Question: 29. Let Xl . . ' Xm ; Yl , . 0 y be independently normally distributed with common variance 0 2 and means

29. Let Xl • •. . ' Xm ; Yl , . 0" y" be independently normally distributed with common variance 0 2 and means E(X;) = a + P(u; - u), E(lj) = r + 8(vj - 0), where the u's and v's are known numbers. Determine the UMP invariant tests of the linear hypotheses H: P = 8 and H: a = v, P= 8.

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