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.
a) Is this an experiment or an observational study? Explain.
b) What is the response variable?
c) How many treatments are involved?
d) Based on the two-way ANOVA results, management concluded that shift has a significant impact on the length of the part and that consequently operator inexperience is the root cause of the part problems. Do you agree with this conclusion? Explain.

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Shift Morning Morning Morning Morning Morning Morning Morning Morning Morning Aftenoon Afternoon Aftemoon Aftemoon Afternoon Aftemoon Afternoon Afternoon Aftemoon Night Night Night Night Night ight Night Night Night Size Error Machine Setting 3.6 2.1 0.9 2.6 0.6 2.3 3.2 2.4 1.8 3.2 2.5 2.3 3.8 6.7 5.8 2.8 5.3 Sum of Mean DF Squares Square Source MachSet F-ratio P-value 2 17.1119 8.55593 7.3971 0.0045 Shift 2 24.9607 12.4804 10.790 0.0008 Interaction 4 14970 0.374259 0.32357 0.8585 Error Total 18 20.8200 1.1566 26 64.3896