Maity and Sherman [2] considered the situation where one variance is known but the other one
unknown. Without loss of generality, we assume that the first variance, σ2
1 , is known. Maity and
Sherman proposed the following test statistic:
T3 =
Y¯1 − Y¯2 − μ0
σ2
1
n1
+
S2
2
n2