Optimum Sample Size for Choosing the Population Having the Smallest Variance (Large Sample Size Results)

Abstract

Suppose we have k + 1 populations, each normally distributed. Let σ₀ ² be the smallest variance, and a = σ _i /σ₀. Let p ₀(a) be the probability of correct selection when a ₁ = a ₂ = ···= a . Let W (σ _i , σ₀) be the cost of selection of the wrong population and C(n) be the cost of sampling n individuals from each population. It is shown under general conditions that the maximum expected loss over all possible variance values is proportional to for large n, and that the maximum occurs for where x* is the value which maximizes x[1 − p ₀(x)].