Ch9 Fundamentals of Hypothesis Testing

# Ch9 Fundamentals of Hypothesis Testing - 106 Chapter 9...

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Unformatted text preview: 106 Chapter 9: Fundamentals of Hypothesis Testing: One-Sample Tests CHAPTER 9 9.1 H is used to denote the null hypothesis. 9.2 H 1 is used to denote the alternative hypothesis. 9.3 α is used to denote the significance level, or the chance of committing a Type I error. 9.4 β is used to denote the risk or the chance of committing a Type II error. 9.5 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. 9.6 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. 9.7 β is the probability of making a Type II error – that is, the probability of incorrectly failing to reject the null hypothesis when it is false. 9.8 The power of a test is the complement, which is (1 - β ), of the probability β of making a Type II error. 9.9 It is possible to incorrectly reject a true null hypothesis because the mean of a single sample can fall in the rejection region even though the hypothesized population mean is true. 9.10 It is possible to not reject a false null hypothesis because the mean of a single sample can fall in the non-rejection region even though the hypothesized population mean is false. 9.11 β will increase. 9.12 Other things being equal, the closer the hypothesized mean is to the actual mean, the larger the risk of committing a Type II error will be. 9.13 α is the probability of incorrectly convicting the defendant when he is innocent. β is the probability of incorrectly failing to convict the defendant when he is guilty. 9.14 Under the French judicial system, unlike ours in the United States, the null hypothesis assumes the defendant is guilty, the alternative hypothesis assumes the defendant is innocent. A Type I error would be not convicting a guilty person and a Type II error would be convicting an innocent person. 107 Chapter 9: Fundamentals of Hypothesis Testing: One-Sample Tests 9.15 (a) A Type I error is the mistake of approving an unsafe drug. A Type II error is not approving a safe drug. (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 longer time to approve a new drug. 9.16 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. 9.17 H : μ = 70 pounds. The cloth has a mean breaking strength of 70 pounds....
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## This note was uploaded on 12/22/2011 for the course BUSINESS bus 152 taught by Professor Çeşmecibaşı during the Spring '11 term at Middle East Technical University.

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Ch9 Fundamentals of Hypothesis Testing - 106 Chapter 9...

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