74. Let XI"'" x" be a sample from Na, a2 ) , and consider the UMP invariant level-a test of H: ~/a :=; 80 (Section 6.4). Let an(F) be the actual significance level of this test when XI" ' " X; is a sample from a distribution F with E(X,) = t Var(X,) = a2 < 00 . Then the relation an(F) -> a will not in general hold unless 80 = o. [Use the fact that the joint distribution of j;(X -~) and j;(S2 - a2) tends to the bivariate normal distribution with mean zero and covariance matrix ( a2 J.L3) J.L3 J.L4 - a2 ' where S2 = E(X, - X)2/n and J.Lk = E(X, - ~)k. See for example Serfling (1980).]