A note on a two-sample T test with one variance unknown

This note revisits Maity and Sherman's two-sample testing problem with one variance known but the other one unknown [A. Maity, M. Sherman, The two-sample t test with one variance unknown, The American Statistician 60 (2006) 163-166]. Inspired by the fact that the number of degrees of freedom used in their testing method is overestimated, we propose in this note a new testing method by introducing an unbiased estimator of the number of degrees of freedom. Simulation studies indicate that the proposed testing method provides a more accurate control than Maity and Sherman's method.