Question: 7. If X. .. , X is a sample from N(~. a2). the UMP unbiased tests of :::; 0 and = 0 can be obtained

7. If X••. .. , X" is a sample from N(~. a2). the UMP unbiased tests of :::; 0 and = 0 can be obtained from Problems 5 and 6 by making an orthogonal transformation to variables Z., ... , Z" such that ZI = Iii X. [Then n n n n L zl = L zl - zf = L xl - nX2 = L (x, - x(] i - 2 i - I i-I i=1

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