Suppose a coin is tossed 100 times and the number of heads arerecorded. We want to test whether the coin is fair. Again, a coinis called fair if there is a fifty-fifty chance that the outcome isa head or a tail. We reject the null hypothesis if the number ofheads is larger than 55 or smaller than 45.
Write your H_0 and H_A in terms of the probability of heads, sayp.
Find the Type I error rate if the null hypothesis is true.
Calculate the power of the test if the true chance of head is0.4
Find the p-value if the observed number of heads is 65.
