Question

Let X ∼ Bin(2,p). Suppose we want to test H0 : p = p_0 versus H1 : p = p_1, with p_0 < p_1. For each of the following values of significance level α:

(a) α = 0

(b) α = (p_0)^2

(c) α=(p_0)^2 +2p_0(1−p_0)

(d) α = 1

use the Neyman-Pearson Test to construct the most powerful α-level test. In other words, to receive full credit you need to write down the rejection region in terms of X for the NP Test and then specify 4 values for the cut-off such that the desired level of significance is achieved.

Answer 1