Imagine", "probability": 0.833984375}, {"start": 3152.51, "end": 3152.87, "word": " that", "probability": 0.896484375}, {"start": 3152.87, "end": 3154.67, "word": " I", "probability": 0.89501953125}, {"start": 3154.67, "end": 3155.31, "word": " have", "probability": 0.64013671875}, {"start": 3155.31, "end": 3155.77, "word": " selected", "probability": 0.88916015625}, {"start": 3155.77, "end": 3157.03, "word": " 200", "probability": 0.8623046875}, {"start": 3157.03, "end": 3157.51, "word": " samples.", "probability": 0.82861328125}, {"start": 3160.27, "end": 3160.73, "word": " Now,", "probability": 0.95068359375}, {"start": 3160.81, "end": 3161.01, "word": " how", "probability": 0.93115234375}, {"start": 3161.01, "end": 3161.45, "word": " many", "probability": 0.89501953125}, {"start": 3161.45, "end": 3163.11, "word": " X", "probability": 0.478271484375}, {"start": 3163.11, "end": 3163.51, "word": " bar", "probability": 0.78564453125}, {"start": 3163.51, "end": 3165.05, "word": " will", "probability": 0.84033203125}, {"start": 3165.05, "end": 3165.47, "word": " be", "probability": 0.95068359375}, {"start": 3165.47, "end": 3165.93, "word": " between", "probability": 0.873046875}, {"start": 3165.93, "end": 3166.17, "word": " these", "probability": 0.857421875}, {"start": 3166.17, "end": 3166.33, "word": " two", "probability": 0.90625}, {"start": 3166.33, "end": 3166.75, "word": " values?", "probability": 0.9697265625}, {"start": 3167.63, "end": 3168.43, "word": " 95", "probability": 0.95947265625}, {"start": 3168.43, "end": 3168.93, "word": "%", "probability": 0.98291015625}, {"start": 3168.93, "end": 3169.09, "word": " of", "probability": 0.96240234375}, {"start": 3169.09, "end": 3170.07, "word": " these", "probability": 0.79150390625}, {"start": 3170.07, "end": 3170.51, "word": " 200.", "probability": 0.85400390625}], "temperature": 1.0}, {"id": 117, "seek": 319316, "start": 3171.1, "end": 3193.16, "text": " So how many 95%? How many means in this case? 95% out of 200 is 190. 190. Just multiply. 95 multiplies by 200. It will give 190.", "tokens": [407, 577, 867, 13420, 4, 30, 1012, 867, 1355, 294, 341, 1389, 30, 13420, 4, 484, 295, 2331, 307, 37609, 13, 37609, 13, 1449, 12972, 13, 13420, 12788, 530, 538, 2331, 13, 467, 486, 976, 37609, 13], "avg_logprob": -0.3034539442313345, "compression_ratio": 1.205607476635514, "no_speech_prob": 0.0, "words": [{"start": 3171.1, "end": 3171.36, "word": " So", "probability": 0.728515625}, {"start": 3171.36, "end": 3171.54, "word": " how", "probability": 0.61083984375}, {"start": 3171.54, "end": 3171.84, "word": " many", "probability": 0.90234375}, {"start": 3171.84, "end": 3173.02, "word": " 95", "probability": 0.56103515625}, {"start": 3173.02, "end": 3173.44, "word": "%?", "probability": 0.63330078125}, {"start": 3173.92, "end": 3174.14, "word": " How", "probability": 0.93115234375}, {"start": 3174.14, "end": 3174.38, "word": " many", "probability": 0.904296875}, {"start": 3174.38, "end": 3174.76, "word": " means", "probability": 0.8876953125}, {"start": 3174.76, "end": 3175.56, "word": " in", "probability": 0.662109375}, {"start": 3175.56, "end": 3175.74, "word": " this", "probability": 0.94873046875}, {"start": 3175.74, "end": 3176.06, "word": " case?", "probability": 0.92333984375}, {"start": 3178.9, "end": 3179.8, "word": " 95", "probability": 0.7216796875}, {"start": 3179.8, "end": 3180.32, "word": "%", "probability": 0.93359375}, {"start": 3180.32, "end": 3180.94, "word": " out", "probability": 0.892578125}, {"start": 3180.94, "end": 3181.16, "word": " of", "probability": 0.9736328125}, {"start": 3181.16, "end": 