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 total cost of sampling for a pre-specified value of the bound on the error of estimation of ???? = 0.04. Determine the overall sample size ???? and the individual sample sizes ???????? and ???????? when

(a) ????̇ ???? = 0.5, ????̇ ???? = 0.45 and ???????? = $12, ???????? = 10.

(b) ????̇ ???? = 0.25, ????̇ ???? = 0.35 and ???????? = $5, ???????? = 2.

(c) no reasonable prior guesses of ???????? and ???????? are available, ???????? = $5 and ???????? = $10.