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Unformatted text preview: 80 Chapter 8: Fundamentals of Hypothesis Testing CHAPTER 8 8.1 H is used to denote the null hypothesis. 8.2 H 1 is used to denote the alternative hypothesis. 8.3 α is used to denote the significance level, or the chance of committing a Type I error. 8.4 β is used to denote the consumer’s risk, or the chance of committing a Type II error. 8.5 1 – β represents the power of a statistical test – that is, the probability of correctly rejecting the null hypothesis when in reality the null hypothesis is false and should be rejected. 8.6 α is the probability of making a Type I error – that is, the probability of incorrectly rejecting the null hypothesis when in reality the null hypothesis is true and should not be rejected. 8.7 β is the probability of making a Type II error – that is, the probability of incorrectly failing to reject the null hypothesis when in reality the null hypothesis is false and should be rejected. 8.8 The power of a test is the complement of the probability β of making a Type II error. 8.9 It is possible to incorrectly reject a true null hypothesis because it is possible for the mean of a single sample to fall in the rejection region even though the hypothesized population mean is true. 8.10 It is possible to incorrectly fail to reject a false null hypothesis because it is possible for the mean of a single sample to fall in the nonrejection region even though the hypothesized population mean is false. 8.11 β will increase. 8.12 Other things being equal, the closer the hypothesized mean is to the actual mean, the larger is the risk of committing a Type II error. 8.13 α is the probability of incorrectly convicting the defendant when he is actually innocent. β is the probability of incorrectly failing to convict the defendant when he is actually guilty. 8.14 Under the French judicial system, unlike ours in the United States, the null hypothesis is that the defendant is guilty, the alternative hypothesis is that the defendant is innocent. The meaning of α and β risks would also be switched. 80 81 Chapter 8: Fundamentals of Hypothesis Testing 8.15 (a) A Type I error is the mistake made when an unsafe drug is being approved. A Type II error is committed when a safe drug is not being approved. (b) The consumer groups are trying to avoid a Type I error. (c) The industry lobbyists are trying to avoid a Type II error. (d) To lower both Type I and Type II errors, the FDA can require more information and evidence in the form of more rigorous testing. This can easily translate into the longer time it takes to approve a new drug. 8.16 H : μ = 20 minutes. 20 minutes is adequate travel time between classes. H 1 : μ ≠ 20 minutes. 20 minutes is not adequate travel time between classes....
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 Spring '08
 Harris
 Statistical hypothesis testing

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