The operations manager for an appliance manufacturer wants to determine the optimal length of time for the washing cycle

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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, D) and four levels of washing cycle (18, 20, 22, 24 minutes) are specifically selected for analysis. In order to run the experiment, 32 standard household laundry loads are randomly assigned, 2 each, to the 16 detergent-washing cycle time combinations. The results are measured in pounds of dirt removed. The results of the analysis are presented below.

WORKSHEET 1 General Linear Model: Dirt versus Detergent, Time Factor Information Factor Type Levels Values Detergent Fixed 4 A, B, C, D Time Fixed 4 18, 20, 22, 24 Analysis of Variance Source Detergent Time Detergent*Time Error Total DF Adj SS Adj MS F-Value P-value 3 0.000413 0.000138 0.79 0.519 3 0.027337 0.009112 52.07 0.000 9 0.002338 0.000260 1.48 0.235 16 0.002800 0.000175 31 0.032888 Model Summary S R-sq R-sq(adj) R-sq(pred) 0.0132288 91.49% 83.50% 65.94% Regression Equation Dirt = 0.14688 - 0.00063 Detergent A + 0.00563 Detergent_B - 0.00063 Detergent C -0.00437 Detergent_D-0.04313 Time_18 -0.01063 Time_20+ 0.02688 Time_22 +0.02687 Time_24 -0.00313 Detergent*Time_A 18 -0.00562 Detergent*Time_A 20 +0.00688 Detergent*Time_A 22 +0.00188 Detergent*Time_A 24 +0.00063 Detergent*Time_B 18 +0.00313 Detergent*Time_B 20 -0.00438 Detergent*Time_B 22 + 0.00062 Detergent*Time_B 24 -0.01812 Detergene*Time_C18 +0.00937 Detergent*Time_C 20 +0.00187 Detergent*Time_C22-0.00688 Detergent+Time_C24 +0.02063 Detergent Time_D 18 -0.00687 Detergent*Time_D 20 -0.00437 Detergent*Time_D 22 -0.00938 Detergent Time_D 24

Based on the post hoc analysis, what washing cycle should be used for this type of household clothes washer? Consider energy usage and relative performance. Tukey Pairwise Comparisons: Time Grouping Information Using the Tukey Method and 95% Confidence Time N Mean Grouping 24 8 0.17375 A 22 8 0.17375 A 20 8 0.13625 B 18 8 0.10375 Means that do not share a letter are significantly different. 22 24 Ô Ồ Ồ Ô 20 18