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: Feed Rate Depth of Cut (in) (in/min) 0.15 0.18 0.20 0.25 0.20 74. 64, 60 79, 68, 73 82, 88, 92 99. 104, 96 0.25 92. 86. 88 98, 104. 88 99, 108, 95 104, 110. 99 0.30 99. 98. 102 104, 99, 95 108, 110, 99 114, 111, 107 1. Manually find the interaction effect of Feed Rate and Depth of Cut. (15 points) 2. Plot the data in the interaction plot. Does it appear that interaction effects are present? Does it appear that factor Feed Rate and factor Depth of Cut main effects are present? Discuss. (15 points) 3. Manually obtain the ANOVA table (15 points) 4. Manually find the main effects of Feed Rate and Depth of Cut. (15 points) 5. Compute a 95 percent confidence interval estimate (Tukey's test) of the mean difference in response for feed rates of 0.20 and 0.25 in min. (10 points) 6. Perform above analyses using Minitab and compare it with the results that you obtained manually. (30 points)