We have two coins, C0 and C1, that looks identical but have different probabilities
(0.5 and 0.7 respectively) of showing Heads. A coin is chosen at random and then is tossed X
times until a Head comes up. Denote by H0 and H1 the hypotheses that the chosen coin is C0 and
C1 respectively.
(a) Construct the rejection region of the likelihood ratio test for H0 vs H1 of significance level α
(b) What is the significance level of a test that rejects H0 if X ≥ 8?
(c) Find the p-value of the likelihood ration test for observation X = k.