Suppose that X1, . . . , Xn form a random sample from the uniform distribution on

Question:

Suppose that X1, . . . , Xn form a random sample from the uniform on the interval [0, θ], where the value of θ is unknown, and it is desired to test the following hypotheses:
H0: θ ≤ 3,
H1: θ >3.
a. Show that for each level of significance α0 (0 ≤ α0 < 1), there exists a UMP test that specifies that H0 should be rejected if max{X1, . . . , Xn} ≥ c.
b. Determine the value of c for each possible value of α0.
Distribution
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