Anational survey of 47,000 american house- holds in 2006 found that 32.4% of the households included a pet cat. this survey result was reported in the 2011 statis- tical 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 hvpotheses and the values of the z-statistic and p-value. also state your test decision using the 0.01 signiicance 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 vou tell?

e. does the confidence interval indicate that the population proportion is much different from 1/3? explain.