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A biologist considered studying the effects of various environmental pollutants on the health of mice by using a 27- 4 fractional factorial design.

a. How many factors are involved? How many levels are there for each factor? How many trials will be required for a single replicate of the experiment? Can a test for lack of fit be obtained?

b. The biologist decided to augment the design with six center-point replicates. Can a test for lack of fit now be obtained? If so, can the biologist determine which factors caused a curvature effect?

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