3181.76, "word": " 200", "probability": 0.92578125}, {"start": 3181.76, "end": 3182.26, "word": " is", "probability": 0.92431640625}, {"start": 3182.26, "end": 3184.6, "word": " 190.", "probability": 0.6806640625}, {"start": 3185.48, "end": 3186.38, "word": " 190.", "probability": 0.398681640625}, {"start": 3187.52, "end": 3187.96, "word": " Just", "probability": 0.81201171875}, {"start": 3187.96, "end": 3188.52, "word": " multiply.", "probability": 0.908203125}, {"start": 3188.84, "end": 3189.3, "word": " 95", "probability": 0.95947265625}, {"start": 3189.3, "end": 3190.28, "word": " multiplies", "probability": 0.6510009765625}, {"start": 3190.28, "end": 3190.46, "word": " by", "probability": 0.96728515625}, {"start": 3190.46, "end": 3190.86, "word": " 200.", "probability": 0.9140625}, {"start": 3192.02, "end": 3192.12, "word": " It", "probability": 0.345703125}, {"start": 3192.12, "end": 3192.2, "word": " will", "probability": 0.7998046875}, {"start": 3192.2, "end": 3192.44, "word": " give", "probability": 0.87353515625}, {"start": 3192.44, "end": 3193.16, "word": " 190.", "probability": 0.837890625}], "temperature": 1.0}, {"id": 118, "seek": 322220, "start": 3202.74, "end": 3222.2, "text": " values between 362.12 and 373.8. Take any value, will have any value between these two values.", "tokens": [4190, 1296, 8652, 17, 13, 4762, 293, 13435, 18, 13, 23, 13, 3664, 604, 2158, 11, 486, 362, 604, 2158, 1296, 613, 732, 4190, 13], "avg_logprob": -0.33203125573121584, "compression_ratio": 1.2179487179487178, "no_speech_prob": 0.0, "words": [{"start": 3202.74, "end": 3204.14, "word": " values", "probability": 0.1995849609375}, {"start": 3204.14, "end": 3205.54, "word": " between", "probability": 0.283203125}, {"start": 3205.54, "end": 3209.86, "word": " 362", "probability": 0.898193359375}, {"start": 3209.86, "end": 3210.56, "word": ".12", "probability": 0.9267578125}, {"start": 3210.56, "end": 3211.92, "word": " and", "probability": 0.8779296875}, {"start": 3211.92, "end": 3212.88, "word": " 373", "probability": 0.932373046875}, {"start": 3212.88, "end": 3213.66, "word": ".8.", "probability": 0.7130126953125}, {"start": 3214.44, "end": 3215.2, "word": " Take", "probability": 0.5205078125}, {"start": 3215.2, "end": 3215.46, "word": " any", "probability": 0.91015625}, {"start": 3215.46, "end": 3215.88, "word": " value,", "probability": 0.97314453125}, {"start": 3217.16, "end": 3217.42, "word": " will", "probability": 0.372802734375}, {"start": 3217.42, "end": 3217.94, "word": " have", "probability": 0.9140625}, {"start": 3217.94, "end": 3218.26, "word": " any", "probability": 0.908203125}, {"start": 3218.26, "end": 3218.68, "word": " value", "probability": 0.9814453125}, {"start": 3218.68, "end": 3220.86, "word": " between", "probability": 0.81396484375}, {"start": 3220.86, "end": 3221.2, "word": " these", "probability": 0.8564453125}, {"start": 3221.2, "end": 3221.48, "word": " two", "probability": 0.87060546875}, {"start": 3221.48, "end": 3222.2, "word": " values.", "probability": 0.619140625}], "temperature": 1.0}, {"id": 119, "seek": 325390, "start": 3228.0, "end": 3253.9, "text": " In the previous one, we assumed that the population is normal distribution. If we go back a little bit here, we assumed the population is normal. If the population is normal, then the standard distribution of X bar is also normal distribution with minimum standard deviation of sigma over R. 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You don't have any information about your population, and you are looking for the sampling distribution of X bar. In this case, we can apply a new theorem called central limit theorem. 