The article “Students Increasingly Turn to Credit Cards” (San Luis Obispo Tribune, July 21, 2006) reported that 37% of college freshmen and 48% of college seniors carry a credit card balance from month to month. Suppose that the reported percentages were based on random samples of 1000 college freshmen and 1000 college seniors.
a. Construct a 90% confidence interval for the proportion of college freshmen who carry a credit card balance from month to month.
b. Construct a 90% confidence interval for the proportion of college seniors who carry a credit card balance from month to month.
c. Explain why the two 90% confidence intervals from Parts (a) and (b) are not the same width.