2. Show that the asymptotic distribution of T in the nonnormal case is N(0, (+R)(1 + R)1)...

2.

Show that the asymptotic distribution of T in the nonnormal case is N(0, (θ+R)(1 + Rθ)−1) for large m and n. Thus, if R = 1, T is asymptotically N(0,1) as in the normal theory case assuming equal variances, even though the two samples come from nonnormal populations with unequal variances. Conclude that the test is robust in the case of large, equal sample sizes (Scheffé [101, p. 339]).