# Hypothesis Testing with One Sample

## Additional Information and Full Hypothesis Test Examples

1. In a hypothesis test problem, you may see words such as "the level of significance is 1 percent". The "1 percent" is the preconceived or preset α.
2. The statistician setting up the hypothesis test selects the value of α to use before collecting the sample data.
3. If no level of significance is given, a common standard to use is 
4. When you calculate the p-value and draw the picture, the p-value is the area in the left tail, the right tail, or split evenly between the two tails. For this reason, we call the hypothesis test left, right, or two tailed.
5. The alternative hypothesis, , tells you if the test is left, right, or two-tailed. It is the key to conducting the appropriate test.
6. H  never has a symbol that contains an equal sign.
7. Thinking about the meaning of the : A data analyst should have more confidence that he made the correct decision to reject the null hypothesis with a smaller p-value (for example, 0.001 as opposed to 0.04) even if using the 0.05 level for alpha. Similarly, for a large p-value such as 0.4, as opposed to a p-value of 0.056 (alpha = 0.05 is less than either number), a data analyst should have more confidence that she made the correct decision in not rejecting the null hypothesis.  This makes the data analyst use judgment rather than mindlessly applying rules.
The following examples illustrate a left-, right-, and two-tailed test.

### Full Hypothesis Test Examples

The next example is a poem written by a statistics student named Nicole Hart. The solution to the problem follows the poem. Notice that the hypothesis test is for a single population proportion. This means that the null and alternate hypotheses use the parameter p. The distribution for the test is normal. The estimated proportion p′ is the proportion of fleas killed to the total fleas found on Fido. This is sample information. The problem gives a preconceived α = 0.01, for comparison, and a 95 percent confidence interval computation. The poem is clever and humorous, so please enjoy it!

### Chapter Review

The hypothesis test itself has an established process. This can be summarized as follows:

Notice that in performing the hypothesis test, you use α and not β. β is needed to help determine the sample size of the data that are used in calculating the p-value. Remember that the quantity 1 – β is called the Power of the Test. A high power is desirable. If the power is too low, statisticians typically increase the sample size while keeping α the same. If the power is low, the null hypothesis might not be rejected when it should be.

### Homework

For each of the word problems, use a solution sheet to do the hypothesis test. The solution sheet is found in 
Hypothesis testing: For the following 10 exercises, answer each question.
1. State the null and alternate hypotheses.
2. State the p-value.
3. State alpha.
4. What is your decision?
5. Write a conclusion.
6. Answer any other questions asked in the problem.

### References

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