With reference to Exercise 12.12, if n = 100, 0 = 0.40, 1 = 0.30, and a is as large as possible with-out exceeding 0.05,

With reference to Exercise 12.12, if n = 100, θ0 = 0.40, θ1 = 0.30, and a is as large as possible with-out exceeding 0.05, use the normal approximation to the binomial distribution to find the probability of committing a type II error.
In exercise
Use the Neyman-Pearson lemma to indicate how to construct the most powerful critical region of size α to test the null hypothesis θ = θ0, where θ is the parameter of a binomial distribution with a given value of n, against the alternative hypothesis θ = θ1 < θ0.