To establish a comparison of customer satisfaction levels, the National Association of Auto Dealers has taken a sample of 200 recent buyers of an American made car, and 200 recent buyers of a Japanese made auto. 120 of the American car buyers and 142 of the Japanese car buyers expressed a “very high level of satisfaction” with their purchases.
a. Construct the 90% confidence interval estimate of the difference in the population proportion of American vs. Japanese car buyers who would express this level of satisfaction.
b. Suppose organizers of the study want the 90% interval to have a margin of error no larger than .04. Assuming sample sizes will be equal, how large a sample from each of these populations would you recommend? Use the results from the original samples of size 200 as “pilot” study results.
c. Suppose you had no prior sample information. Reconsider your sample size recommendation in part b and recalculate the appropriate sample sizes.