Telephone pollsters often interview between 1000 and 1500 individuals regarding their opinions on various 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 difference between the opinions of men and women on this issue
a) If 1000 men and 1000 women are to be interviewed, how accurately could you estimate the difference in the proportions who think that the performance of their atheltics teams has a positive impact on the perceived prestige of the institutions? Find a bound on the error of estimation
b) suppose that you were designing the survey and wished to estimate the difference in a pair of proportions , correct to within .02, probability .9. How many interviewees should be included in each sample?