### Statistical Comparison of Catalysts in a Chemical Process 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 92 with a standard deviation of 2. Assume that yield measurements are approximately normally distributed with the same standard deviation. #### (a) Hypothesis Testing **Question:** Is there evidence to support the claim that catalyst 2 produces a higher mean yield than catalyst 1? Use \( \alpha = 0.01 \). **Answer:** Yes. #### (b) Confidence Interval **Question:** Find a 99% confidence interval on the difference in mean yields that can be used to test the claim in part (a). Round your answer to two decimal places (e.g., 98.76). **Result:** \( \mu_1 - \mu_2 \leq -2.60 \). This data provides insights into the effectiveness of different catalysts and establishes whether the observed differences are statistically significant.