Heat-treating metal parts is a widely used manufacturing process. An article in the Journal of Metals (1989, Vol. 41) described an experiment to investigate flatness distortion from heat-treating for three types of gears and two heat-treating times. The data follow:

(a) Is there any evidence that flatness distortion is different for the different gear types? Is there any indication that heat-treating time affects the flatness distortion? Do these factors interact? Use α = 0.05.

(b) Construct graphs of the factor effects that aid in drawing conclusions from this experiment.

(c) Analyze the residuals from this experiment. Comment on the validity of the underlying assumptions.

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Time (minutes) Gear Type 20-tooth 90 120 0.0265 0.0560 0.0340 0.0650 24-tooth 0.0430 0.0720 0.0510 0.0880 28-tooth 0.0405 0.0620 0.0575 0.0825