Let X1, . . . , Xn ∼ iid Exp(θ) and consider the test for H0...

Let X1, . . . , Xn ∼ iid Exp(θ) and consider the test for H0 : θ ≥ θ0 vs H1 : θ < θ0.

(a) Find the size-α LRT. Express the rejection region in the form of R = {X > c ¯ } where c will depend on a value from the χ 2 2n distribution.

(b) Find the appropriate value of c.

(c) Find the formula for the P-value of this test.

(d) Compare this test to the Karlin-Rubin UMP test.

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orchestra answered 2 years ago

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