Confidence intervals for the difference of two normal population means with one variance unknown

Abstract

Motivated by the recent work of Maity and Sherman (2006). The two-sample ttest with one variance unknown. The American Statistician 60, 163-166], we investigate, in this paper, confidence intervals for the difference between the means of two normal populations with one variance unknown. Asymptotic coverage probabilities and expected lengths of confidence intervals are derived. Monte Carlo simulations results indicate that the new confidence interval, based on Maity and Sherman, for the difference between two normal means with one variance unknown gives a shorter expected length than that of the well-known Welch-Satterthewaite confidence interval when the ratio of their population variances is large; otherwise, the Welch-Satterthewaite confidence interval is preferable.