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

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Presentation transcript:

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

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

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

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

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)

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

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)

Homework P – 24