Question

In: Statistics and Probability

Suppose X1, ..., Xn are i.i.d. from an exponential distribution with mean θ. If we are...

Suppose X1, ..., Xn are i.i.d. from an exponential distribution with mean θ. If we are testing H0 : θ = θ0 vs Ha : θ > θ0. Suppose we reject H0 when ( X¯n/ θ0) > 1 + (1.645/ √n)

(a) (10 points) Calculate the power function G(ζ). You may leave your answer in terms of the standard normal cdf Φ(x).

(b) (5 points) Is this test consistent?

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