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 overall sample size ???? and the individual sample sizes ???????? and ???????? when

???? = 0.03. Determine the values of ????, ????????, and ???????? when

(a) ????̇ ???? = 0.50 and ????̇ ???? = 0.54.

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

(c) ????̇ ???? = 0.30 and ????̇ ???? = 0.35.