In a recent research poll, 83.4% of 500 randomly selected men in the U.S. were able to state the name of our current vice president. When 500 randomly selected women in the U.S. were asked, 79% were able to do so. (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 can state the name of our current vice president. (b) Explain, in the context of this problem, what is meant by "95% confidence." (c) Based on this confidence interval, is there convincing evidence that the true proportion of men who can name the current vice president is different than the true proportion of women that can name the current vice president? Explain.