Question

An engineer is interested in the effects of cutting speed (A), tool geometry (B), and cutting angle (C) on the life (in hours) of a machine tool. Two levels of each factor are chosen, and three replicates of a 2^3 factorial design are run. The results are as follows Treatment Replicate A B C Combination I II III - - - (1) 22 31 25 + - - a 32 43 29 - + - b 35 34 50 + + - ab 55 47 46 - - + c 44 45 38 + - + ac 40 37 36 - + + bc 60 50 54 + + + abc 39 41 47 a. Estimate all the main effects and interaction effects by hand. Which effects appear to be large? b. Use Minitab (or any other software) to do analysis of variance (ANOVA) to confirm your conclusions in part (a).

          An engineer is interested in the effects of cutting speed (A), tool geometry (B), and cutting angle (C) on the life (in hours) of a machine tool. Two levels of each factor are chosen, and three replicates of a 2^3 factorial design are run. The results are as follows

Treatment Replicate
A B C Combination I II III
- - - (1) 22 31 25
+ - - a 32 43 29
- + - b 35 34 50
+ + - ab 55 47 46
- - + c 44 45 38
+ - + ac 40 37 36
- + + bc 60 50 54
+ + + abc 39 41 47

a. Estimate all the main effects and interaction effects by hand. Which effects appear to be large?
b. Use Minitab (or any other software) to do analysis of variance (ANOVA) to confirm your conclusions in part (a).

An engineer is interested in the effects of cutting speed (A), tool geometry (B), and cutting angle (C) on the life (in hours) of a machine tool. Two levels of each factor are chosen, and three replicates of a 2^3 factorial design are run. The results are as follows

Treatment Replicate
A B C Combination I II III
- - - (1) 22 31 25
+ - - a 32 43 29
- + - b 35 34 50
+ + - ab 55 47 46
- - + c 44 45 38
+ - + ac 40 37 36
- + + bc 60 50 54
+ + + abc 39 41 47

a. Estimate all the main effects and interaction effects by hand. Which effects appear to be large?
b. Use Minitab (or any other software) to do analysis of variance (ANOVA) to confirm your conclusions in part (a).

Added by Catalina G.

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