784 APPENDIX D 29. pn = 19>35, or 0.543. CI: 37.8% 6 p 6 70.8%. Greater height does not appear to be an advantage for presidential candidates. If greater height is an advantage, then taller candidates should win substantially more than 50% of the elections, but the confidence interval shows that the percentage of elections won by taller candidates is likely to be anywhere between 37.8% and 70.8%. 31. a. 1844 (Table: 1842) b. 1266 (Table: 1265) 33. a. 4269 b. 609 c. Yes, there is a substantial decrease in the sample size. 35. a. 1537 b. 1449 37. a. 752 b. 295 c. No. A sample of the people you know is a convenience sample, not a simple random sample, so it is very possible that the results would not be representative of the population. 39. 1238 (Table: 1237) 41. a. The requirement of at least 5 successes and at least 5 failures is not satisfied, so the normal distribution cannot be used. b. 6.67% Section 7-2 1. a. 85.74 min 6 m 6 91.76 min b. The best point estimate is x = 88.75 minutes. The margin of error is E = 3.01 minutes. 3. We have 95% confidence that the limits of 85.74 minutes and 91.76 minutes contain the true value of the mean of the population of all times between eruptions. 5. a. ta>2 = 2.030 b. E = 235.3 g c. 2914.7 g 6 m 6 3385.3 g d. We have 95% confidence that the limits of 2914.7 g and 3385.3 g contain the true value of the mean birth weight of all girls. 7. a. ta>2 = 2.724 b. E = 0.00259 lb c. 0.82151 lb 6 m 6 0.82669 lb d. We have 99% confidence that the limits of 0.82151 lb and 0.82669 lb contain the true value of the mean weight of Pepsi in cans. 9. 98.08°F 6 m 6 98.32°F. Because the confidence interval does not contain 98.6°F, it appears that the mean body temperature is not 98.6°F, as is commonly believed. 11. 71.4 min 6 m 6 126.4 min. The confidence interval includes the mean of 102.8 min that was measured before the treatment, so the mean could be the same after the treatment. This result suggests that the zopiclone treatment does not have a significant effect. 13. 126.3 mm 6 m 6 141.2 mm 15. 9.2 minutes 6 m 6 35.8 minutes. Five of the listed values are 5, so the data do not appear to be from a normally distributed population. Also, the sample size is not greater than 30, so the requirement of a “normal distribution or n 7 30” is not satisfied. It is very possible that the confidence interval is not a good estimate of the population mean. 17. 1.8 6 m 6 3.4. The given numbers are just substitutes for the four DNA base names, so the numbers don’t measure or count anything, and they are at the nominal level of measurement. The confidence interval has no practical use. 19. 0.284 ppm 6 m 6 1.153 ppm. Using the FDA guideline, the confidence interval suggests that there could be too much c. If the value of 980°F is discarded as an error, the mean appears to be 98.61°F. It is also reasonable to believe that the value of 980°F was incorrectly entered without the decimal point, and if 980°F is changed to 98.0°F, the mean appears to be 98.54°F. Chapter 7 Answers Section 7-1 1. The confidence level, such as 95%, was not provided. 3. pn = 0.51 is the sample proportion; qn = 0.49 (found from evaluating 1 - pn); n = 1144 is the sample size; E = 0.035 is the margin of error; p is the population proportion, which is unknown. The value of a is 0.05. 5. 1.645 7. 2.81 9. 0.154 { 0.038 11. 0.0847 6 p 6 0.153 13. a. 0.367 b. E = 0.0610 c. 0.306 6 p 6 0.428 d. We have 95% confidence that the interval from 0.306 to 0.428 contains the true value of the population proportion of successful challenges. 15. a. pn = 0.143 b. E = 0.00815 c. 0.135 6 p 6 0.152 d. We have 90% confidence that the interval from 0.135 to 0.152 actually does contain the true value of the population proportion of returned surveys. 17. 0.462 6 p 6 0.529. Because 0.512 is contained within the confidence interval, there is not strong evidence against 0.512 as the value of the proportion of boys in all births. 19. a. 14.7% 6 p 6 33.5% b. Because the two confidence intervals overlap, it is very possible that both genders have the same success rates. Neither gender appears to be substantially more successful in their challenges. 21. a. 0.5 b. 0.439 c. 0.363 6 p 6 0.516 d. If the touch therapists really had an ability to select the correct hand by sensing an energy field, their success rate would be significantly greater than 0.5, but the sample success rate of 0.439 and the confidence interval suggest that they do not have the ability to select the correct hand by sensing an energy field. 23. a. 236 b. 0.402 6 p 6 0.516 (Using x = 236: 0.403 6 p 6 0.516) c. 0.431 6 p 6 0.487 d. The 99% confidence interval is wider than the 80% confidence interval. A confidence interval must be wider in order to be more confident that it captures the true value of the population proportion. 25. 95% CI: 0.0419 6 p 6 0.0421. 99% CI: 0.0418 6 p 6 0.0422. For both confidence levels, the upper and lower confidence interval limits are very close to each other, suggesting that the estimates are very accurate. Also, there is not much difference between the 95% CI and the 99% CI. The extremely large sample size is giving us confidence interval estimates with a very narrow range, so we are getting very precise estimates. 27. Sustained care: 77.6% 6 p 6 88.1% (using x = 164). Standard care: 56.1% 6 p 6 69.5% (using x = 125). The two confidence intervals do not overlap. It appears that the success rate is higher with sustained care.
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