1. Chapter 9: Hypothesis Tests for One Population Mean 9.2 Terms, Errors, and Hypotheses

2. Vocab Test statistic – The statistic used as a basis for deciding whether the null hypothesis should be rejected Rejection region – The set of values for the test statistic that leads to rejection of the null hypothesis Nonrejection region – The set of values for the test statistic that leads to nonrejection of the null hypothesis Critical values – The values of the test statistic that separate the rejection and nonrejection regions – Considered part of the rejection region

4. Types of Incorrect Decisions Type I – Rejecting the null hypothesis when it is in fact true Type II – Not rejecting the null hypothesis when it is in fact false

5. Example 9.5 Consider the pretzel packaging hypothesis test: H0: μ = 454 g (the packaging machine is working properly) Ha: μ ≠ 454 g (the packaging machine is not working properly) Where μ is the mean net weight of all bags of pretzels packaged. Explain what each of the following would mean: Type I error Type II error Correct Decision

6. Type I Error Probability Called the significance level of the hypothesis test Denoted by α The probability of a Type I error (rejecting a true null hypothesis)

7. Type II Error Probability Denoted by β Probability of a Type II Error (not rejecting the null when it is false) Note: For a fixed sample size, the smaller we specify the significance level, α, the larger will be the probability, β, of not rejecting a false null hypothesis

8. Possible Conclusions for a Hypothesis Test Suppose that a hypothesis test is conducted at a small confidence level. – If the null hypothesis is rejected, we conclude that the alternative hypothesis is true (results are statistically significant) – If the null hypothesis is not rejected, we conclude that the data do not provide sufficient evidence to support the alternative hypothesis (results are not statistically significant)

9. Homework P. 397 14 – 24