A component can be manufactured according to either of two designs and with either a more expensive or a less expensive material. Several components are manufactured with each combination of design and material, and the lifetimes of each are measured (in hours). A two-way analysis of variance was performed to estimate the effects of design and material on component lifetime. The cell means and main effect estimates are presented in the following table.

The process engineer recommends that design 2 should be used along with the more expensive material. He argues that the main effects of both design 2 and the more expensive material are positive, so using this combination will result in the longest component life. Do you agree with the recommendation? Why or why not?

Transcribed Image Text:

Main Effects Cell Means More expensive Less expensive Design 1 Design 2 14 Design 1 Design 2 -14 More expensive Less expensive 118 120 -16 60 122 16 ANOVA table Source DF SS MS F P Material Design Interaction 1 2352.0 2352.0 10.45 0.012 1 3072.0 3072.0 13.65 0.006 1 2700.0 2700.0 12.00 0.009 Error 8 1800.0 225.00 Total 11 9924.0