The Bureau of Labor Statistics report referenced in the previous exercise also indicated that 7.3% of high school graduates were unemployed in October 2013 and 5.7% of high school graduates were unemployed in October 2014. Suppose that the reported percentages were based on independently selected representative samples of 400 high school graduates in each of these two years.

a. Construct and interpret a 99% confidence interval for the difference in the proportion of high school graduates who were unemployed in these two years.

b. Is the confidence interval from Part (a) wider or narrower than the confidence interval calculated in the previous exercise? What are two reasons why it is wider or narrower?