The operations manager for an appliance manufacturer wants to determine the optimal length of time for the washing cycle of a household clothes washer. An experiment is designed to measure the effect of detergent brand and washing cycle time on the amount of dirt removed from standard household laundry loads. Four brands of detergent (A, B, C, and D) and four levels of washing cycle (18, 20, 22, and 24 minutes) are specifically selected for analysis. In order to run the experiment, 32 standard household laundry loads (having equal weight and dirt) are randomly assigned, 2 each, to the 16 detergent/washing cycle time combinations. The results, in pounds of dirt removed (stored in Laundry), are as follows:

At the 0.05 level of significance,
a. Is there an interaction between detergent brand and washing cycle time?
b. Is there an effect due to detergent brand?
c. Is there an effect due to washing cycle time?
d. Plot the mean amount of dirt removed (in pounds) for each detergent brand for each washing cycle time.
e. If appropriate, use the Tukey procedure to determine differences between detergent brands and between washing cycle times.
f. What washing cycle time should be used for this type of household clothes washer?
g. Repeat the analysis, using washing cycle time as the only factor. Compare your results to those of (c), (e), and (f).

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WASHING CYCLE TIME (IN MINUTES) DETERGENT BRAND 8 20 2224 0. 0.13 0.17 0.17 0.09 0.13 0.19 0.18 0.12 0.14 0.17 0.19 0.10 0.15 0.18 0.17 0.08 0.16 0.18 0.20 0.09 0.13 0.17 0.16 0. 0.12 0.16 0.15 0.13 0.13 0.17 0.17