Chapter 8: Problem 5
If in Example \(8.2 .2\) of this section \(H_{0}: \theta=\theta^{\prime}\), where \(\theta^{\prime}\) is a fixed positive number, and \(H_{1}: \theta<\theta^{\prime}\), show that the set \(\left\\{\left(x_{1}, x_{2}, \ldots, x_{n}\right): \sum_{1}^{n} x_{i}^{2} \leq c\right\\}\) is a uniformly most powerful critical region for testing \(H_{0}\) against \(H_{1}\).
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