Let X have the exponential distribution with parameter . Suppose that we wish to test the hypotheses

Question:

Let X have the exponential with parameter β. Suppose that we wish to test the hypotheses
H0: β = 1,
H1: β = 1.
We shall use a test procedure that rejects H0 if either X ≤ c1 or X ≥ c2.
a. Find the equation that must be satisfied by c1 and c2 in order for the test procedure to have level of significance α0.
b. Find a pair of finite, nonzero values (c1, c2) such that the test procedure has level of significance α0 = 0.1.
Distribution
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