In a recent Pew Research poll, 287 out of 522 randomly selected men in the U. S. were able to identify Egypt when it was highlighted on a map of the Middle East. When 520 randomly selected women were asked, 233 were able to do so. (a) Construct and interpret a 95% confidence interval for the difference in the proportion of U. S. men and the proportion of U. S. women who can identify Egypt on a map. (b) Explain, in the context of this problem, what is meant by "95% confidence." (c) Based on this confidence interval, would we reject the hypothesis that there is no difference in these two proportions against a two-sided alternative at the α = 0.05 level? Justify your answer.