A sample of 500 male registered voters showed that 57% of them voted in the last presidential election. Another sample of 400 female registered voters showed that 55% of them voted in the same election.
a. Construct a 97% confidence interval for the difference between the proportions of all male and all female registered voters who voted in the last presidential election.
b. Test at a 1% significance level whether the proportion of all male voters who voted in the last presidential election is different from that of all female voters.