282 CHAPTER 6 Normal Probability Distributions 9. Sampling Distribution of the Sample Median a. Find the value of the population median. b. Table 6-2 describes the sampling distribution of the sample mean. Construct a similar table representing the sampling distribution of the sample median. Then combine values of the median that are the same, as in Table 6-3. (Hint: See Example 2 on page 276 for Tables 6-2 and 6-3, which describe the sampling distribution of the sample mean.) c. Find the mean of the sampling distribution of the sample median. d. Based on the preceding results, is the sample median an unbiased estimator of the population median? Why or why not? 10. Sampling Distribution of the Sample Proportion a. For the population, find the proportion of odd numbers. b. Table 6-2 describes the sampling distribution of the sample mean. Construct a similar table representing the sampling distribution of the sample proportion of odd numbers. Then combine values of the sample proportion that are the same, as in Table 6-3. (Hint: See Example 2 on page 276 for Tables 6-2 and 6-3, which describe the sampling distribution of the sample mean.) c. Find the mean of the sampling distribution of the sample proportion of odd numbers. d. Based on the preceding results, is the sample proportion an unbiased estimator of the population proportion? Why or why not? In Exercises 11–14, use the population of {2, 3, 5, 9} of the lengths of hospital stay (days) of mothers who gave birth, found from Data Set 6 “Births” in Appendix B. Assume that random samples of size n = 2 are selected with replacement. 11. Sampling Distribution of the Sample Mean a. After identifying the 16 different possible samples, find the mean of each sample, and then construct a table representing the sampling distribution of the sample mean. In the table, combine values of the sample mean that are the same. (Hint: See Table 6-3 in Example 2 on page 276.) b. Compare the mean of the population {2, 3, 5, 9} to the mean of the sampling distribution of the sample mean. c. Do the sample means target the value of the population mean? In general, do sample means make good estimators of population means? Why or why not? 12. Sampling Distribution of the Median Repeat Exercise 11 using medians instead of means. 13. Sampling Distribution of the Range Repeat Exercise 11 using ranges instead of means. 14. Sampling Distribution of the Variance Repeat Exercise 11 using variances instead of means. 15. Births: Sampling Distribution of Sample Proportion When two births are randomly selected, the sample space for genders is bb, bg, gb, and gg (where b = boy and g = girl). Assume that those four outcomes are equally likely. Construct a table that describes the sampling distribution of the sample proportion of girls from two births. Does the mean of the sample proportions equal the proportion of girls in two births? Does the result suggest that a sample proportion is an unbiased estimator of a population proportion? 16. Births: Sampling Distribution of Sample Proportion Repeat Exercise 15 using three births instead of two births. 17. MCAT The Medical College Admissions Test (MCAT) is used to help screen applicants to medical schools. Like many such tests, the MCAT uses multiple-choice questions with each
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