Please help! Serious answers only. A company that sells glassware has two manufacturing plants. In a quality control inspection of a random sample of 150 pieces of glassware from plant A, 8% of the pieces had a defect. In a random sample of 200 pieces from plant B, 6% of the pieces had a defect.

(a) Construct and interpret a 99% confidence interval for the true difference in the proportion of pieces from plant A that are defective and the proportion of pieces from plant B that are defective.

(b) Based on this confidence interval, is there convincing evidence that the true proportion of pieces from plant A that are defective is different from the true proportion of pieces from plant B that are defective? Explain.