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 a fixed total cost of sampling of

???? = $5000. Determine the overall sample size ???? and the individual sample sizes ????????

and ???????? when

(a) ????̇ ???? = 0.15, ????̇ ???? = 0.20, ???????? = $4, and ???????? = 6.

(b) ????̇ ???? = 0.55, ????̇ ???? = 0.45, ???????? = $15, and ???????? = 20.

(c) no reasonable prior guesses of ???????? and ???????? are available, ???????? = $7.50, and ???????? =

$12.