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In this case, the sampling distribution of the sample means will be not exactly normal, but approximately normally as long as the sample size is large enough. 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Now, this one looks like skewed distribution to the right. Now, as the sample gets large enough, then it becomes normal. 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In this case, the central tendency mu of X bar is same as mu. The variation is also sigma over root N. So again, standard distribution of X bar becomes normal as N. The theorem again says", "tokens": [440, 4188, 307, 787, 291, 362, 281, 3048, 257, 2416, 6889, 13, 682, 341, 1389, 11, 264, 5777, 18187, 2992, 295, 1783, 2159, 307, 912, 382, 2992, 13, 440, 12990, 307, 611, 12771, 670, 5593, 426, 13, 407, 797, 11, 3832, 7316, 295, 1783, 2159, 3643, 2710, 382, 426, 13, 440, 20904, 797, 1619], "avg_logprob": -0.259232945875688, "compression_ratio": 1.4759036144578312, "no_speech_prob": 0.0, "words": [{"start": 3429.52, "end": 3429.78, "word": " The", "probability": 0.6025390625}, {"start": 3429.78, "end": 3430.28, "word": " condition", "probability": 0.93408203125}, {"start": 3430.28, "end": 3430.58, "word": " is", "probability": 0.94580078125}, {"start": 3430.58, "end": 3430.98, "word": " only", "probability": 0.91357421875}, {"start": 3430.98, "end": 3431.3, "word": " you", "probability": 0.7880859375}, {"start": 3431.3, "end": 3431.48, "word": " have", "probability": 0.94873046875}, {"start": 3431.48, "end": 3431.62, "word": " to", "probability": 0.9697265625}, {"start": 3431.62, "end": 3432.18, "word": " select", "probability": 0.865234375}, {"start": 3432.18, "end": 3433.16, "word": " a", "probability": 0.94287109375}, {"start": 3433.16, "end": 3433.48, "word": " large", "probability": 0.96044921875}, {"start": 3433.48, "end": 3433.86, "word": " sample.", "probability": 0.4833984375}, {"start": 3434.58, "end": 3434.76, "word": " In", "probability": 0.92138671875}, {"start": 3434.76, "end": 3434.98, "word": " this", "probability": 0.94970703125}, {"start": 3434.98, "end": 3435.36, "word": " case,", "probability": 0.919921875}, {"start": 3435.96, "end": 3436.2, "word": " the", "probability": 0.8857421875}, {"start": 3436.2, "end": 3436.64, "word": " central", "probability": 0.37744140625}, {"start": 3436.64, "end": 3437.24, "word": " tendency", "probability": 0.87890625}, {"start": 3437.24, "end": 3437.52, "word": " mu", "probability": 0.302978515625}, {"start": 3437.52, "end": 3437.68, "word": " of", "probability": 0.399169921875}, {"start": 3437.68, "end": 3437.8, "word": " X", "probability": 0.6318359375}, {"start": 3437.8, "end": 3438.0, "word": " bar", "probability": 0.93408203125}, {"start": 3438.0, "end": 3438.26, "word": " is", "probability": 0.94287109375}, {"start": 3438.26, "end": 3438.82, "word": " same", "probability": 0.73046875}, {"start": 3438.82, "end": 3439.04, "word": " as", "probability": 0.9599609375}, {"start": 3439.04, "end": 3439.34, "word": " mu.", "probability": 0.89599609375}, {"start": 3440.0, "end": 3440.26, "word": " The", "probability": 0.8798828125}, {"start": 3440.26, "end": 3440.68, "word": " variation", "probability": 0.84765625}, {"start": 3440.68, "end": 3441.46, "word": " is", "probability": 0.951171875}, {"start": 3441.46, "end": 3442.0, "word": " also", "probability": 0.88623046875}, {"start": 3442.0, "end": 3442.72, "word": " sigma", "probability": 0.8740234375}, {"start": 3442.72, "end": 3443.56, "word": " over", "probability": 0.91064453125}, {"start": 3443.56, "end": 