Statement of a problem № m40756


Assume that X1, . . . , Xn are i.i.d. with the normal distribution that has mean μ and variance 1. Suppose that we wish to test the hypotheses H0: μ ≥ μ0, H1: μ<μ0. Find a test statistic T such that, for every c, the test δc that rejects H0 when T ≥ c has power function π(μ|δc) that is decreasing in μ.

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