Question

Two catalysts are being analyzed to determine how they affect the mean yield of a chemical process. Specifically, catalyst 1 is currently in use, but catalyst 2 is acceptable. Since catalyst 2 is cheaper, it should be adopted, providing it does not change the process yield. An experiment is run in the pilot plant and results in the data shown.(a) Is there any difference between the mean yields? Use α = 0.05 and assume equal variances. (b) Find the 100(1-α) % confidence interval for (µ1 - µ2). Use α = 0.05.

Observation Number	Catalyst 1	Catalyst 2
1	91.50	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

given data and necessary calculations are:-

Catalyst 1()	catalyst 2 ()
91.5	89.19	0.570025	12.54576
94.18	90.95	3.705625	3.175524
92.18	90.46	0.005625	5.161984
95.39	93.21	9.828225	0.228484
91.79	97.19	0.216225	19.87376
89.07	97.04	10.14423	18.55886
94.72	91.07	6.076225	2.762244
89.21	92.75	9.272025	0.000324
sum= 738.04	sum=741.86	sum=39.8182	sum=62.307

the pooled sd be:-

a).hypothesis:-

here we will do 2 sample t test assuming equal variances.

the test statistic be:-

df = (

t critical value for 95% confidence level = 2.145

[ using t distribution table for df = 14,alpha = 0.05,both sided test]

decision:-

so, we fail to reject the null hypothesis.

conclusion:-

there is not sufficient evidence to support the claim that there is a difference between the mean yields at 0.05 level of significance.

b). the 95% confidence interval for difference (µ1 - µ2) be:-

( -3.37, 2.42 )

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