Question

Two- Way ANOVA

Product development engineers and marketers at a household washing machine manufacturing firm want to determine the optimal length of time for a washing cycle. Part of the study includes understanding the relationship between the detergent used (four brands) and the length of the washing cycle (18, 20, 22, or 24 minutes). In order to run the experiment, 32 standard household laundry loads (having equal amount of dirt and the same total weights) are randomly assigned to the 16 detergent-washing cycle combinations. The results (in pounds of dirt removed) are shown below. (Note: The higher the number, the more dirt removed).

	Cyle Time (in min)
Detergent Brand	18	20	22	24
A	0.13	0.12	0.19	0.15
	0.11	0.11	0.17	0.18
B	0.14	0.15	0.18	0.2
	0.1	0.14	0.17	0.18
C	0.16	0.15	0.18	0.19
	0.17	0.14	0.19	0.21
D	0.09	0.12	0.16	0.15
	0.13	0.13	0.16	0.17

1. Draw an interaction plot of the detergent means by cycle time.
2. Compute the ANOVA using Excel and, using the 0.05 significance level, test the interaction effect of brand and cycle time on “dirt removed.”
3. Based on your results in part (b), conduct the appropriate tests of hypotheses for differences in factor means.

Answer 1

(a)

(b)

p- value for interaction > 0.05, so there is no significant interaction between brand and cycle time on dirt removed.

(c) Both the factors (Brand and Cycle Time) have p- values < 0.05, so both the main factors are significant. The mean dirt removed is significantly different for both brands and cycle times.

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