According to the U.S. Census Bureau, 43% of men who worked at home were college graduates. In a sample of 500 women who worked at home, 162 were college graduates.

a. Find a point estimate for the proportion of college graduates among women who work at home.

b. Construct a 98% confidence interval for the proportion of women who work at home who are college graduates.

c. Based on the confidence interval, is it reasonable to believe that the proportion of college graduates among women who work at home is the same as the proportion of college graduates among men who work at home? Explain.