Please review question below.

Q3 Q3 16 Points Problem 3. [16 pts] Toss a coin 8 times to determine whether or not it is fair, given the significance level or = 0.1. Let X be the number of heads in the 8 tosses. Let p denote the probability that the coin comes up heads. We test Ho : p = 1/2 against H1 : p # 1/2. Below is the probability mass functions of a Binomial(8, 0.5) random variable. X ~ Binomial(8, 0.5) k 0 1 2 3 4 5 6 7 8 P(X = k) 0.0039 0.0313 0.1093 0.2188 0.2734 0.2188 0.1093 0.0313 0.0039 (a) [8 pts] Find the critical region in terms of X by one-proportion z test and exact binomial test respectively. (b) [8 pts] If a = 7 is observed, what is the p-value of one-proportion z test and exact binomial test respectively