Lesson_8_Workbook_Version_F12_Space

Standard deviation but is reasonably

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Unformatted text preview: it be left ­ tail or right ­tail? Why? PROBLEM # 8.6 In hypothesis testing, what is meant by the decision rule? What role does it play in the hypothesis testing procedure? PROBLEM # 8.7 What is the central limit theorem, and how is it applicable to hypothesis testing? PROBLEM # 8.8 If the population standard deviation is known, but the sample size is less than 30, what assumption is necessary to use the z ­statistic in carrying out a hypothesis test for the population mean? 2 PROBLEM # 8.9 For a sample of 35 items from a population for which the standard deviation is ! =20.5, the sample mean is 458.0. At the 0.05 level of significance, test H0:! = 450 versus H1:! ≠450. Determine and interpret the p ­value for the test. 1. Set up hypotheses: H0: H1: Level of significance: α = 2. What is the appropriate test statistic to use? 3. Calculate the test statistics value 4. Find the critical value for the test statistic 5. Define your decision rule: 6. Make your decision: 7. Interpret the conclusion in context: 1 2 3 4 5 6 7 A z-Test of a Mean Sample mean Population standard deviation Sample size Hypothesized mean Alpha B 458.0 20.5 35 450 0.05 C z Stat P(Z<=z) one-tail z Critical one-tail P(Z<=z) two-tail z Critical two-tail D 2.31 0.0105 1.645 0.0210 1.960 3 PROBLEM # 8.10 For each of the following tests and z ­values, determine the p ­value for the test: a. Right ­tail test and z=1.54 b. Left ­tail test and z= ­1.03 c. Two ­tail test and z=1.27 PROBLEM # 8.11 For a sample of 12 items from a normally distributed population for which the standard deviation is ! =17.0, the sample mean is 230.8. At the 0.05 level of significance, test H0:! ≤ 220 versus H1:! >220. Determine and interpret the p ­value for the test. 1. Set up hypotheses: H0: H1: Level of significance: α = 2. What is the appropriate test statistic to use? 3. Calculate the test statistics value 4. Find the critical value for the test statistic 5. Define your decision rule: 6. Make your decision: 7. Interpret the conclusion in context: 4 PROBLEM # 8.12 In the past, patrons of a cinema complex have spent an average of $5.00 for popcorn and other snacks, with a standard deviation of $1.80. The amounts of these expenditures have been normally distributed. Following an intensive publicity campaign by a local medical society, the mean expenditure for a sample of 18 patrons is found to be $4.20. In a one ­tail test at the 0.05 level o...
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