A70 ODD ANSWERS 37. np nq = 1 − np npnq 0.0 1.0 0.00 0.1 0.9 0.09 0.2 0.8 0.16 0.3 0.7 0.21 0.4 0.6 0.24 0.5 0.5 0.25 0.6 0.4 0.24 0.7 0.3 0.21 0.8 0.2 0.16 0.9 0.1 0.09 1.0 0.0 0.00 np nq = 1 − np npnq 0.45 0.55 0.2475 0.46 0.54 0.2484 0.47 0.53 0.2491 0.48 0.52 0.2496 0.49 0.51 0.2499 0.50 0.50 0.2500 0.51 0.49 0.2499 0.52 0.48 0.2496 0.53 0.47 0.2491 0.54 0.46 0.2484 0.55 0.45 0.2475 np = 0.5 gives the maximum value of npnq. Section 6.3 Activity (page 329) 1 – 2. Answers will vary. Section 6.4 (page 334) 1. Yes 3. x2 R = 14.067, x 2 L = 2.167 5. x2 R = 32.852, x 2 L = 8.907 7. x2 R = 52.336, x 2 L = 13.121 9. (a) (7.33, 20.89) (b) (2.71, 4.57) 11. (a) (755, 2401) (b) (27, 49) 13. (a) (0.0426, 0.1699) (b) (0.2063, 0.4122) With 95% confidence, you can say that the population variance is between 0.0426 and 0.1699, and the population standard deviation is between 0.2063 and 0.4122 inch. 15. (a) (52.41, 281.98) (b) (7.24, 16.79) With 99% confidence, you can say that the population variance is between 52.41 and 281.98, and the population standard deviation is between 7.24 and 16.79 thousand dollars. 17. (a) (5.46, 45.70) (b) (2.34, 6.76) With 99% confidence, you can say that the population variance is between 5.46 and 45.70, and the population standard deviation is between 2.34 and 6.76 days. 19. (a) (128, 492) (b) (11, 22) With 95% confidence, you can say that the population variance is between 128 and 492, and the population standard deviation is between 11 and 22 grains per gallon. 21. (a) (0.04, 0.11) (b) (0.21, 0.32) With 80% confidence, you can say that the population variance is between 0.04 and 0.11, and the population standard deviation is between 0.21 and 0.32 day. 23. (a) (1809.40, 6597.92) (b) (42.54, 81.23) With 98% confidence, you can say that the population variance is between 1809.40 and 6597.92, and the population standard deviation is between 42.54 and 81.23 seconds. 25. Yes, because all of the values in the confidence interval are less than 0.5. 27. No, because 0.25 is contained in the confidence interval. 29. Sample answer: Unlike a confidence interval for a population mean or proportion, a confidence interval for a population variance does not have a margin of error. The left and right endpoints must be calculated separately. Uses and Abuses for Chapter 6 (page 336) 1 – 2. Answers will vary. 3. (a) No (b) Yes Review Exercises for Chapter 6 (page 338) 1. (a) 103.5 (b) 11.7 3. (a) (91.8, 115.2). With 90% confidence, you can say that the population mean waking time is between 91.8 and 115.2 minutes past 5:00 a.m. (b) Yes. If the population mean is within 10% of the sample mean, then it falls inside the confidence interval. 5. E = 1.675, x = 22.425 7. 78 people 9. 1.383 11. 2.624 13. (a) 11.2 (b) (60.9, 83.3) 15. (a) 0.7 (b) (6.1, 7.5) 17. (146, 184). With 90% confidence, you can say that the population mean height is between 146 and 184 feet. 19. (a) 0.420, 0.580 (b) (0.393, 0.447); (0.388, 0.452) (c) The 95% interval is slightly wider. 21. (a) 0.325, 0.675 (b) (0.322, 0.327); (0.321, 0.328) (c) The 95% interval is slightly wider. 23. Yes. It would be unusual because it is outside both confidence intervals. 25. (a) 385 adults (b) 335 adults (c) Having an estimate of the population proportion reduces the minimum sample size needed. 27. x2 R = 23.337, x 2 L = 4.404 29. x 2 R = 24.996, x 2 L = 7.261 31. (a) (13.28, 70.38) (b) (3.64, 8.39) With 95% confidence, you can say that the population variance is between 13.28 and 70.38, and the population standard deviation is between 3.64 and 8.39. Quiz for Chapter 6 (page 340) 1. (a) 2.46 (b) 0.030 (c) (2.43, 2.49). With 95% confidence, you can say that the population mean winning time is between 2.439 and 2.499 hours. (d) No. It falls outside the confidence interval. 2. 28 champions 3. (a) x = 6.61, s ≈ 3.38 (b) (4.65, 8.57). With 90% confidence, you can say that the population mean amount of time is between 4.65 and 8.57 minutes. (c) (4.79, 8.43). With 90% confidence, you can say that the population mean amount of time is between 4.79 and 8.43 minutes. This confidence interval is narrower than the one in part (b). 4. (109,990, 156,662). With 95% confidence, you can say that the population mean annual earnings is between $109,990 and $156,662. 5. Yes
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