Consider testing the hypotheses H 0 : = 0 versus H 1 : = 1

Consider testing the hypotheses H₀: θ = 0 versus H₁: θ = 1 based on a random sample of size n = 16 from a normal distribution with mean θ and known variance of 64.

(a) Calculate the power for the likelihood ratio test at level α = .01.

(b) A researcher wants to obtain a power of at least 0.9 for rejecting the null (fixing α = 0.01). What is the sample size n that needs to be collected to achieve this power?