Suppose we observe X Bin(n, p) where n is known by design and p = (0, 1) is the parameter of interest. (a)Derive a UMP test for Ho: p ≤po versus H₁ :p> po where po € (0, 1) is a fixed constant. 2 (b) Consider the specific case of po = 0.5. Use the central limit theorem (normal approximation to the binomial) to determine the value of n such that a UMP test satisfies Pr(reject Holp = 0.5) = 0.05 and Pr(reject Holp = 0.8) = 0.9.

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