In the New York Times article "College Graduates Fare Well in Jobs Market, Even through Recession," C. Rampell noted that college graduates have suffered through the recession and lackluster recovery with remarkable resilience. Of a random sample of 1020 college graduates, 35 were unemployed; and of a random sample of 1008 high-school graduates (no college), 69 were unemployed.
a. At the 1% significance level, do the data provide sufficient evidence to conclude that college graduates have a lower unemployment rate than high-school graduates?
b. Find and interpret a 98% confidence interval for the difference in unemployment rates of college and high-school graduates.