Allocation of Total Sample Size When Only the Stratum Means Are of Interest

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Abstract
In a recent stratified sample survey of telephone switchboards, the total sample size n was limited in advance to a certain small number. Associated with the ith switchboard of type k was the number Yki of telephone sets behind it. The main items to be estimated were the means y k , of five designated strata. It was proposed that the sample means y k should have sampling variances as nearly as possible in a given ratio, so as to reflect different degrees of interest in the various strata. The basic problem considered here is to find an appropriate integer valued allocation of n among the strata. The problem can be tackled in several ways. We present two graphical procedures, two nonlinear integer programming algorithms, and a dynamic programming technique. All but the first two guarantee optimum solutions. The methods appear in increasing order of complexity and in increasing order of generality.

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