Optimal sample sizes for estimating the difference in means between two normal populations treating confidence interval length as a random variable

Abstract

For estimating the difference (μ₁ - μ₂) between two population means based on random samples of sizes n ₁ and n ₂ from two normal populations with possibly unequal variances optimal sample sizes are determined based on the (unconditional) criterion that the length of a 100(l-α)% confidence interval for (μ₁μ₂) is no greater than 2h with probability at least (1 -δ). Consideration is also given to a conditional criterion involving the further requirement that the confidence interval must contain the value of (μ₁μ₂). and results based on the use of these two criteria are compared. For either the unconditional or conditional criterion, the optimal value of the ratio that minimizes the total sample size (n ₁ + n ₂) is found numerically to be approximately equal to the ratio .

Keywords:

• optimal sample size ratio
• population mean difference