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Optimum Sample Size for a Problem in Choosing the Population with the Largest Mean

Paul N. Somerville
Journal of the American Statistical Association
Vol. 65, No. 330 (Jun., 1970), pp. 763-775
DOI: 10.2307/2284586
Stable URL: http://www.jstor.org/stable/2284586
Page Count: 13
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Optimum Sample Size for a Problem in Choosing the Population with the Largest Mean
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Abstract

Given k + 1 normal populations, identically distributed with a common known variance σ2 and unknown means, it is required to select N individuals in two stages as follows. In the first stage, n individuals are selected from each of the populations. In the second stage, the remaining N - n(k + 1) individuals are selected from the population producing the largest mean in the first stage. A cost unique to the first stage is C(n) = c0 + c1nα, where c0, c1 and α are positive constants. The cost, common to both stages, of choosing an individual from the ith population is c20 - μi), where c2 is a positive constant, μi is the mean of the ith population, and μ0 is the largest of the k + 1 means. A minimax solution for the optimum n is obtained and tables give T = n/N for various values of M = (2N)1/2c1/(c2σ).

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