3444.4, "word": " root", "probability": 0.931640625}, {"start": 3444.4, "end": 3444.64, "word": " N.", "probability": 0.40478515625}, {"start": 3448.74, "end": 3449.38, "word": " So", "probability": 0.935546875}, {"start": 3449.38, "end": 3449.7, "word": " again,", "probability": 0.74951171875}, {"start": 3450.0, "end": 3450.26, "word": " standard", "probability": 0.70703125}, {"start": 3450.26, "end": 3450.88, "word": " distribution", "probability": 0.84619140625}, {"start": 3450.88, "end": 3451.08, "word": " of", "probability": 0.94091796875}, {"start": 3451.08, "end": 3451.26, "word": " X", "probability": 0.97607421875}, {"start": 3451.26, "end": 3451.54, "word": " bar", "probability": 0.9462890625}, {"start": 3451.54, "end": 3452.12, "word": " becomes", "probability": 0.88232421875}, {"start": 3452.12, "end": 3453.1, "word": " normal", "probability": 0.8486328125}, {"start": 3453.1, "end": 3453.46, "word": " as", "probability": 0.89453125}, {"start": 3453.46, "end": 3453.74, "word": " N.", "probability": 0.361572265625}, {"start": 3454.8, "end": 3455.12, "word": " The", "probability": 0.85498046875}, {"start": 3455.12, "end": 3455.44, "word": " theorem", "probability": 0.77587890625}, {"start": 3455.44, "end": 3455.7, "word": " again", "probability": 0.8896484375}, {"start": 3455.7, "end": 3456.1, "word": " says", "probability": 0.8759765625}], "temperature": 1.0}, {"id": 127, "seek": 348442, "start": 3457.72, "end": 3484.42, "text": " If we select a random sample from unknown population, then the standard distribution of X part is approximately normal as long as N gets large enough. 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So if my n is large, it means above 30, or 30 and above this.", "tokens": [1171, 881, 37870, 11, 498, 291, 500, 380, 458, 264, 1900, 3909, 11, 297, 3673, 2217, 307, 1547, 281, 764, 420, 281, 3079, 300, 20904, 13, 407, 498, 297, 307, 5044, 813, 2217, 11, 309, 486, 976, 257, 3832, 7316, 300, 307, 6217, 2710, 13, 407, 498, 452, 297, 307, 2416, 11, 309, 1355, 3673, 2217, 11, 420, 2217, 293, 3673, 341, 13], "avg_logprob": -0.2316894493997097, "compression_ratio": 1.5290697674418605, "no_speech_prob": 0.0, "words": [{"start": 3486.27, "end": 3486.53, "word": " For", "probability": 0.4990234375}, {"start": 3486.53, "end": 3486.95, "word": " most", "probability": 0.91259765625}, {"start": 3486.95, "end": 3487.71, "word": " distributions,", "probability": 0.86328125}, {"start": 3489.53, "end": 3489.99, "word": " if", "probability": 0.89794921875}, {"start": 3489.99, "end": 3490.13, "word": " you", "probability": 0.96044921875}, {"start": 3490.13, "end": 3490.33, "word": " don't", "probability": 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3512.11, "end": 3530.61, "text": " For fairly symmetric distribution, I mean for nearly symmetric distribution, the distribution is not exactly normal, but approximately normal. In this case, N to be large enough if it is above 15. So, N greater than 15 will usually have same distribution as almost normal.", "tokens": [1171, 6457, 32330, 7316, 11, 286, 914, 337, 6217, 32330, 7316, 11, 264, 7316, 307, 406, 2293, 2710, 11, 457, 10447, 2710, 13, 682, 341, 1389, 11, 426, 281, 312, 2416, 1547, 498, 309, 307, 3673, 2119, 13, 407, 11, 426, 5044, 813, 2119, 486, 2673, 362, 912, 7316, 382, 1920, 2710, 13], "avg_logprob": -0.28327547289707045, "compression_ratio": 1.625, "no_speech_prob": 0.0, "words": [{"start": 3512.11, "end": 3512.39, "word": " For", "probability": 0.36328125}, {"start": 3512.39, "end": 3512.91, "word": " fairly", "probability": 0.475341796875}, {"start": 3512.91, "end": 