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Q50Section C (Section C)50 of 60

Type-II error probability in normal test

Let X1,X2,…,X25X_1, X_2, \dots, X_{25} be a random sample from a N(μ,1)N(\mu, 1) distribution, where μ∈R\mu\in\mathbb{R} is unknown. Consider testing of the hypothesis H0:μ=5.2H_0: \mu=5.2 against H1:μ=5.6H_1: \mu=5.6. The null hypothesis is rejected if and only if 125∑i=125Xi>k\frac{1}{25}\sum_{i=1}^{25} X_i > k, for some constant kk. If the size of the test is 0.050.05, then the probability of type-II error equals __________ (round off to 22 decimal places)

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