Suppose that Y1, Y2,..., Yn denote a random sample from a population having an
Chapter 10, Problem 10.101(choose chapter or problem)
Suppose that \(Y_{1}, Y_{2}, \ldots, Y_{n}\) denote a random sample from a population having an exponential distribution with mean \(\theta\).
a Derive the most powerful test for \(H_{0}: \theta=\theta_{0}\) against \(H_{a}: \theta=\theta_{a}\), where \(\theta_{a}<\theta_{0}\).
b Is the test derived in part (a) uniformly most powerful for testing \(H_{0}: \theta=\theta_{0}\) against \(H_{a}: \theta<\theta_{0}\)?
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