3513.45, "word": " symmetric", "probability": 0.77783203125}, {"start": 3513.45, "end": 3514.09, "word": " distribution,", "probability": 0.46337890625}, {"start": 3514.23, "end": 3514.31, "word": " I", "probability": 0.94580078125}, {"start": 3514.31, "end": 3514.45, "word": " mean", "probability": 0.96630859375}, {"start": 3514.45, "end": 3514.75, "word": " for", "probability": 0.78076171875}, {"start": 3514.75, "end": 3515.21, "word": " nearly", "probability": 0.7490234375}, {"start": 3515.21, "end": 3515.79, "word": " symmetric", "probability": 0.82470703125}, {"start": 3515.79, "end": 3516.53, "word": " distribution,", "probability": 0.857421875}, {"start": 3517.11, "end": 3517.33, "word": " the", "probability": 0.79052734375}, {"start": 3517.33, "end": 3517.79, "word": " distribution", "probability": 0.78662109375}, {"start": 3517.79, "end": 3517.99, "word": " is", "probability": 0.8740234375}, {"start": 3517.99, "end": 3518.15, "word": " not", "probability": 0.9404296875}, {"start": 3518.15, "end": 3518.63, "word": " exactly", "probability": 0.89208984375}, {"start": 3518.63, "end": 3518.99, "word": " normal,", "probability": 0.82666015625}, {"start": 3519.55, "end": 3519.79, "word": " but", "probability": 0.91455078125}, {"start": 3519.79, "end": 3520.45, "word": " approximately", "probability": 0.85546875}, {"start": 3520.45, "end": 3520.89, "word": " normal.", "probability": 0.8525390625}, {"start": 3521.33, "end": 3521.55, "word": " In", "probability": 0.92919921875}, {"start": 3521.55, "end": 3521.75, "word": " this", "probability": 0.94384765625}, {"start": 3521.75, "end": 3522.13, "word": " case,", "probability": 0.91796875}, {"start": 3522.71, "end": 3522.91, "word": " N", "probability": 0.1971435546875}, {"start": 3522.91, "end": 3523.01, "word": " to", "probability": 0.60693359375}, {"start": 3523.01, "end": 3523.15, "word": " be", "probability": 0.88671875}, {"start": 3523.15, "end": 3523.43, "word": " large", "probability": 0.96630859375}, {"start": 3523.43, "end": 3523.81, "word": " enough", "probability": 0.87744140625}, {"start": 3523.81, "end": 3524.25, "word": " if", "probability": 0.82373046875}, {"start": 3524.25, "end": 3524.39, "word": " it", "probability": 0.93798828125}, {"start": 3524.39, "end": 3524.53, "word": " is", "probability": 0.92822265625}, {"start": 3524.53, "end": 3524.89, "word": " above", "probability": 0.900390625}, {"start": 3524.89, "end": 3525.43, "word": " 15.", "probability": 0.857421875}, {"start": 3525.89, "end": 3526.31, "word": " So,", "probability": 0.9130859375}, {"start": 3526.35, "end": 3526.49, "word": " N", "probability": 0.77734375}, {"start": 3526.49, "end": 3526.79, "word": " greater", "probability": 0.80419921875}, {"start": 3526.79, "end": 3527.03, "word": " than", "probability": 0.9501953125}, {"start": 3527.03, "end": 3527.37, "word": " 15", "probability": 0.9521484375}, {"start": 3527.37, "end": 3527.63, "word": " will", "probability": 0.84375}, {"start": 3527.63, "end": 3528.17, "word": " usually", "probability": 0.9091796875}, {"start": 3528.17, "end": 3528.45, "word": " have", "probability": 0.350830078125}, {"start": 3528.45, "end": 3528.77, "word": " same", "probability": 0.7119140625}, {"start": 3528.77, "end": 3529.23, "word": " distribution", "probability": 0.7275390625}, {"start": 3529.23, "end": 3529.51, "word": " as", "probability": 0.3330078125}, {"start": 3529.51, "end": 3530.01, "word": " almost", "probability": 0.63720703125}, {"start": 3530.01, "end": 3530.61, "word": " normal.", "probability": 0.79931640625}], "temperature": 1.0}, {"id": 130, "seek": 356430, "start": 3535.48, "end": 