# Question: In Example 7 9 on page 294 we conducted a simulation

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.

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.

## Relevant Questions

For humans, gestation periods are normally distributed with a mean of 266 days and a standard deviation of 16 days. Suppose that you observe the gestation periods for a sample of nine humans. a. Use the technology of your ...The following graph shows the curve for a normally distributed variable. Superimposed are the curves for the sampling distributions of the sample mean for two different sample sizes. a. Explain why all three curves are ...a. What percentage of the waybills constituted the sample? b. What percentage error was made by using the sample to estimate the total revenue due C&O? c. At the time of the study, the cost of a census was approximately ...Information on serum total cholesterol level is published by the Centers for Disease Control and Prevention in National Health and Nutrition Examination Survey. A simple random sample of 12 U.S. females 20 years old or older ...As we mentioned earlier in this section, we stopped the t-table at df = 2000 and supplied the corresponding values of zα beneath. Explain why that makes sense.Post your question