Question: With known probabilities p and q perform either E or F, with X distributed as N(, 1) under E or N(, 1) under F. For

With known probabilities p and q perform either E or F, with X distributed as N(θ, 1) under E or N(−θ, 1) under F. For testing H : θ = 0 against θ > 0 there exist a UMP unconditional and a UMP conditional level-α

test. These coincide and do not depend on the value of p.

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