APPENDIX D 781 b. The mean of the population is 4.75 and the mean of the sample means is also 4.75. c. The sample means target the population mean. Sample means make good estimators of population means because they target the value of the population mean instead of systematically underestimating or overestimating it. 13. a. 33. a. 0.0038; either a very rare event occurred or the husband is not the father. b. 240 days 35. 97.41% (Table: 97.38%). The design is feasible if the loss of 2.59% (Table: 2.62%) of adult drivers is acceptable. 37. a. 75; 12 b. No, the conversion should also account for variation. c. B grade: 66.3 to 75.4 (Table: 66.2 to 75.4) d. Use a scheme like the one given in part (c), because variation is included in the curving process. Section 6-3 1. a. In the long run, the sample proportions will have a mean of 0.00559. b. The sample proportions will tend to have a distribution that is approximately normal. 3. Sample mean; sample variance; sample proportion 5. No. The sample is not a simple random sample from the population of all college students in the United States. It is very possible that incomes of college students in Maine differ substantially from the incomes of college students in the other states. 7. a. 4.7 b. Sample Variance s2 Probability 0.0 3>9 0.5 2>9 8.0 2>9 12.5 2>9 c. 4.7 d. Yes. The mean of the sampling distribution of the sample variances (4.7) is equal to the value of the population variance (4.7), so the sample variances target the value of the population variance. 9. a. 5 b. Sample Median Probability 4.0 1>9 4.5 2>9 5.0 1>9 6.5 2>9 7.0 2>9 9.0 1>9 c. 6.0 d. No. The mean of the sampling distribution of the sample medians is 6.0, and it is not equal to the value of the population median (5.0), so the sample medians do not target the value of the population median. 11. a. x Probability 2 1>16 2.5 2>16 3 1>16 3.5 2>16 4 2>16 5 1>16 5.5 2>16 6 2>16 7 2>16 9 1>16 Range Probability 0 4>16 1 2>16 2 2>16 3 2>16 4 2>16 6 2>16 7 2>16 b. The range of the population is 7.0, but the mean of the sample ranges is 2.875. Those values are not equal. c. The sample ranges do not target the population range of 7.0, so sample ranges do not make good estimators of population ranges. 15. Proportion of Girls Probability 0 0.25 0.5 0.50 1 0.25 Yes. The proportion of girls in 2 births is 0.5, and the mean of the sample proportions is 0.5. The result suggests that a sample proportion is an unbiased estimator of a population proportion. 17. a. Proportion Correct Probability 0 16>25 0.5 8>25 1 1>25 b. 0.2 c. Yes. The sampling distribution of the sample proportions has a mean of 0.2 and the population proportion is also 0.2 (because there is 1 correct answer among 5 choices). Yes, the mean of the sampling distribution of the sample proportions is always equal to the population proportion.
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