794 APPENDIX D 15. 0.69 6 md 6 5.56. Because the confidence interval limits do not contain 0 and they consist of positive values only, it appears that the “before” measurements are greater than the “after” measurements, so hypnotism does appear to be effective in reducing pain. 17. The larger data set changed the results and conclusion. a. H0: md = 0. H1: md 7 0. Test statistic: t = 17.611. P@value = 0.0000 (Table: P@value 6 0.005). Critical value: t = 1.645. Reject H0. There is sufficient evidence to support the claim that for females, the measured weights tend to be higher than the reported weights. (TI data: Test statistic is t = 4.864, the critical value is t = 1.651, and the P-value is 0.0000.) b. 90% CI: 2.94 lb 6 md 6 3.55 lb. Because the confidence interval does not include 0 lb, reject H0. There is sufficient evidence to support the claim that for females, the measured weights tend to be higher than the reported weights. (TI data: 1.02 lb 6 md 6 2.08 lb.) 19. a. H0: md = 0 year. H1: md 6 0 year. Test statistic: t = -5.269. P@value = 0.0000 (Table: 6 0.005). Critical value: t = -1.662. Reject H0. There is sufficient evidence to support the claim that actresses are generally younger than actors. b. 90% CI: -10.2 years 6 md 6 -5.3 years. The confidence interval consists of negative numbers only and does not include 0. 21. a. H0: md = 0. H1: md ≠ 0. Test statistic: t = -77.006. P@value = 0.0000 (Table: P@value 6 0.005). Critical values: t = {1.961. Reject H0. There is sufficient evidence to warrant rejection of the claim that for males, their height is the same as their arm span. (TI data: Test statistic is t = -22.16, critical values are t = {1.967, and the P-value is 0.0000.) 23. H0: md = 0 in. H1: md ≠ 0 in. Test statistic: t = -4.090. P-value = 0.0001 (Table: 60.01). Critical values: t = {1.978 (Table: {1.984 approximately). Reject H0. There is sufficient evidence to warrant rejection of the claim of no difference in heights between mothers and their first daughters. 25. a. 95% CI: -1.31 in. 6 md 6 1.35 in. Because the confidence interval includes the value of 0 in., fail to reject H0. There is not sufficient evidence to warrant rejection of the claim of no difference in heights between fathers and their first sons. There does not appear to be a significant difference. b. Answers vary, but here is a typical 95% confidence interval: -0.98 in. 6 md 6 1.20 in. Because the confidence interval includes the value of 0 in., fail to reject H0. There is not sufficient evidence to warrant rejection of the claim of no difference in heights between fathers and their first sons. There does not appear to be a significant difference. c. The two confidence intervals do not differ by amounts that are very substantial. The conclusions from the two confidence intervals are the same. It appears that the confidence interval constructed using the t distribution and the confidence interval constructed using the bootstrap method are reasonably consistent with each other. Section 9-4 1. a. No. b. No. c. The two samples have standard deviations (or variances) that are very close in value. d. Skewed right Section 9-3 1. H0: md = 0. H1: md 6 0. 3. a. 90% b. 2.015 c. Because the confidence interval limits do not include 0 admissions and the range of values consists of negative values only, there is sufficient evidence to support the claim that fewer hospital admissions due to traffic accidents occur on Friday the 6th than on the following Friday the 13th. 5. a. H0: md = 0. H1: md 7 0. Test statistic: t = 0.407. P@value = 0.3469 (Table: P@value 7 0.10). Critical value: t = 1.833. Fail to reject H0. There is not sufficient evidence to support the claim that for females, the measured weights tend to be higher than the reported weights. b. 90% CI: -1.30 lb 6 md 6 2.04 lb. Because the confidence interval includes 0, fail to reject H0. There is not sufficient evidence to support the claim that for females, the measured weights tend to be higher than the reported weights. 7. a. H0: md = 0. H1: md 6 0. Test statistic: t = -4.438. P@value = 0.0011 (Table: P@value 6 0.005). Critical value: t = -2.896. Reject H0. There is sufficient evidence to support the claim that for the population of freshman male college students, the weights in September are less than the weights in the following April. b. 98% CI: -1.5 kg 6 md 6 -0.3 kg. Because the confidence interval does not include 0 kg, reject H0. There is sufficient evidence to support the claim that for the population of freshman male college students, the weights in September are less than the weights in the following April. c. The test does not address the specific weight gain of 15 lb, but it does suggest that males gain weight during their freshman year. 9. a. H0: md = 0. H1: md ≠ 0. Test statistic: t = 0.890. P@value = 0.3924 (Table: P@value 7 0.20). Critical values: t = {2.201. Fail to reject H0. There is not sufficient evidence to warrant rejection of the claim that the population of differences has a mean equal to 0. b. 95% CI: -3.1 6 md 6 7.2. Because the confidence interval includes 0, fail to reject H0. There is not sufficient evidence to warrant rejection of the claim that the population of differences has a mean equal to 0. 11. a. H0: md = 0 year. H1: md 6 0 year. Test statistic: t = -2.609. P@value = 0.0142 (Table: 6 0.025). Critical value: t = -1.833. Reject H0. There is sufficient evidence to support the claim that for the population of ages of Best Actresses and Best Actors, the differences have a mean less than 0. There is sufficient evidence to conclude that Best Actresses are generally younger than Best Actors. b. 90% CI: -16.5 years 6 md 6 -2.9 years. The confidence interval consists of negative numbers only and does not include 0. 13. H0: md = 0 in. H1: md ≠ 0 in. Test statistic: t = -1.379. P-value = 0.2013 (Table: 70.20). Critical values: t = {2.262. Fail to reject H0. There is not sufficient evidence to warrant rejection of the claim that there is no difference in heights between mothers and their first daughters.
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