Question:

Two catalysts are being analyzed to determine how they affect the mean yield of a chemical process. Assume that changing the catalyst has no effect on the variance of the yield. Specifically, catalyst 1 is currently in use, but catalyst 2 is acceptable. Since catalyst 2 is cheaper, it should be adopted, provided it does not change the process yield. An experiment is run in the pilot plant and eight observations of yield are taken for each catalyst. The summary of the 8 observations is shown below.

Catalyst 1: \({{\bar{x}}_{1}}\) = 92.255, s ₁ = 2.39; Catalyst 2: \({{\bar{x}}_{2}}\) = 92.733, s ₂ = 2.98

1. Compute the value of the statistic that you would use to determine if there is any difference between the mean yields?
2. What distribution does your statistic obey?

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