Question: S Optimality of the power function on the null hypothesis. Let R and .X;F; P# W # 2 / be a statistical model

S Optimality of the power function on the null hypothesis. Let ‚ R and .X;F; P# W

# 2 ‚/ be a statistical model with increasing likelihood ratios relative to a statistic T .

For given #0 2 ‚, let ' be a uniformly most powerful level-˛ test of the null hypothesis H0 W # #0 against the alternative H1 W # > #0. Show that the power function of ' is minimal on the null hypothesis, in that G'.#/ G .#/ for all # #0 and every test with E#0. / D ˛.

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