Quality control: Four machines are used with three different materials to fabricate a certain part. Each combination of machine and material is run for three days, and the number of satisfactory parts made each day is counted. A two-way ANOVA is performed to determine whether the mean number of satisfactory parts differs among machines or materials.

The following MINITAB output presents the ANOVA table.

a. Can you reject the null hypothesis of no interactions? Explain.

b. Can the main effect of material on number of satisfactory parts be interpreted? If so, interpret the main effect, using the α = 0.05 level of significance. If not, explain why not.

c. Can the main effect of machine on number of satisfactory parts be interpreted? If so, interpret the main effect, using the α = 0.05 level of significance. If not, explain why not.

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Analysis of Variance for Parts Source Material Machine Interaction Error 24 12362 DF SS MS F P 39.056 19.528 5.618 0.010 120.11 40.037 11.52 0.000 20.722 3.4537 0.994 0.452 83.423 3.4760 Total 35 263.31