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: p_A- p_B= 0 versus H_a: p_A- p_B> 0 and obtain a p-value of 0.112.

(a) Which of the following is an appropriate interpretation of this p-value?

If the true proportions of defective dishes at the two plants are equal, there is a .112 probability of getting samples in which the differencep_A-p_Bis greater than or equal to 0.03.

If the true proportions of defective dishes at the two plants are equal, there is a 0.112 probability of getting samples in which the differencep_A-p_Bis equal to 0.03.

The probability of making a Type I error is 0.112.

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 0.112.

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 differencep_A-p_Bis 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 H_a: p_A- p_C> 0. Compared to the previous test (A-B):

the new test of A-C would have

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a smaller

an indeterminable

the same

a larger

test statistic and

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an indeterminable

a larger

the same

a smaller

p-value.