Equivalent Test In this exercise we will show that a hypothesis test involving a multinomial experiment with only two categories is equivalent to a hypothesis test for a proportion (Section 7-3). Assume that a particular multinomial experiment has only two possible outcomes, A and B, with observed frequencies of f1 and f2, respectively.

a. Find an expression for the x2 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, ( f1 1 f2) 2.

b. The test statistic z 5 ( 2 p) is used to test the claim that a population proportion is equal to some value p. With the claim that p 5 0.5, a 5 0.05, and 5 f1 ( f1 1 f2), show that z2 is equivalent to x2 [from part (a)]. Also show that the square of the critical z score is equal to the critical x2 value from part (a).