5.28. A manufacturer of laundry products is investigating the performance of a newly formulated stain remover. The new formulation is compared to the original formulation with respect to its ability to remove a standard tomato-like stain in a test article of cotton cloth using a factorial experiment. The other factors in the experiment are the number of times the test article is washed (1 or 2) and whether or not a detergent booster is used. The response variable is the stain shade after washing (12 is the darkest, 0 is the lightest). The data are shown in the following table.

(a) Conduct an analysis of variance. Using 4 $ 0.05, what conclusions can you draw?

(b) Investigate model adequacy by plotting the residuals.

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Number of Washings 1 Number of Washings 2 Formulation Booster Booster Yes No Yes No New 6,5 6,5 3,2 4,1 Original 10,9 11, 11 10,9 9, 10