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 a = 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 a = 0.05 level of significance. If not, explain why not.

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Analysis of Variance for Parts Sour ce Materiail Machine Interaction Error Total DF 2 3 39.056 120.11 20.722 83.423 263.31 MS 19.528 40.037 3.4537 3.4760 5.618 11.52 0.994 0.010 0.000 0.452 24 35