Question

Suppose that the rejection region of a test 𝜓 has the form 𝑅={𝑋⎯⎯⎯⎯⎯𝑛:𝑋⎯⎯⎯⎯⎯𝑛>𝑐} . Find the smallest 𝑐 such that 𝜓 has level 𝛼 .

(If applicable, type abs(x) for |𝑥| , Phi(x) for Φ(𝑥)=𝐏(𝑍≤𝑥) where 𝑍∼N(0,1) , and q(alpha) for 𝑞𝛼 , the 1−𝛼 quantile of a standard normal variable.)

What is
𝑐≥ ?