3564.3, "text": " For normal population, as we mentioned, of distributions, the semantic distribution of the mean is always. Okay, so again, there are three cases. For most distributions, N to be large, above 30. In this case, the distribution is nearly normal. For fairly symmetric distributions, N above 15 gives", "tokens": [1171, 2710, 4415, 11, 382, 321, 2835, 11, 295, 37870, 11, 264, 47982, 7316, 295, 264, 914, 307, 1009, 13, 1033, 11, 370, 797, 11, 456, 366, 1045, 3331, 13, 1171, 881, 37870, 11, 426, 281, 312, 2416, 11, 3673, 2217, 13, 682, 341, 1389, 11, 264, 7316, 307, 6217, 2710, 13, 1171, 6457, 32330, 37870, 11, 426, 3673, 2119, 2709], "avg_logprob": -0.2694052323218315, "compression_ratio": 1.6779661016949152, "no_speech_prob": 0.0, "words": [{"start": 3535.48, "end": 3535.74, "word": " For", "probability": 0.285888671875}, {"start": 3535.74, "end": 3536.26, "word": " normal", "probability": 0.78564453125}, {"start": 3536.26, "end": 3536.78, "word": " population,", "probability": 0.7470703125}, {"start": 3536.92, "end": 3537.0, "word": " as", "probability": 0.9248046875}, {"start": 3537.0, "end": 3537.14, "word": " we", "probability": 0.947265625}, {"start": 3537.14, "end": 3537.52, "word": " mentioned,", "probability": 0.775390625}, {"start": 3537.76, "end": 3537.84, "word": " of", "probability": 0.7275390625}, {"start": 3537.84, "end": 3538.42, "word": " distributions,", "probability": 0.80322265625}, {"start": 3539.16, "end": 3539.38, "word": " the", "probability": 0.91455078125}, {"start": 3539.38, "end": 3539.64, "word": " semantic", "probability": 0.28125}, {"start": 3539.64, "end": 3540.3, "word": " distribution", "probability": 0.84326171875}, {"start": 3540.3, "end": 3540.58, "word": " of", "probability": 0.958984375}, {"start": 3540.58, "end": 3540.74, "word": " the", "probability": 0.91796875}, {"start": 3540.74, "end": 3540.96, "word": " mean", "probability": 0.92529296875}, {"start": 3540.96, "end": 3541.48, "word": " is", "probability": 0.9384765625}, {"start": 3541.48, "end": 3542.96, "word": " always.", "probability": 0.70458984375}, {"start": 3546.68, "end": 3547.32, "word": " Okay,", "probability": 0.560546875}, {"start": 3547.58, "end": 3547.94, "word": " so", "probability": 0.93798828125}, {"start": 3547.94, "end": 3548.22, "word": " again,", "probability": 0.9013671875}, {"start": 3548.7, "end": 3548.88, "word": " there", "probability": 0.8955078125}, {"start": 3548.88, "end": 3549.02, "word": " are", "probability": 0.9443359375}, {"start": 3549.02, "end": 3549.2, "word": " three", "probability": 0.818359375}, {"start": 3549.2, "end": 3549.68, "word": " cases.", "probability": 0.900390625}, {"start": 3551.44, "end": 3551.98, "word": " For", "probability": 0.9189453125}, {"start": 3551.98, "end": 3552.38, "word": " most", "probability": 0.88818359375}, {"start": 3552.38, "end": 3552.96, "word": " distributions,", "probability": 0.458740234375}, {"start": 3553.46, "end": 3553.56, "word": " N", "probability": 0.53369140625}, {"start": 3553.56, "end": 3553.76, "word": " to", "probability": 0.94189453125}, {"start": 3553.76, "end": 3553.9, "word": " be", "probability": 0.9521484375}, {"start": 3553.9, "end": 3554.26, "word": " large,", "probability": 0.95458984375}, {"start": 3554.6, "end": 3554.9, "word": " above", "probability": 0.95458984375}, {"start": 3554.9, "end": 3555.3, "word": " 30.", "probability": 0.88037109375}, {"start": 3555.8, "end": 3556.06, "word": " In", "probability": 0.95751953125}, {"start": 3556.06, "end": 3556.28, "word": " this", "probability": 0.943359375}, {"start": 3556.28, "end": 3556.48, "word": " case,", "probability": 