An insurance company is interested in estimating the mean length of hospital stay following heart bypass surgery. A stratified random sample of public and private hospitals will be used for estimating the mean length of hospital stay following a heart bypass surgery. Suppose there is $15,000 available for the total cost of sampling,

and the initial setup cost of sampling is ????0 = $10, 000. Use Table 3.13 to determine

(a) the optimal allocation sampling proportions.

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

(c) the strata sample sizes.

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Hospital N SD Cost Public 15,000 Private 24 2 15 18 10,000 25,000