ODD ANSWERS A71 6. (a) 0.830 (b) (0.810, 0.849). With 90% confidence, you can say that the population proportion of U.S. adults who say that the energy situation in the United States is very or fairly serious is between 81.1% and 84.9%. (c) Yes. The values fall outside the confidence intervals. (d) 585 adults 7. (a) (5.41, 38.08) (b) (2.32, 6.17). With 95% confidence, you can say that the population standard deviation is between 2.32 and 6.17 minutes. Real Statistics—Real Decisions for Chapter 6 (page 342) 1. (a) Yes, there has been a change in the mean concentration level because the confidence interval for Year 1 does not overlap the confidence interval for Year 2. (b) No, there has not been a change in the mean concentration level because the confidence interval for Year 2 overlaps the confidence interval for Year 3. (c) Yes, there has been a change in the mean concentration level because the confidence interval for Year 1 does not overlap the confidence interval for Year 3. 2. The concentrations of cyanide in the drinking water have increased over the three-year period. 3. The width of the confidence interval for Year 2 may have been caused by greater variation in the levels of cyanide than in other years, which may be the result of outliers. 4. Increase the sample size. 5. Answers will vary. (a) Sample answer: The sampling distribution of the sample means was used because the “mean concentration” was used. The sample mean is the most unbiased point estimate of the population mean. (b) Sample answer: No, because typically s is unknown. They could have used the sample standard deviation. Chapter 7 Section 7.1 (page 359) 1. The two types of hypotheses used in a hypothesis test are the null hypothesis and the alternative hypothesis. The alternative hypothesis is the complement of the null hypothesis. 3. You can reject the null hypothesis, or you can fail to reject the null hypothesis. 5. False. In a hypothesis test, you assume the null hypothesis is true. 7. True 9. False. A small P-value in a test will favor rejection of the null hypothesis. 11. H0: m … 645 (claim); Ha: m 7 645 13. H0: s = 5; Ha: s ≠ 5 (claim) 15. H0: p Ú 0.45; Ha: p 6 0.45 (claim) 17. c; H0: m … 3 18. d; H0: m Ú 3 1 2 3 4 μ 1 2 3 4 μ 19. b; H0: m = 3 20. a; H0: m … 2 1 2 3 4 μ 1 2 3 4 μ 21. Right-tailed 23. Two-tailed 25. m 7 8 H0: m … 8; Ha: m 7 8 (claim) 27. s … 320 H0: s … 320 (claim); Ha: s 7 320 29. p = 0.54 H0: p = 0.54 (claim); Ha: p ≠ 0.54 31. A type I error will occur when the actual proportion of new customers who return to buy their next textbook is at least 0.60, but you reject H0: p Ú 0.60. A type II error will occur when the actual proportion of new customers who return to buy their next textbook is less than 0.60, but you fail to reject H0: p Ú 0.60. 33. A type I error will occur when the actual standard deviation of the length of time to play a game is less than or equal to 12 minutes, but you reject H0: s … 12. A type II error will occur when the actual standard deviation of the length of time to play a game is greater than 12 minutes, but you fail to reject H0: s … 12. 35. A type I error will occur when the actual proportion of applicants who become campus security officers is at most 0.25, but you reject H0: p … 0.25. A type II error will occur when the actual proportion of applicants who become campus security officers is greater than 0.25, but you fail to reject H0: p … 0.25. 37. H0: The proportion of homeowners who have a home security alarm is greater than or equal to 14%. Ha: The proportion of homeowners who have a home security alarm is less than 14%. H0: p Ú 0.14; Ha: p 6 0.14 Left-tailed because the alternative hypothesis contains 6. −z P-value area z 39. H0: The standard deviation of the 18-hole scores for a golfer is greater than or equal to 2.1 strokes. Ha: The standard deviation of the 18-hole scores for a golfer is less than 2.1 strokes. H0: s Ú 2.1; Ha: s 6 2.1 Left-tailed because the alternative hypothesis contains 6. −z P-value area z 41. H0: The percentage of responses to a survey is 100%. Ha: The percentage of responses to a survey is not 100%. H0: p = 1; Ha: p ≠ 1 Two-tailed because the alternative hypothesis contains ≠. −z z P-value area z 1 2 P-value area 1 2
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