792 APPENDIX D b. 95% CI: 0.0828 6 p1-p2 6 0.118. Because the confidence interval limits do not contain 0, there is sufficient evidence to warrant rejection of the claim that Connecticut and New York have the same proportion of cars with rear license plates only. There appears to be a significant difference between the proportions of cars with rear license plates only. 19. a. H0: p1 = p2. H1: p1 ≠ p2. Test statistic: z = -2.63. P-value: 0.0085 (Table: 0.0086). Critical values: z = {2.575. Reject H0. There is sufficient evidence to reject the claim that the proportions of blue eyes are the same for females and males. b. 99% CI: -0.112 6 p1 - p2 6 -0.00116. Because the confidence interval limits do not contain 0, there appears to be a significant difference between the two sample proportions. Because the confidence interval consists of negative values only, it appears that the proportion of blue eyes among females is less than the proportion of blue eyes among males. c. The professors used a convenience sample of their students. Convenience samples are typically problematic for making inferences about population parameters, but in this case there isn’t anything about eye color that would seem to make someone more or less likely to be a student in a statistics class, so the data do not appear to have the typical bias of a convenience sample. 21. a. H0: p1 = p2. H1: p1 6 p2. Test statistic: z = -1.17. P-value = 0.1214 (Table: 0.1210). Critical value: z = -2.33. Fail to reject H0. There is not sufficient evidence to support the claim that the rate of left-handedness among males is less than that among females. b. 98% CI: -0.0848 6 p1 - p2 6 0.0264 (Table: -0.0849 6 p1 - p2 6 0.0265). Because the confidence interval limits include 0, there does not appear to be a significant difference between the rate of left-handedness among males and the rate among females. There is not sufficient evidence to support the claim that the rate of left-handedness among males is less than that among females. c. The rate of left-handedness among males does not appear to be less than the rate of left-handedness among females. 23. The samples should include 4802 men and 4802 women. 25. a. 0.0227 6 p1 - p2 6 0.217; because the confidence interval limits do not contain 0, it appears that p1 = p2 can be rejected. b. 0.491 6 p1 6 0.629; 0.371 6 p2 6 0.509; because the confidence intervals do overlap, it appears that p1 = p2 cannot be rejected. c. H0: p1 = p2. H1: p1 ≠ p2. Test statistic: z = 2.40. P-value: 0.0164. Critical values: z = {1.96. Reject H0. There is sufficient evidence to reject p1 = p2. d. Reject p1 = p2. Least effective method: Using the overlap between the individual confidence intervals. 27. ANSUR I 1988: pn 1 = 1774>3982. ANSUR II 2012: pn 2 = 4082>6068. H0: p1 = p2. H1: p1 ≠ p2. Test statistic: z = -22.59. P-value: 0.0000 (Table: 0.0002). Critical values: z = {2.575. 99% CI: -0.253 6 p1-p2 6 -0.202. Reject H0. There is sufficient evidence to warrant rejection of the claim that the proportion of males in the sample in Data Set 1 “ANSUR I 1988” is the same as the proportion of males in the sample in Data Set 2 “ANSUR b. 98% CI: -0.266 6 p 6 -0.126. Because the confidence interval limits do not contain 0, there is a significant difference between the two proportions. Because the interval consists of negative numbers only, it appears that the claim is supported. The difference between the populations does appear to have practical significance. 11. a. H0: p1 = p2. H1: p1 7 p2. Test statistic: z = 6.44. P-value = 0.0000 (Table: 0.0001). Critical value: z = 2.33. Reject H0. There is sufficient evidence to support the claim that the proportion of people over 55 who dream in black and white is greater than the proportion of those under 25. b. 98% CI: 0.117 6 p1 - p2 6 0.240. Because the confidence interval limits do not include 0, it appears that the two proportions are not equal. Because the confidence interval limits include only positive values, it appears that the proportion of people over 55 who dream in black and white is greater than the proportion of those under 25. c. The results suggest that the proportion of people over 55 who dream in black and white is greater than the proportion of those under 25, but the results cannot be used to verify the cause of that difference. 13. a. H0: p1 = p2. H1: p1 7 p2. Test statistic: z = 6.11. P-value = 0.0000 (Table: 0.0001). Critical value: z = 1.645. Reject H0. There is sufficient evidence to support the claim that the fatality rate is higher for those not wearing seat belts. b. 90% CI: 0.00559 6 p1 - p2 6 0.0123. Because the confidence interval limits do not include 0, it appears that the two fatality rates are not equal. Because the confidence interval limits include only positive values, it appears that the fatality rate is higher for those not wearing seat belts. c. The results suggest that the use of seat belts is associated with fatality rates lower than those associated with not using seat belts. 15. a. H0: p1 = p2. H1: p1 ≠ p2. Test statistic: z = -4.41. P-value: 0.00001 (Table: 0.0002). Critical values: z = {1.96. Reject H0. There is sufficient evidence to reject the claim of no difference between the two rates of correct responses. It appears that the dogs do a better job of correctly identifying subjects without malaria. b. 95% CI: -0.284 6 p1-p2 6 -0.118. Because the confidence interval limits do not contain 0, there is a significant difference between the two sample proportions. Because the confidence interval consists of negative values only, it appears that the proportion of correct identifications made with subjects having malaria is less than the proportion of correct identifications made with subjects not having malaria. c. With correct identification rates of 70.3% and 90.3%, the dogs are doing quite well for subjects with malaria and subjects without malaria, but they do a much better job of correctly identifying patients without malaria. 17. a. H0: p1 = p2. H1: p1 ≠ p2. Test statistic: z = 7.11. P-value: 0.0000 (Table: 0.0002). Critical values: z = {1.96. Reject H0. There is sufficient evidence to warrant rejection of the claim that Connecticut and New York have the same proportion of cars with rear license plates only.
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