An experiment was devised to test whether the parameter of a sample from the density f(y) yey, y 0 is equal to a believed value 0 50 (a) Derive the most powerful test for the null hypothesis H0 0 vs alternative hypothesis Ha a for a 40 (b) Discuss whether this test is uniformly most powerful to test against a composite alternative Ha 0

Question: An experiment was devised to test whether the parameter of a sample from the density f(y) = yey, y > 0 is equal to

An experiment was devised to test whether the parameter λ of a sample from the density f(y) = yeλy, y > 0 is equal to a believed value λ0 = 50. (a) Derive the most powerful test for the null hypothesis H0 : {λ = λ0} vs alternative hypothesis Ha : {λ = λa} for λa = 40. (b) Discuss whether this test is uniformly most powerful to test against a composite alternative Ha : {λ < λ0}.

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