APPENDIX D 793 15. a. H0: m1 = m2. H1: m1 7 m2. Test statistic: t = 32.771. P@value = 0.0000 (Table: 6 0.005). Critical value: t = 1.667 (Table: 1.685). Reject H0. There is sufficient evidence to support the claim that pre-1964 quarters have a mean weight that is greater than the mean weight of post-1964 quarters. b. 90% CI: 0.52522 lb 6 m1 - m2 6 0.58152 (Table: 0.52492 lb 6 m1 - m2 6 0.58182) c. Yes. Vending machines are not affected very much because pre-1964 quarters are mostly out of circulation. 17. a. H0: m1 = m2. H1: m1 6 m2. Test statistic: t = -1.085. P@value = 0.1442 (Table: P@value 7 0.10). Critical value: t = -1.708 (Table: -1.796). Fail to reject H0. There is not sufficient evidence to support the claim that the mean weight of the 1988 male population is less than the mean weight of the 2012 male population. b. 90% CI: -11.77 kg 6 m1 - m2 6 2.63 kg (Table: -12.14 kg 6 m1 - m2 6 3.00 kg) 19. a. H0: m1 = m2. H1: m1 7 m2. Test statistic: t = 16.084. P@value = 0.0000 (Table: 6 0.005). Critical value: t = 2.538 (Table: 2.718). Reject H0. There is sufficient evidence to support the claim that the contents of cans of regular Coke have weights with a mean that is greater than the mean for Diet Coke. b. 98% CI: 0.02794 lb 6 m1 - m2 6 0.03841 lb (Table: 0.02756 lb 6 m1 - m2 6 0.03878 lb) c. The contents in cans of regular Coke appear to weigh more, probably due to the sugar present in regular Coke but not diet Coke. 21. a. H0: m1 = m2. H1: m1 6 m2. Test statistic: t = -20.393. 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 the mean weight of the 1988 male population is less than the mean weight of the 2012 male population. It does appear that the male population is getting heavier. (TI data: Test statistic is t = -5.282, P-value is 0.0000, critical value is t = -1.648.) b. 90% CI: -7.60 kg 6 m1 - m2 6 -6.47 kg (TI data: -7.50 kg 6 m1 - m2 6 -3.93 kg) 23. H0: m1 = m2. H1: m1 6 m2. Test statistic: t = -0.132. P-value = 0.4477 (Table: 70.10). Critical value: t = -1.669 (Table: -1.688). Fail to reject H0. There is not sufficient evidence to support the claim that men talk less than women. 25. With pooling, df increases dramatically to 97, but the test statistic decreases from 2.282 to 1.705 (because the estimated standard deviation increases from 2.620268 to 3.507614), the P-value increases to 0.0457, and the 90% confidence interval becomes wider. With pooling, these results do not show greater significance. 27. H0: m1 = m2. H1: m1 ≠ m2. Test statistic: t = 15.322. P@value = 0.0000 (Table: P@value 6 0.01). Critical values: t = {2.080. Reject H0. There is sufficient evidence to warrant rejection of the claim that the two populations have the same mean. II 2012.” The proportion of males in ANSUR II 2012 appears to be significantly higher than in ANSUR I 1988. (TI data: With sample proportions of 227>500 and 319>500, test statistic is z = -5.84, P@value = 0.0000, and the confidence interval is -0.264 6 p1-p2 6 -0.104.) Section 9-2 1. Only parts (b) and (c) describe independent samples. 3. a. Yes b. Yes c. 98% 5. a. H0: m1 = m2. H1: m1 6 m2. Test statistic: t = -4.084. P@value = 0.0001 (Table: P@value 6 0.005). Critical value: t = -1.695 (Table: -1.729). Reject H0. There is sufficient evidence to support the claim that giving candy does result in greater tips. b. 90% CI: -3.78 6 m1 - m2 6 -1.56 (Table: -3.80 6 m1 - m2 6 -1.54) 7. a. H0: m1 = m2. H1: m1 7 m2. Test statistic: t = 2.095. P@value = 0.0196 (Table: P@value 7 0.01). Critical value: t = 2.372 (Table: 2.403). Fail to reject H0. There is not sufficient evidence to support the claim that rubbing with alcohol results in a lower bacteria count. b. 98% CI: -4 6 m1 - m2 6 72 (Table: -5 6 m1 - m2 6 73) c. Yes, the null hypothesis is rejected with a 0.05 significance level, so the conclusion changes to this: There is sufficient evidence to support the claim that rubbing with alcohol results in a lower bacteria count. 9. a. H0: m1 = m2. H1: m1 ≠ m2. Test statistic: t = 2.647. P@value = 0.0101 (Table: 6 0.02). Critical values: t = {1.995 (Table: {2.032). Reject H0. There is sufficient evidence to warrant rejection of the claim that the samples are from populations with the same mean. Color does appear to have an effect on word recall scores. Red appears to be associated with higher word memory recall scores. b. 95% CI: 0.88 6 m1 - m2 6 6.28 (Table: 0.83 6 m1 - m2 6 6.33). The confidence interval includes positive numbers only, so the mean score with a red background appears to be greater than the mean score with a blue background. c. The background color does appear to have an effect on word recall scores. Red appears to be associated with higher word memory recall scores. 11. a. H0: m1 = m2. H1: m1 7 m2. Test statistic: t = 0.132. P-value = 0.4480 (Table: 7 0.10). Critical value: t = 1.691 (Table: 1.729). Fail to reject H0. There is not sufficient evidence to support the claim that the magnets are effective in reducing pain. b. 90, CI: -0.59 6 m1 - m2 6 0.69 (Table: -0.61 6 m1 - m2 6 0.71). c. Magnets do not appear to be effective in treating back pain. It is valid to argue that the magnets might appear to be effective if the sample sizes were larger. 13. a. H0: m1 = m2. H1: m1 ≠ m2. Test statistic: t = -0.393. P@value = 0.6959 (Table: P@value 7 0.20). Critical value: t = {2.012 (Table: {2.060). Fail to reject H0. There is not sufficient evidence to warrant rejection of the claim that the mean commuting time with the heavier bicycle is the same as the mean commuting time with the lighter bicycle. b. 95% CI: -3.7 min 6 m1 - m2 6 2.5 min
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