Question: A study in the July 7, 2009, issue of USA TODAY stated that the 401(k) participation rate among U.S. employees of Asian heritage is 76%, whereas the participation rate among U.S. employees of Hispanic heritage is 66%. Suppose that these results were based on random samples of 100 U.S. employees from each group.
a. Construct a 95% confidence interval for the difference between the two population proportions.
b. Using the 5% significance level, can you conclude that the 401(k) participation rates are different for all U.S. employees of Asian heritage and all U.S. employees of Hispanic heritage? Use the critical-value and p-value approaches.
c. Repeat parts a and b for both sample sizes of 200 instead of 100. Does your conclusion change in part b?