A national survey of 47,000 American households in 2006 found that 32.4% of the households included a pet cat. Th is survey result was reported in the 2011 Statistical Abstract of the United States, which listed the American Veterinary Medical Association as the source. No information was provided about how the sample households were selected.
a. Conduct a theory-based test of whether one-third of all American households include a pet cat. Report the null and alternative hypotheses and the values of the z-statistic and p-value. Also state your test decision using the 0.01 significance level.
b. Explain why the p-value turned out to be so small even though the observed sample proportion appears to be quite close to 1/3.
c. Determine a 99% confidence interval for the population proportion of American households that include a pet cat.
d. Is the confidence interval consistent with the significance test result? How can you tell?
e. Does the confidence interval indicate that the population proportion is much different from 1/3? Explain.