Robert Altoff is vice president for engineering for a manufacturer of household washing machines. As part of new product development, he wishes to determine the optimal length of time for the washing cycle. A part of the development is to study 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 amounts 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.

a. Draw an interaction plot of the detergent means by cycle time.
b. Compute the ANOVA with statistical software and, using the .05 significance level, test the interaction effect of brand and cycle time on “dirt removed.”
c. Based on your results in part (b), conduct the appropriate tests of hypotheses for differences in factor means.
d. Interpret the results in a briefreport.

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Cycle Time (min) Detergent Brand 18 0.13 0.11 0.140.15 0.18 0.20 0.10 0.14 0.17 0.18 0.16 0.17 0.14 0.19 0.21 0.09 0.13 20 0.12 0.11 0.19 0.17 24 0.15 0.18 0.15 0.18 0.19 0.12 0.13 0.16 0.16 0.15 0.17