0.91943359375}, {"start": 3556.54, "end": 3556.66, "word": " the", "probability": 0.58447265625}, {"start": 3556.66, "end": 3557.0, "word": " distribution", "probability": 0.7431640625}, {"start": 3557.0, "end": 3557.3, "word": " is", "probability": 0.94189453125}, {"start": 3557.3, "end": 3557.56, "word": " nearly", "probability": 0.54345703125}, {"start": 3557.56, "end": 3558.16, "word": " normal.", "probability": 0.63427734375}, {"start": 3559.78, "end": 3560.46, "word": " For", "probability": 0.9345703125}, {"start": 3560.46, "end": 3560.92, "word": " fairly", "probability": 0.80908203125}, {"start": 3560.92, "end": 3561.26, "word": " symmetric", "probability": 0.6611328125}, {"start": 3561.26, "end": 3561.9, "word": " distributions,", "probability": 0.65283203125}, {"start": 3562.14, "end": 3562.3, "word": " N", "probability": 0.98583984375}, {"start": 3562.3, "end": 3562.5, "word": " above", "probability": 0.9111328125}, {"start": 3562.5, "end": 3563.1, "word": " 15", "probability": 0.923828125}, {"start": 3563.1, "end": 3564.3, "word": " gives", "probability": 0.7490234375}], "temperature": 1.0}, {"id": 131, "seek": 359096, "start": 3564.66, "end": 3590.96, "text": " almost normal distribution. But if the population by itself is normally distributed, always the sample mean is normally distributed. So that's the three cases. Now for this example, suppose we have a population. It means we don't know the distribution of that population.", "tokens": [1920, 2710, 7316, 13, 583, 498, 264, 4415, 538, 2564, 307, 5646, 12631, 11, 1009, 264, 6889, 914, 307, 5646, 12631, 13, 407, 300, 311, 264, 1045, 3331, 13, 823, 337, 341, 1365, 11, 7297, 321, 362, 257, 4415, 13, 467, 1355, 321, 500, 380, 458, 264, 7316, 295, 300, 4415, 13], "avg_logprob": -0.18101415431724405, "compression_ratio": 1.7106918238993711, "no_speech_prob": 0.0, "words": [{"start": 3564.66, "end": 3565.12, "word": " almost", "probability": 0.239013671875}, {"start": 3565.12, "end": 3565.58, "word": " normal", "probability": 0.85400390625}, {"start": 3565.58, "end": 3566.18, "word": " distribution.", "probability": 0.837890625}, {"start": 3567.04, "end": 3567.26, "word": " But", "probability": 0.93798828125}, {"start": 3567.26, "end": 3567.72, "word": " if", "probability": 0.83544921875}, {"start": 3567.72, "end": 3568.52, "word": " the", "probability": 0.890625}, {"start": 3568.52, "end": 3568.96, "word": " population", "probability": 0.95849609375}, {"start": 3568.96, "end": 3569.3, "word": " by", "probability": 0.90869140625}, {"start": 3569.3, "end": 3569.78, "word": " itself", "probability": 0.83837890625}, {"start": 3569.78, "end": 3570.1, "word": " is", "probability": 0.951171875}, {"start": 3570.1, "end": 3570.5, "word": " normally", "probability": 0.8916015625}, {"start": 3570.5, "end": 3571.1, "word": " distributed,", "probability": 0.90869140625}, {"start": 3571.54, "end": 3572.08, "word": " always", "probability": 0.8544921875}, {"start": 3572.08, "end": 3572.4, "word": " the", "probability": 0.8876953125}, {"start": 3572.4, "end": 3572.64, "word": " sample", "probability": 0.53955078125}, {"start": 3572.64, "end": 3573.02, "word": " mean", "probability": 0.630859375}, {"start": 3573.02, "end": 3573.82, "word": " is", "probability": 0.9462890625}, {"start": 3573.82, "end": 3574.2, "word": " normally", "probability": 0.89599609375}, {"start": 3574.2, "end": 3574.64, "word": " distributed.", "probability": 0.92724609375}, {"start": 3575.24, "end": 3575.44, "word": " So", "probability": 0.94677734375}, {"start": 3575.44, "end": 3575.66, "word": " that's", "probability": 