When a random sample of 64 male students was asked their opinion on a proposal, 28 of them expressed support. Also, when a random sample of 85 female students was asked their opinion on the proposal. 31 of them expressed support.
(a) Use an appropriate hypothesis test to assess whether there is sufficient evidence to conclude that the support for the proposal is different for men and women.
(b) Construct a 99% two-sided confidence interval that illustrates the difference in support between men and women.