796 APPENDIX D 8. Because the confidence interval includes the value of 0°F, it appears that there is not a significant difference between the temperatures at 8 AM and the temperatures at 12 AM. 9. True 10. False Chapter 9: Review Exercises 1. H0: p1 = p2. H1: p1 6 p2. Test statistic: z = -3.49. P-value: 0.0002. Critical value: z = -1.645. Reject H0. There is sufficient evidence to support the claim that money in a large denomination is less likely to be spent relative to an equivalent amount in smaller denominations. 2. 90% CI: -0.528 6 p1 - p2 6 -0.206. The confidence interval limits do not contain 0, so it appears that there is a significant difference between the two proportions. Because the confidence interval consists of negative values only, it appears that p1 is less than p2, so it appears that money in a large denomination is less likely to be spent relative to an equivalent amount in smaller denominations. 3. H0: md = 0°F. H1: md ≠ 0°F. Test statistic: t = -0.262. P@value = 0.7995 (Table: P@value 7 0.10). Critical values: t = {2.262. Fail to reject H0. There is not sufficient evidence to warrant rejection of the claim that differences between actual temperatures and temperatures forecast five days earlier are from a population with a mean of 0°F. There does not appear to be a difference between actual temperatures and temperatures forecast five days earlier. 4. 95% CI: -3.9°F 6 md 6 3.1°F. Because the confidence interval includes 0°F, fail to reject H0. There is not sufficient evidence to warrant rejection of the claim that differences between actual temperatures and temperatures forecast five days earlier are from a population with a mean of 0°F. There does not appear to be a difference between actual temperatures and temperatures forecast five days earlier. It appears that weather forecasters are doing a good job. 5. a. H0:p1 = p2. H1:p1 7 p2. Test statistic: z = 2.64. P-value: 0.0041. Critical value: z = 2.33. Reject H0. There is sufficient evidence to support the claim that the rate of success for smoking cessation is greater with the sustained care program. 6. a. 98% CI: 0.0135 6 p1 - p2 60.200 (Table: 0.0134 6 p 6 0.200). Because the confidence interval limits do not contain 0, there is a significant difference between the two proportions. Because the interval consists of positive numbers only, it appears that the success rate for the sustained care program is greater than the success rate for the standard care program. b. Based on the samples, the success rates of the programs are 25.8% (sustained care) and 15.1% (standard care). That difference does appear to be substantial, so the difference between the programs does appear to have practical significance. c. The more successful of the two programs has a success rate of only 25.8%, so there is a failure rate of about 74% for those who try to stop smoking with the sustained care program. The time required and cost of the sustained program relative to standard care must be considered when determining practical significance. If sustained care is much more time consuming and expensive, the practical significance will be lower. b. Bootstrapping: Results vary but this is typical: 98% CI: 0.02844 lb 6 m1 - m2 6 0.03773 lb. Because the confidence interval does not include 0, it appears that there is a significant difference between the two sample means. 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. 13. a. Randomization: Typical result: With 1000 resamples, 336 of the values of d are 0.37 lb or greater, so the value of d = 0.37 lb can easily occur by chance. There is not sufficient evidence to support the claim that for females, the measured weights tend to be higher than the reported weights. b. Bootstrapping: Typical result: 90% CI: -1.02 lb 6 md 6 1.78 lb. Because the confidence interval does include 0, there is not sufficient evidence to support the claim that for females, the measured weights tend to be higher than the reported weights. 15. a. Randomization: Typical result: With 1000 resamples, 5 of the values of d are -0.889 kg or less, so the value of d = -0.889 kg is very unlikely to occur by chance. 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. Bootstrapping: Typical result: 98% CI: -1.3 kg 6 md 6 -0.4 kg. Because the confidence interval does not include 0 and consists of negative values only, 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. 17. Typical result from 1000 resamples: 95% CI: 0.02909 lb 6 m1 - m2 6 0.03478 lb. Typical result from 10,000 resamples: 0.02908 lb 6 m1 - m2 6 0.03474 lb. The differences are very small, so the larger number of resamples does not have much of an effect on the results. Chapter 9: Quick Quiz 1. H0: p1 = p2. H1: p1 ≠ p2. 2. pn 1 = 102>288 = 0.354, p n 2 = 75>277 = 0.271, p = 0.313 3. a. 0.0324 b. Reject H0 and conclude that there is sufficient evidence to warrant rejection of the claim that patients treated with dexamethasone and patients given a placebo have the same rate of complete resolution. It appears that the rates of complete resolution are different. 4. a. 95% CI: 0.00732 6 p1 - p2 6 0.159 b. The confidence interval does not include 0, so it appears that the two proportions are not equal. There appears to be a significant difference between the success rate in the treatment group and the success rate in the placebo group. 5. a. The two samples are independent because they are not matched or paired in any way. b. t = 22.092 (or 22.095 if using original data) 6. F = 2.9265 (or 2.9233 if using original data) 7. a. Because each pair of data is matched by the same subject, the two sets of data are dependent. b. H0: md = 0°F. H1: md ≠ 0°F.
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