Question: 5. With known probabilities p and q perform either or 3&, with X distributed as N(8, 1) under or N( -8,1) under 3&. For testing

5. With known probabilities p and q perform either or 3&", with X distributed as N(8, 1) under or N( -8,1) under 3&". For testing H : 8 = 0 against 8> 0 there exist a UMP unconditional and a UMP conditional level-a test. These coincide and do not depend on the value of p .

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