Hi, I need help with this statistics question. Please show the steps clearly. Thank you!

Problem 4. [17 pts] Toss a coin 8 times to determine Whether or not it is fair, given the signicance level a : 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 H0 : p = 1 f 2 against H1 : p % 1 / 2. Below is the probability mass functions of a Binomial(8, 0.5) random variable. X N Binomial(8, 0.5) Is: 0 1 2 3 4 5 6 7 8 P(X = 11:) 0.0039 0.0313 0.1093 0.2188 0.2734 0.2188 0.1093 0.0313 0.0039 (a) [9 pts] Find the critical region in terms of X by oneproportion 2 test and exact binomial test respectively. (b) [8 pts] If x : 7 is observed, What is the pvalue of oneproportion 2 test and exact binomial test respectively