The likelihood of not rejecting the null hypothesis when the null hypothesis is false is ß, the probability of a type error. The likelihood of rejecting the null hypothesis when the null hypothesis is false is then 1-6. P191+ P292 Refer to the formula for ß as a function of proportions p₁ and P₂, where 2/2 is the critical value based on significance level a, (mp₁ + no ₂) = (ma₁ +na₂) m and in are the sample sizes of Brand A and Brand B samples, respectively, and a m (m + n) (m+n) B(D₂, P₂)-2/2√ √√5 ( ² + ²) - (0₂₁ - 0₂) - 0²/2√ √ ( = + ²) - (0₁-0₂) Given a 0.01, the critical value for this calculation is 2/2 Z20.005- Use the table standard normal curve areas to determine the critical value, rounded to two decimal places. ²a/2 = ²0.005 - Calculate using p₁ -0.50, P₂0.25, and m = n = 100. 5- (mp. + np₂) (m + n) 0.5(100)+([ 100 100 w 100 100 (100) Calculated using p₁ -0.50, P₂0.25, and mn 100, where d₁1-P₁ and 4₂1-P₂¹ (ma+na₂) (m+n) (10.5)(100)+(1-[ 0 + Calculate , rounding the result to five decimal places. P191+ P292 m 0.50(1-0.50) 0.25(1-[ 100 100 0 1)(100)