The production manager of a large casting firm is studying different methods to increase productivity in the workforce of the company. The process engineer and personnel in the human resources department develop three new incentive plans (plans B, C, and D) and design a study to compare these incentive plans with the current plan (plan A). Twenty workers are randomly assigned to each of the four plans. The response variable is the total number of units produced by each worker during 1 month on the incentive plan. The data are given in the following table.

a. State the null and alternative hypotheses being tested by the F statistic in the AOV table.
b. Is there significant evidence (α = .05) that the mean output associated with the four incentive plans is different?
c. Use Tukey€™s W procedure to identify the pairs of incentive plans that have different output means.

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