APPENDIX D 785 19. The sample size is 192, which is practical. 21. Two-line wait times: 208.8 sec 6 s 6 283.0 sec (Table: 213.3 sec 6 s 6 291.3 sec.) Single-line wait times: 174.3 sec 6 s6236.3 sec (Table: 178.0 sec 6 s 6 243.2 sec.) Because the confidence intervals overlap, it is possible that the different line configurations have the same variation, so these results do not support the expectation that the single line has less variation. Requirements: The strict normality requirement is questionable for both data sets, especially the two-line wait times. 23. x2 L = 78.085 and x2 R = 134.756. The values from the given approximation are quite close to the actual critical values. Section 7-4 1. (1) The sample must be collected in an appropriate way, such as a simple random sample. (2) The sample means found from the generated bootstrap samples should have a distribution that is approximately symmetric. 3. There is no universal exact number, but there should be at least 1000 bootstrap samples, and the use of 10,000 or more is common. 5. 0.000 6 p 6 0.500 7. a. 0.1 kg 6 m 6 8.6 kg b. 1.9 kg 6 s 6 6.3 kg 9. Answers vary, but here are typical answers. a. -0.8 kg 6 m 6 7.8 kg b. 1.2 kg 6 s 6 7.0 kg 11. a. Answers vary, but here is a typical answer: 128.4 mm 6 m 6 139.3 mm. b. The confidence interval obtained from the bootstrap method is very close to this confidence interval from Exercise 13 in Section 7-2: 126.3 mm 6 m 6 141.2 mm. 13. a. Answers vary, but here is a typical answer: 11.9 minutes 6 m 6 34.3 minutes. b. The confidence interval given in part (a) is likely to be better. Given that the sample data do not appear to be from a normally distributed population, the use of the t distribution is questionable, so the confidence interval found in Exercise 15 in Section 7-2 might not be a good estimate of m. 15. a. Answers vary, but here is a typical answer: 1.5 in. 6 s 6 3.1 in. b. The confidence interval obtained from the bootstrap method is close to this confidence interval from Exercise 13 in Section 7-3: 1.9 in. 6 s 6 3.4 in. 17. a. Answers vary, but here is a typical answer: 1080.0 cm3 6 m 6 1169.0 cm3 b. Answers vary, but here is a typical answer: 79.0 cm3 6 s 6 152.8 cm3 19. Answers vary, but here is a typical result: 0.135 6 p 6 0.152. The result is essentially the same as the confidence interval of 0.135 6 p 6 0.152 found in Exercise 15 from Section 7-1. 21. Answers vary, but here is a typical result: 0.0208 6 p 6 0.0317. This is quite close to the confidence interval of 0.0205 6 p 6 0.0311 found in Exercise 14 from Section 7-1. 23. a. Answers vary, but here is a typical result: 2.5 6 s 6 3.3. b. 2.4 6 s 6 3.7 mercury in fish because it is possible that the mean is greater than 1 ppm. Also, one of the sample values exceeds the FDA guideline of 1 ppm, so at least some of the fish have too much mercury. 21. The sample size is 97, and it does appear to be very practical. 23. 925 (Table: 927). The sample should not be obtained from one movie at one theater, because that sample could be easily biased. Instead, a simple random sample of the broader population should be obtained. 25. a. 425 b. 212 c. The result from part (a) is substantially larger than the result from part (b). The result from part (b) is likely to be better because it uses s instead of the estimated s obtained from the range rule of thumb. 27. The required sample size is 38,415 (Table: 38,416). The sample appears to be too large to be practical for a telephone survey. 29. Females: 72.0 bpm 6 m 6 76.1 bpm. Males: 67.8 bpm 6 m 6 71.4 bpm. Adult females appear to have a mean pulse rate that is higher than the mean pulse rate of adult males. Good to know. 31. 41.0 minutes 6 m 6 44.3 minutes (TI data: 40.0 minutes 6 m 6 44.9 minutes) 33. Using the class limits of 66-75 for the “over 65” group, the summary statistics are n = 195, x = 40.1 years, s = 11.3 years. CI: 38.5 years 6 m 6 41.7 years. Section 7-3 1. a. Unlike confidence interval estimates of p or m, confidence interval estimates of s or s 2 are not created using a distribution that is symmetric, so there is no “{E” as in confidence interval estimates of p or m. b. The format of 10.9 bpm{3.3 bpm implies that s = 10.9 bpm, which is not the case. Because the chi-square distribution is not symmetric, confidence interval estimates of s or s 2 cannot be expressed in the format of s { E. 3. 0.130 1million cells>mL2 2 6 s 2 6 0.206 1million cells>mL2 2 5. df = 24. x2 L = 12.401 and x2 R = 39.364. CI: 0.19 mg 6 s 6 0.33 mg. 7. df = 146. x2 L = 105.741 (Table: 67.328) and x2 R = 193.761 (Table: 140.169). CI: 1.70 11000 cells>mL2 6 s 6 2.30 11000 cells>mL2. [Table: 2.00 11000 cells>mL2 6 s 6 2.89 11000 cells>mL2.] 9. 0.55°F 6 s 6 0.72°F (Table: 0.56°F 6 s 6 0.74°F) 11. 29.6 min 6 s 6 71.6 min. No, the confidence interval does not indicate whether the treatment is effective. 13. 1.9 in. 6 s 6 3.4 in. Because the confidence interval includes the value of 2.9 in., it is very possible that the standard deviation of heights of women who are professional soccer players is the same as the standard deviation of heights of women in the general population. There is not sufficient evidence to support the claim that women who are professional soccer players have heights that vary less than women in the general population. 15. Female: 0.50 6 s 6 1.32. Male: 0.24 6 s 6 0.64. Because the two confidence intervals overlap, it is possible that females and males have the same amount of variation, so there does not appear to be a significant difference in variation. 17. The sample size is 85, which is very practical.
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