ODD ANSWERS A69 49. (a) 66 servings (b) No.Yes. The 95% CI is (28.252, 29.748). If the population mean is within 3% of the sample mean, then it falls outside the CI. If the population mean is within 0.3% of the sample mean, then it falls within the CI. 51. (a) 7 cans (b) Yes. The 90% CI is (127.3, 128.2) and 128 ounces falls within that interval. 53. (a) 74 balls (b) Yes. The 99% CI is (27.360, 27.640) and there are amounts less than 27.6 inches that fall within that interval. 55. Sample answer: A 99% CI may not be practical to use in all situations. It may produce a CI so wide that it has no practical application. 57. (a) 0.707 (b) 0.949 (c) 0.962 (d) 0.975 (e) 0.711 (f) 0.937 (g) 0.964 (h) 0.979 The finite population correction factor approaches 1 as the sample size decreases and the population size remains the same. The finite population correction factor approaches 1 as the population size increases and the sample size remains the same. 59. Sample answer: E = zc s2 n Write the original equation. E2n = zc s Multiply each side by 2n. 2n = zc s E Divide each side by E. n = a zc s E b 2 Square each side. Section 6.2 (page 315) 1. The mean, median, and mode are all equal to 0. The distribution is bell-shaped and symmetric about the mean. The total area under the curve is equal to 1. 3. 1.833 5. 2.947 7. 2.664 9. (10.9, 14.1) 11. (4.1, 4.5) 13. E = 3.7, x = 18.4 15. t = 3.10 17. 6.0; (29.5, 41.5). With 95% confidence, you can say that the population mean commute time is between 29.5 and 41.5 minutes. 19. 153.83; (372.67, 680.33). With 95% confidence, you can say that the population mean cell phone price is between $372.67 and $680.33. 21. 6.4; (29.1, 41.9). With 95% confidence, you can say that the population mean commute time is between 29.1 and 41.9 minutes. This confidence interval is slightly wider than the one found in Exercise 17. 23. Yes 25. (a) 1185 (b) 168.1 (c) (1034.3, 1335.7) 27. (a) 7.49 (b) 1.64 (c) (6.28, 8.70) 29. Yes 31. (a) 68,757.94 (b) 15,834.18 (c) (61,892.21, 75,623.67) 33. Yes 35. Use a t-distribution because s is unknown and n Ú 30. (26.0, 29.4). With 95% confidence, you can say that the population mean BMI is between 26.0 and 29.4. 37. Use standard normal distribution because s is known and the weights are known to be normally distributed. (12.14, 15.22). With 95% confidence, you can say that the population mean weight of two-year-old males is between 12.14 pounds and 15.22 pounds. 39. Neither distribution can be used because n 6 30 and the mileages are not normally distributed. 41. No. They are not making good tennis balls because the t@value for the sample is t = 10, which is not between -t0.99 = -2.797 and t0.99 = 2.797. Section 6.2 Activity (page 318) 1 – 2. Answers will vary. Section 6.3 (page 325) 1. True 3. 0.060, 0.940 5. 0.330, 0.670 7. E = 0.014, np = 0.919 9. E = 0.042, np = 0.554 11. (0.723, 0.757); (0.720, 0.761) With 90% confidence, you can say that the population proportion of U.S. adults who say they have made a New Year’s resolution is between 72.3% and 75.7%. With 95% confidence, you can say it is between 72.0% and 76.1%. The 95% confidence interval is slightly wider. 13. (0.321, 0.399) With 99% confidence, we can say that the population proportion of U.S. adults who say they worry a great deal about the possibility of a future terrorist attack is between 32.1% and 39.9%. 15. (0.052, 0.060) 17. (a) 601 adults (b) 399 adults (c) Having an estimate of the population proportion reduces the minimum sample size needed. 19. (a) 752 families (b) 425 families (c) Having an estimate of the population proportion reduces the minimum sample size needed. 21. No. It falls within both confidence intervals. 23. Yes. The minimum sample size needed is 399 adults. 25. France: (0.283, 0.357) Germany: (0.215, 0.285) United Kingdom: (0.272, 0.348) United States: (0.311, 0.389) 27. Cyberterrorism: (0.796, 0.844) Development of nuclear weapons by Iran: (0.723, 0.777) The spread of infectious diseases throughout the world: (0.692, 0.748) Global warming or climate change: (0.550, 0.610) The military power of Russia: (0.410, 0.470) The conflict between the Israelis and the Palestinians: (0.291, 0.349) 29. (0.281, 0.339) is approximately a 98.5% CI. 31. (0.68, 0.74) is approximately a 96.3% CI. 33. (0.534, 0.606) is approximately a 99.9% CI. 35. If nnp 6 5 or nnq 6 5, the sampling distribution of np may not be normally distributed, so zc cannot be used to calculate the confidence interval.
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