The American Medical Association (AMA) wishes to estimate the mean number of hours per week surgeons and nonsurgical doctors work, and a stratified random sample using optimal allocation will be used for estimating the mean. Suppose that a bound on the error of estimation of ???? = 0.5 is desired, and the initial setup cost of sampling is ????0 = $6000. Use Table 3.14 to determine

(a) the optimal allocation sampling proportions.

(b) the sample size for a stratified sample using optimal allocation that produces the smallest total cost for the desired bound on the error of estimation.

(c) the strata sample sizes.

(d) the total cost of sampling.

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Type of Doctor N SD Cost Surgeon Nonsurgical 20,000 80,000 100,000 25 2 20 10 20