A company that sells dishware has two plants. In a quality control inspection of a random sample of 200 dishes from plant A, 8% of the dishes had at least one defect. In a random sample of 200 dishes from plant B, 5% of the dishes had at least one defect. To determine if there is convincing evidence that the true proportion of defective dishes from plant A is more than the true proportion of defective dishes from plant B, we test the hypotheses H0: pA - p3 = 0 versus Ha: pA - p3 > 0 and obtain a p-value of 0.112. (a) Which of the following is an appropriate interpretation of this p-value? Q If the true proportions of defective dishes at the two plants are equal, there is a .112 probability of getting samples in which the difference 13;; - g is greater than or equal to 0.03. O The probability of making a Type I error is 0.112. Q If the true proportion of defective dishes at plant A is more than the true proportion of defective dishes at plant B, there is a 0.112 probability of getting samples in which the difference [3A - 133 is equal to 0.03. O The probability that the true proportion of defective dishes at plant A is more than the true proportion of defective dishes at plant B is 0.1 12. Q If the difference in the true proportions of defective dishes at the two plants truly equals .03, there is a 0.112 probability of getting samples in which the difference f>A - 133 is equal to 0.03. (b) Suppose the company adds a third plant (plant C), and in a quality control inspection of a random sample of 200 dishes from plant C, 3% of the dishes have a defect. The company tests whether plant A has a higher proportion of defective dishes than plant C using Ha: pA - pc > 0. Compared to the previous test (A-B): the new test of A-C would have test statistic and p-value