Question

Two catalysts are being analyzed to determine how they affect the mean yield of a chemical process. Specifically, catalyst 1 is currently used. Because catalyst 2 is cheaper, it should be adopted, if it does not change the process yield. A test is run in the pilot plant and results in the data shown in the Table below. Both populations are assumed normal.

a) Assuming equal variances, using a hypothesis test at 5% alpha level, show if there is any difference in the mean yields.

b) Assuming unequal variances, using a hypothesis test at 5% alpha level, show if catalyst 2 yields greater mean than catalyst 1.

c) Find a 95% confidence interval for the mean of catalyst 1 minus that of catalyst 2 assuming equal variances.

Observation#	Catalyst 1	Catalyst 2
1	91.5	89.19
2	94.18	90.95
3	92.18	90.46
4	95.39	93.21
5	91.79	97.19
6	89.07	97.04
7	94.72	91.07
8	89.21	92.75

Answer 1

First we need to find the mean and SD of both data sets:

Descriptive statistics
	Catalyst 1	Catalyst 2
count	8	8
mean	92.2550	92.7325
sample standard deviation	2.3850	2.9835
sample variance	5.6883	8.9010
minimum	89.07	89.19
maximum	95.39	97.19
range	6.32	8

(a)

Conclusion: We cannot conclude that there is any difference in the mean yields..

(b)

Conclusion: We cannot conclude that catalyst 2 yields greater mean than catalyst 1.

(c)