Two catalysts may be used in a batch chemical process. Twelve batches were prepared using catalyst 1, resulting in an average yield of 85 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 the claim that catalyst 2 produces higher mean yield than catalyst 1? Use a = 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). Round your answer to two decimal places (e.g. 98.76). M1-M₂ ≤ i

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### Chemical Process Analysis Using Two Catalysts

**Overview:**
In a batch chemical process, two types of catalysts have been utilized to compare their effectiveness in terms of yield. Each catalyst was tested through multiple batches:

- **Catalyst 1:** 
  - **Number of Batches:** 12
  - **Average Yield:** 85
  - **Sample Standard Deviation:** 3

- **Catalyst 2:** 
  - **Number of Batches:** 15
  - **Average Yield:** 89
  - **Sample Standard Deviation:** 2

Assume the yield measurements are normally distributed with the same standard deviation for both catalysts.

**Analysis:**

**(a) Hypothesis Testing:**
Determine if there is statistical evidence to support that Catalyst 2 provides a higher mean yield than Catalyst 1 using a significance level of \(\alpha = 0.01\).

**(b) Confidence Interval Analysis:**
Calculate a 99% confidence interval for the difference in the mean yields of the two catalysts. Round the final answer to two decimal places (e.g., 98.76).

**Expression:**
\[
\mu_1 - \mu_2 \leq \text{[Input answer here]}
\]

This segment is designed to assess comprehension of hypothesis testing and confidence interval calculations in a chemical engineering context.
Transcribed Image Text:### Chemical Process Analysis Using Two Catalysts **Overview:** In a batch chemical process, two types of catalysts have been utilized to compare their effectiveness in terms of yield. Each catalyst was tested through multiple batches: - **Catalyst 1:** - **Number of Batches:** 12 - **Average Yield:** 85 - **Sample Standard Deviation:** 3 - **Catalyst 2:** - **Number of Batches:** 15 - **Average Yield:** 89 - **Sample Standard Deviation:** 2 Assume the yield measurements are normally distributed with the same standard deviation for both catalysts. **Analysis:** **(a) Hypothesis Testing:** Determine if there is statistical evidence to support that Catalyst 2 provides a higher mean yield than Catalyst 1 using a significance level of \(\alpha = 0.01\). **(b) Confidence Interval Analysis:** Calculate a 99% confidence interval for the difference in the mean yields of the two catalysts. Round the final answer to two decimal places (e.g., 98.76). **Expression:** \[ \mu_1 - \mu_2 \leq \text{[Input answer here]} \] This segment is designed to assess comprehension of hypothesis testing and confidence interval calculations in a chemical engineering context.
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