In developing the sampling plan for estimating the difference between two proportions

???????? and ???????? (i.e., ???????? − ????????) with independent samples, suppose the goal is to minimize the bound on the error of estimation for an overall sample size fixed at

???? = 100. Determine the sample sizes ???????? and ???????? when

(a) ????̇ ???? = 0.60 and ????̇ ???? = 0.50.

(b) ????̇ ???? = 0.20 and ????̇ ???? = 0.50.

(c) ????̇ ???? = 0.75 and ????̇ ???? = 0.80.