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.

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2-Proportion Test

In a 2-proportion test, two separate proportions are measured at the same time, and their similarity is evaluated. It is also known as a 2-proportion z-test, and a comparison of two different proportions is done in this method.