Question

An experiment is conducted to compare the effects of weathering on the paint of three different types. To do so, identical surfaces are coated with some paint of each type that has been exposed to four different environments. Measurements of the degree of deterioration we made for each surface. What can you say about the different paint types and different environments and their effects on paint degradation?

Deteriorat Paint Type Environment 9.42 A 9.14 A 10.82 A 11.82 A 8.51 A 7.4 A 10.08 A 10.11 A 11.37 B 12.43 B 13.56 B 11.31 B 11.14 B 10.55 B 14.7 B 14.35 B 9.85 C 11.84 C 12.13 C 11.34 C 10.09 C 9.03 C 10.87 C 12.7 C WNNW W NN wwNNW

Answer 1

Analysis of Variance

Source	DF	Adj SS	Adj MS	F-Value	P-Value
Paint Type	2	30.575	15.2873	18.30	0.000
Environment	3	26.837	8.9455	10.71	0.000
Error	18	15.038	0.8354
Lack-of-Fit	6	6.026	1.0043	1.34	0.314
Pure Error	12	9.012	0.7510
Total	23	72.449

The hypothesis being tested is:

H0: There is no main effect of Paint Type

Ha: There is a main effect of Paint Type

The p-value is 0.000.

Since the p-value (0.000) 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 Paint Type.

The hypothesis being tested is:

H0: There is no main effect of Environment

Ha: There is a main effect of Environment

The p-value is 0.000.

Since the p-value (0.000) 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 Environment.

The hypothesis being tested is:

H0: There is no interaction effect

Ha: There is an interaction effect

The p-value is 0.314.

Since the p-value (0.314) is greater than the significance level (0.05), we cannot reject the null hypothesis.

Therefore, we cannot conclude that there is an interaction effect.

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