Question: In developing the sampling plan for estimating the difference between two proportions ???????? and ???????? (i.e., ???????? ????????) with independent samples, suppose the goal

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.

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