In a recent research poll, 83.4% of 500 randomly selected men in the U. S. knew the name of our current vice president. When 500 randomly selected women in the U. S. were asked, 79% knew the vice president’s name.

(a) Construct and interpret a 95% confidence interval for the true difference in the proportion of U. S. men and the proportion of U. S. women who know the name of our current vice president.

(b) Based on this confidence interval, is there convincing evidence that the true proportion of men who know the name of the current vice president is different than the true proportion of women that know the name the current vice president? Explain.