Two catalysts may be used in a batch chemical process. Twelve batches were prepared using catalyst 1, resulting in an average yield of 86 and a sample standard deviation of 3. Fifteen batches were prepared using catalyst 2, and they resulted in an average yield of 89 with a standard deviation of 2. Assume that yield measurements are approximately normally distributed with the same standard deviation.

(a) Is there evidence to support a claim that catalyst 2 produces a higher mean yield than catalyst 1? Use α = 0.01.

(b) Find a 99% confidence interval on the difference in mean yields that can be used to test the claim in part (a).