The likelihood of not rejecting the null hypothesis when the null hypothesis is false is , the probability of a type II error. The likelihood of rejecting the null hypothesis when the null hypothesis is false is then 1 - B. Refer to the formula for $ as a function of proportions p, and p,, where z , is the critical value based on significance level a, p = - (mp ] + np2) = _ (mq, + 192 ) , m and n are the sample sizes of Brand A and Brand B samples, respectively, and ( m + n ) ( m + n ) 0 = 1 P191 + P292 m B(P ,1 P2 ) = 0 20/2 \\/ 1 9 ( m + 7 ) -(P3 - P2) ] - 0[- za/2\\/ Pa (in + :) -(P1 - P2) Given a = 0.01, the critical value for this calculation is Zo/2 = Zo,005. Use the table of standard normal curve areas to determine the critical value, rounded to two decimal places. Z a/2 = 20.005 = 1 Calculate p using p, = 0.50, p, = 0.25, and m = n = 100. 10 ( mp , + np 2 ) ( m + n ) 0.5(100) + (100) 11 100 + 100 Calculate q using p, = 0.50, p, = 0.25, and m = n = 100, where q, = 1 - p, and 92 = 1 - P2. ( mq 1 + 19 2 ) ( m + n ) (1 - 0.5)(100) + 1 - (100) 11 100 + 100 Calculate o, rounding the result to five decimal places. 0 = 1 P191 + P292 m n 0.50 1 - 0.50 0.25(1- 100 100