1. An engineer is interested in the effects of cutting speed (A), tool geometry (B), and cutting angle (C) on the life (in hour) of a machine tool. Two levels of each factor are chosen, and 3 replicates of a 23 factorial design are run. The results follow: Treatment Replicate A B C Combination I 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 the factor effects. Which effects seem to be large? b. Use the effect significance tests to confirm your conclusions for part a). c. Reduce your model based on a=0.05 d. Check model adequacy for the reduced model e. Based on an analysis of the effect plots from the reduced model, what coded factor levels of A, B, and C would you recommend using? 2. Based on the full model from number #1 a. Create 95% confidence intervals for the effects b. Based on these intervals, which factors would you keep in the model and why? c. Does this analysis agree with what you found in part c of #1(explain)? 3. An experiment was run to try to improve the yield of a chemical process. The factors used in this experiment were temperature (T), concentration (C) and type of catalyst (K). The results of the experiment are given below a. Determine the main effects and interactions and comment on which ones you think are real b. Use the significance test to reduce your model C. Check for model adequacy d. Create the appropriate effect plots and give a recommendation for settings for each input