Problem bank

Problem 44 of 333HardStatisticsP044

UMP test for normal mean

  1. Given X1,…,Xn∼N(μ,σ2)X_1, \ldots, X_n \sim N(\mu, \sigma^2) with σ2\sigma^2 known. Test H0:μ=0H_0: \mu = 0 vs H1:μ>0H_1: \mu > 0. Construct the uniformly most powerful test at level α\alpha.