(See Solution) Let X ~ Bin;(10, p), p ∈ 1/4, 1/2. The simple hypothesis H_0: p=1/2 is rejected and alternative simple hypothesis H_A: p=1/4 is accepted,
Question: Let \(X \sim \operatorname{Bin}(10, p), p \in\left\{\frac{1}{4}, \frac{1}{2}\right\}\). The simple hypothesis \(H_{0}: p=\frac{1}{2}\) is rejected and alternative simple hypothesis \(H_{A}: p=\frac{1}{4}\) is accepted, if the observed value of \(X_{1}\), the random sample of size 1 , is less than or equal to 3 . Find the power function of the test.
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