Dental researchers conducted an investigation of the manufacture of dental resins in which the response variable was the hardness of the resin. The factors were the distance between the curing tip and the surface of the resin during manufacture, and the depth of the resin at which the hardness was measured. The following MINITAB output presents the results.

a. Test the null hypothesis of no interaction between depth and distance.

b. If the null hypothesis of no interaction is not rejected, test the hypothesis that there is no main effect of depth. Interpret the result.

c. If the null hypothesis of no interaction is not rejected, test the hypothesis that there is no main effect of distance. Interpret the result.

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Analysis of Variance for Hardness Source DF SS MS F P Depth 5 3855.4 771.08 33.874 0.000 Distance 2 4111.8 2055.9 90.314 0.000 Interaction 10 47.486 4.7846 0.2102 0.994 Error 54 1229.2 22.764 Total 71 9244.2