Choosing sample sizes, continued. As the previous exercise noted, using the guessed value 0.5 for both p1 and p2 gives a conservative margin of error

Choosing sample sizes, continued. As the previous exercise noted, using the guessed value 0.5 for both ˆp1 and ˆp2 gives a conservative margin of error in confidence intervals for the difference between two population proportions. You are planning a survey and will calculate a 95% confidence interval for the difference in two proportions when the data are collected. You would like the margin of error of the interval to be less than or equal to 0.04. You will use the same sample size n for both populations.

(a) How large a value of n is needed?

(b) Give a general formula for n in terms of the desired margin of error m and the critical value z∗.