Suppose that X1, , Xn form a random sample from the exponential distribution with unknown parameter , and suppose that it is desired to test the following hypotheses H0 1 2, H1 1 2 Show that at every level of significance 0 (0 0 1), there exists a UMP test that specifies rejecting H0 when Xn c, for some constant c

Question: Suppose that X1, . . . , Xn form a random sample from the exponential distribution with unknown parameter , and suppose that it is

Suppose that X1, . . . , Xn form a random sample from the exponential with unknown parameter β, and suppose that it is desired to test the following hypotheses:
H0: β ≥ 1/2,
H1: β < 1/2.
Show that at every level of significance α0 (0 < α0 < 1), there exists a UMP test that specifies rejecting H0 when Xn ≥ c, for some constant c.

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