Question

For a particular chemical synthesis, the effect of precursor concentration and catalyst amount were studied.

	Catalyst amount 0.5 kG	Catalyst amound 1 kG
Precursor concentration 15%	17, 18, 21	31, 28, 29
Precursor concentration 30%	28, 24, 27	34, 37, 41

Calculate the : a)effect of each factor and interaction between factors, b)significance of each factor and interactions, c) residuals between the actual value and the linear statistical model based on the estimates from 1. Do you think the residuals are normally distributed.

Answer 1

Source	SS	df	MS	F	p-value
Factor 1	184.08	1	184.083	31.56	.0005
Factor 2	352.08	1	352.083	60.36	.0001
Interaction	0.08	1	0.083	0.01	.9078
Error	46.67	8	5.833
Total	582.92	11

The hypothesis being tested is:

H0: There is no main effect of Precursor concentration

Ha: There is a main effect of Precursor concentration

The p-value is 0.0005.

Since the p-value (0.0005) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that there is a main effect of Precursor concentration.

The hypothesis being tested is:

H0: There is no main effect of Catalyst amount

Ha: There is a main effect of Catalyst amount

The p-value is 0.0001.

Since the p-value (0.0001) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that there is a main effect of the Catalyst amount.

The hypothesis being tested is:

H0: There is no interaction effect of Catalyst amount and Precursor concentration

Ha: There is an interaction effect of Catalyst amount and Precursor concentration

The p-value is 0.9078.

Since the p-value (0.9078) is greater than the significance level (0.05), we cannot reject the null hypothesis.

Therefore, we cannot conclude that there is an interaction effect of Catalyst amount and Precursor concentration.

The residuals are:

RESI
-1.66667
-0.66667
2.33333
1.66667
-2.33333
0.66667
-0.00000
-0.00000
0.00000
0.00000
0.00000
0.00000

Yes, the residuals are normally distributed.

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