A manufacturing company that makes dental drills was experiencing problems with a specific part on the production line. Management suspected a machining problem that resulted in the length of the part varying outside of target specification. Two factors were?examined: the machine setting?(at three?levels) and the shift?(morning, afternoon, and?night). New hires were typically scheduled for night?shift, and management believed that their relative inexperience may also be contributing to the variation. Three parts were randomly selected and measured from each treatment combination. The deviation from specified size was measured in microns. The data and?two-way ANOVA results are shown. Complete parts a through d below.

Full data set O Size Machine Size Machine Size Machine Error Setting Shift Error Setting Shift Error Setting Shift 1.2 Morning 2.1 Afternoon 3.9 Night 3.7 Morning 2.5 Afternoon 5.4 Night 3.4 Morning 5.1 Afternoon 4.9 Night 2 Morning 1.7 Afternoon 2.8 Night Morning 4 4 Afternoon 6.6 Night 2.5 Morning 3.1 Afternoon 5.7 Night 0.5 Morning 2.6 Afternoon 2.9 Night 2.4 Morning 4.9 Afternoon 3.1 Night 3.1 Morning 2.4 Afternoon 5.4 Night Sum of Mean Source DF Squares Square F-ratio P-value Machine Setting 2 17 .0319 8.51593 7. 6161 0 .0040 Shift 2 24 .4230 12 .2115 10 .921 0.0008 Interaction 4 1 .1370 0.284259 D . 25422 0.9033 Error 18 20 .1267 1 . 11815 Total 26 62.7185