Question

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 $\alpha=0.01$. b. Find a $99 \%$ confidence interval on the difference in mean yields that can be used to test the claim in part (a).

          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 $\alpha=0.01$.
b. Find a $99 \%$ confidence interval on the difference in mean
yields that can be used to test the claim in part (a).

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Added by Cindy L.

Probability with Applications in Engineering, Science, and Technology

Matthew A. Carlton • Jay L. Devore 2nd Edition

Instant Answer

Solved by Expert Juan Nicolás

12/11/2021

Step 1

Given: - Sample mean for catalyst 1, $\bar{x}_1 = 86$ - Sample standard deviation for catalyst 1, $s_1 = 3$ - Sample size for catalyst 1, $n_1 = 12$ - Sample mean for catalyst 2, $\bar{x}_2 = 89$ - Sample standard deviation for catalyst 2, $s_2 = 2$ - Sample size Show more…

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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 $\alpha=0.01$. b. Find a $99 \%$ confidence interval on the difference in mean yields that can be used to test the claim in part (a).

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