In a Pew Research poll, 287 out of 522 randomly selected U.S. men were able to identify Egypt when it was highlighted on a map of the Middle East. When 520 randomly selected U.S. women were asked, 233 were able to do so.

a. Construct and interpret a 95% confidence interval for the difference in the true proportion of U.S. men and U.S. women who can identify Egypt on a map.

b. Based on your interval, is there convincing evidence of a difference in the true proportions of U.S. men and women who can identify Egypt on a map? Justify your answer.