5. Telephone pollsters often interview between 1000 and 1500 individuals regarding their opinions on var- ious issues. Does the performance of colleges' athletic teams have a positive impact on the public's perception of the prestige of the institutions? A new survey is to be undertaken to see if there is a dif- ference between the opinions of men and women on this issue. In this poll, the pollsters asked 1000 men and 900 women this very question. A total of 880 men replied yes to the question compared to 568 women. (a) (5 pts) Construct a 95% confidence interval for pi - p2, the difference in the proportion of men and women who think that the performance of a colleges' athletic team will have a positive impact on the public's perception of the prestige of the institution. (b) (5 pts) Suppose that you were designing the survey and wished to estimate the difference in a pair of proportions and desired your margin of error to be within 102, with a confidence limit of 90%. How many interviewees should be included in each sample? Assume from a previous survey that pi = 8 and pz = 68. (c) (5 pts) Suppose that you were designing the survey and wished to estimate the difference in a pair of proportions and desired your margin of error to be within .02, with a confidence limit of 90%. How many interviewees should be included in each sample? In this case assume you do not know the values for p1 and pz