HW Problem 1: An engineer suspects that the surface finish of a metal part is influenced by the feed rate and the depth of cut. He selects three feed rates and four depths of cut. He then conducts a factorial experiment and obtains the following data: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 Depth of Cut 0.15 0.15 0.15 0.18 0.18 0.18 0.2 0.2 0.2 0.25 0.25 0.25 0.15 0.15 0.15 0.18 0.18 0.18 0.2 0.2 0.2 0.25 0.25 0.25 0.15 0.15 0.15 0.18 0.18 0.18 0.2 0.2 0.2 0.25 0.25 0.25 Feed Rate 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 Surface Finish 74 64 60 79 68 73 82 88 92 99 104 96 92 86 88 98 104 88 99 108 95 104 110 99 99 98 102 104 99 95 108 110 99 114 107 111 a. Perform an Analysis of Variance (ANOVA) on the response variable of Surface Finish, and draw conclusions. Use alpha = .05 1) 2) 3) 4) Depth of cut is not significant, and feed rate is significant Depth of cut is significant, and feed rate is significant Depth of cut is not significant, and feed rate is not significant Depth of cut is significant, and feed rate is not significant b. What is the p-value for feed rate? c. What is the p-value for depth of cut? d. Plot the residuals on a normal probability scale. Does the residual analysis appear satisfactory (Normal Distribution)? Is the residual Normal: Yes or No 1) Yes, the residuals are a Normal Distribution 2) No, the residuals are not a Normal Distribution e. Compare the depth of cut and feed rates at each level. Select the following that apply: Depth of cut: True or False 1) 2) 3) 4) 5) 6) .15 is different from .18 .15 is different from .20 .15 is different from .25 .18 is different from .20 .18 is different from .25 .20 is different from .25 Reed rates: True or False 7) .20 is different from .25 8) .20 is different from .30 9) .25 is different from .30 f. # 1. 2. 3. Obtain average point estimates of the mean surface finish at each feed rate. Feed Rate .20 .25 .30 Average