(a) Does it appear that the true proportion of non-contaminated Brand A chickens differs from that for Brand B? Carry out a test of hypotheses using a significance level 0.01. State the relevant hypotheses. Calculate the test statistic and P-value. State the conclusion in the problem context. Recall that the null hypothesis for a test of the difference between population proportions is no different than zero, so Ho: P, - P2 = =|0. The alternative hypothesis in this case is that the true proportion of non-contaminated Brand A chickens differs from that Brand B, or that the true proportions are not equal. In other words, Ha: P1 - P2 # # o. Step 2 If mp, mq , np2, and no, are at least 10, we can use the large-sample test procedure with an approximately standard normal distribution. The variables m and n are the sample sizes of Brand A and Brand B, respectively, p, and p, are the sample proportions of non-contaminated chickens of Brand A and Brand B, respectively, and q, = 1 - p, and 4, = 1 - p,. Recall that 34 of 80 chickens from Brand A tested positive, so the number of non-contaminated chickens is 80 - 34 = 46 . The value of p, is the number of non-contaminated Brand A chickens divided by the total number of Brand A chickens, or P, = Calculate mp. mp = 80 46 Recall that 91 = 1 - p1 . Calculate mq1 . ma 1 = 80 (1 - P1 ) = 80(1 -[ We are told that 64 of 80 chickens from Brand B tested positive, so the number of non-contaminated chickens is 80 - 64 = . The value of p2 is the number of non-contaminated Brand B chickens divided by the total number of chickens of Brand B, or p2 = Calculate np 2. np2 = 80 ( Calculate no2, where 92 = 1 - P2. n42 = 80(1 - P2) = 80(1 - Referring to the values calculated above, the number of values less than or equal to 10 is [-Select-- v) , so we [--Select- | use the large-sample test procedure for this data