In this exercise we will show that a hypothesis test involving a binomial experiment is equivalent to a hypothesis test for a proportion (Section 7-5). Assume that a particular experiment has only two possible outcomes, A and B, with observed frequencies of fx and f2, respectively.
a. Find an expression for the x1 test statistic, and find the critical value for a 0.05 significance level. Assume that we are testing the claim that both categories have the same frequency, (/", + f2)/2
b. The test statistic

is used to test the claim that a population proportion is equal to some value p. With the claim that p = 0.5, a = 0.05, and

show that z1 is equivalent to x1 [from part (a)]. Also show that the square of the critical z score is equal to the critical x1 value from part (a).

p-p pa 72 2 2 1 +