Skip to content
Q17Section I (Objective (Q1–Q80))17 of 80

Statistical Inference — identifying the UMP test from its critical region

Let x1,x2,x3,…,xnx_1, x_2, x_3, …, x_n be a random sample from N(0,σ2)N(0, \sigma^2), σ>0\sigma > 0. Which one of the following hypotheses has the critical region ∑i=1nxi2≥2χ(n,α)2\sum_{i=1}^{n} x_i^2 \ge 2\chi^2_{(n,\alpha)} as the UMP critical region of level α\alpha, where P(χ(n)2>χ(n,α)2)=αP(\chi^2_{(n)} > \chi^2_{(n,\alpha)}) = \alpha?

Options

Pick an option to check your answer. In a mock test a wrong answer here costs 0.83 mark.