The American Community Survey collects information about the population in every U.S. county. The average household size in twenty samples of fifty randomly selected counties is shown in Table 7.2.

a. An incredulous observer doubts that these county means are correct. After all, he knows of many households that have more than five people, including his own, which has eight people. Explain to him how it is possible that his own observations of household size can be so different from the county means shown in Table 7.2.

b. If you arranged all of the sample means from Table 7.2 in a distribution, what kind of distribution would it be?

c. Because we have data for all counties in the United States, we know that the mean household size for all counties is 2.53. What proportion of the twenty samples in Table 7.2 fall below the population mean? What proportion of sample means fall above?

d. Based on what you know about normal curves, what proportion of sample means would you have expected to fall above the population mean? What proportion would you have expected to fall below it? Are the proportions in Part c different from what you would expect to find? Explain why or why not.