In 2011 it was estimated that 45% of U.S. households purchased groceries at convenience stores and 29% purchased groceries at wholesale clubs. Consider a follow-up study focusing on the last calendar year.

a. What sample size is needed to estimate the population proportion of U.S. households purchasing groceries at convenience stores to within 0.02 with 95% confidence?
b. What sample size is needed to estimate the population proportion of U.S. households purchasing groceries at wholesale clubs to within 0.02 with 95% confidence?
c. Compare the results of (a) and (b). Explain why these results differ.