0.82373046875}, {"start": 3575.66, "end": 3575.8, "word": " the", "probability": 0.9169921875}, {"start": 3575.8, "end": 3576.12, "word": " three", "probability": 0.90087890625}, {"start": 3576.12, "end": 3577.3, "word": " cases.", "probability": 0.89990234375}, {"start": 3580.04, "end": 3580.86, "word": " Now", "probability": 0.37744140625}, {"start": 3580.86, "end": 3583.44, "word": " for", "probability": 0.6044921875}, {"start": 3583.44, "end": 3583.68, "word": " this", "probability": 0.94482421875}, {"start": 3583.68, "end": 3584.1, "word": " example,", "probability": 0.97900390625}, {"start": 3584.9, "end": 3585.28, "word": " suppose", "probability": 0.82177734375}, {"start": 3585.28, "end": 3586.82, "word": " we", "probability": 0.927734375}, {"start": 3586.82, "end": 3587.22, "word": " have", "probability": 0.94921875}, {"start": 3587.22, "end": 3587.48, "word": " a", "probability": 0.99462890625}, {"start": 3587.48, "end": 3587.9, "word": " population.", "probability": 0.939453125}, {"start": 3588.38, "end": 3588.6, "word": " It", "probability": 0.84326171875}, {"start": 3588.6, "end": 3588.82, "word": " means", "probability": 0.93310546875}, {"start": 3588.82, "end": 3588.96, "word": " we", "probability": 0.9169921875}, {"start": 3588.96, "end": 3589.2, "word": " don't", "probability": 0.973876953125}, {"start": 3589.2, "end": 3589.46, "word": " know", "probability": 0.8955078125}, {"start": 3589.46, "end": 3589.68, "word": " the", "probability": 0.9111328125}, {"start": 3589.68, "end": 3590.14, "word": " distribution", "probability": 0.8486328125}, {"start": 3590.14, "end": 3590.34, "word": " of", "probability": 0.9658203125}, {"start": 3590.34, "end": 3590.5, "word": " that", "probability": 0.93017578125}, {"start": 3590.5, "end": 3590.96, "word": " population.", "probability": 0.93017578125}], "temperature": 1.0}, {"id": 132, "seek": 362102, "start": 3592.42, "end": 3621.02, "text": " And that population has mean of 8. Standard deviation of 3. And suppose a random sample of size 36 is selected. In this case, the population is not normal. It says A population, so you don't know the exact distribution. But N is large. It's above 30, so you can apply the central limit theorem. 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Now, the difference between this lecture and the previous ones was, here we are interested in the exponent of X. 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Here we have 8.2 minus 8 divided by sigma over root N. I will end with Z between minus 0.4 and 0.4. Now, up to this step, it's in U, for chapter 7. Now, Z between minus 0.4 up to 0.4, you have to go back.", "tokens": [8511, 83, 1897, 278, 624, 11, 550, 9845, 538, 12771, 670, 5593, 426, 490, 1293, 4881, 11, 370, 1614, 13, 23, 3175, 1649, 6666, 538, 12771, 670, 5593, 426, 13, 1692, 321, 362, 1649, 13, 17, 3175, 1649, 6666, 538, 12771, 670, 5593, 426, 13, 286, 486, 917, 365, 1176, 1296, 3175, 1958, 13, 19, 293, 1958, 13, 19, 13, 823, 11, 493, 281, 341, 1823, 11, 309, 311, 294, 624, 11, 337, 7187, 1614, 13, 823, 11, 1176, 1296, 3175, 1958, 13, 19, 493, 281, 1958, 13, 19, 11, 291, 362, 281, 352, 646, 13], "avg_logprob": -0.17413015955502226, "compression_ratio": 1.7403314917127073, "no_speech_prob": 0.0, "words": [{"start": 3680.29, "end": 3680.77, "word": " Subtracting", "probability": 0.75830078125}, {"start": 3680.77, "end": 3680.99, "word": " U,", "probability": 0.51025390625}, {"start": 3681.13, "end": 3681.41, "word": " then", "probability": 0.80712890625}, {"start": 3681.41, "end": 3681.69, "word": " divide", "probability": 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