Question: Let X1, . . . , Xn be i.i.d. with the exponential distribution with parameter . Suppose that we wish to test the hypotheses H0:

Let X1, . . . , Xn be i.i.d. with the exponential with parameter θ. Suppose that we wish to test the hypotheses
H0: θ ≥ θ0,
H1: θ <θ0.
Let X = Let δc be the test that rejectsH0 if X ≥ c.
a. Show that π(θ|δc) is a decreasing function of θ.
b. Find c in order to make δc have size α0.
c. Let θ0 = 2, n = 1, and α0 = 0.1. Find the precise form of the test δc and sketch its power function.

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