Question: 10. Let XI ' x be independently normally distributed with known variance aJ and means E( X;) = j' and consider any linear hypothesis

10. Let XI" ' " x" be independently normally distributed with known variance aJ and means E( X;) = j' and consider any linear hypothesis with s n (instead of s < n which is required when the variance is unknown). This remains invariant under a subgroup of that employed when the variance was unknown, and the UMP invariant test has rejection region (112) E(x, - t)2- L(X; - 0 2= L(~j - tr > CaJ with C determined by (113) jOOx;(y) dy = a .

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