6. In a particular trick, a magician appears to ip a coin 3 times; let X be the number of heads that result. The magician will repeat this trick any number of times, so that we can take a random sample of size n from X. Although the magician does not make a claim about whether or not the coin is fair, she does claim that she is ipping the same coin all three times independently. Since it is possible that the magician is decieving us with an illusion (e.g., perhaps she is switching to differently wieghted coins between ips), we test this claim. (a) (4 points) If we take the magician's claim as our null hypothesis, explain why we express this null hypothesis as H0 : X is binomial(3,p). (b) (8 points) Suppose we take a random sample of size n = 100. For i = 0, 1, 2, 3, let Yi denote the number of the samples of X that result in i many heads. Suppose we observe Yo = 43, Y1 = 8, Y2 = 5, Y3 = 44. Do we reject the magician's claim at significance level a = 0.10