In Exercises, use the same population of {4, 5, 9} that was used in Examples 1 and 2. As in Examples 1 and 2, assume that samples of size n=2 are randomly selected with replacement. Sampling...

In Exercises, use the same population of {4, 5, 9} that was used in Examples 1 and 2. As in Examples 1 and 2, assume that samples of size n=2 are randomly selected with replacement.

Sampling Distribution of the Sample Median

a. Find the value of the population median.

b. Table 6-3 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 6-4. (Hint: See Example 1 for Tables 6-3 and 6-4 that 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?

Example 1 Sampling Distribution of the Sample Mean