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Let X1, X2, . . . , Xn be a random sample from the normal distribution...

Let X1, X2, . . . , Xn be a random sample from the normal distribution N(µ, 36). (a) Show that a uniformly most powerful critical region for testing H0 : µ = 50 against H1 : µ < 50 is given by C2 = {x : x ≤ c}. Find the values of c for α = 0.10.

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