A two-factor experiment is conducted to investigate how the tensile strength of a graphite-epoxy composite depends upon the formulation of the composite and the temperature of the composite. Four different composite formulations are considered in the experiment and they are taken to be factor A. Three different temperature levels are considered (low = 1. medium = 2, and high = 3) and they are taken to be factor B. The response variable is tensile strength and it is measured for two different samples at each experimental configuration. The sums of squares SSA = 160.61, SSB = 580.52, SSAB = 58.01. and SSE = 66.71 are obtained. The cell sample averages are 11. = 27.05, 12. = 18.80, l3. = 16.40, 21. = 25.50, 22. = 15.60, 23 = 8.25, 31. = 24.15, 32. = 17.90, 33. = 16.95, 41. = 30.00, 42. = 23.40, and 43. = 17.65.
(a) Construct the analysis of variance table.
(b) Show that there is no evidence of an interaction effect but that there are main effects for both factors.
(c) Construct pairwise confidence intervals to compare the four different graphite-epoxy composite formulations. What conclusions can you draw?