In Example 7.9 on page 294, we conducted a simulation to check the plausibility of the central limit theorem. The variable under consideration there is household size, and the population consists of all U.S. households. A frequency distribution for household size of U.S. households is presented in Table 7.7.
a. Suppose that you simulate 1000 samples of four households each, determine the sample mean of each of the 1000 samples, and obtain a histogram of the 1000 sample means. Would you expect the histogram to be bell shaped? Explain your answer.
b. Carry out the tasks in part (a) and note the shape of the histogram.
c. Repeat parts (a) and (b) for samples of size 10.
d. Repeat parts (a) and (b) for samples of size 100.