An industrial psychologist conducted an experiment to investigate the relationship between worker productivity and a measure of salary incentive for two manufacturing plants; one plant operates under “disciplined management practices” and the other plant uses a traditional management style. The productivity y per worker was measured by recording the number of machined castings that a worker could produce in a four-week period of 40 hours per week. The incentive was the amount x1 of bonus

(in cents per casting) paid for all castings produced in excess of 1,000 per worker for the four-week period. Nine workers were selected from each plant, and three from each group of nine were assigned to receive a 20¢ bonus per casting, three a 30¢ bonus, and three a 40¢ bonus. The productivity data for the 18 workers, three for each type of plant and incentive combination, are shown in Table 12.4.

Table 12.4 Productivity Data (Number of Castings) for Example 12.11 Incentive Management Style 20¢/casting 30¢/casting 40¢/casting Traditional 1,435 1,512 1,491 1,583 1,529 1,610 1,601 1,574 1,636 Disciplined 1,575 1,512 1,488 1,635 1,589 1,661 1,645 1,616 1,689

a. Write a model for mean productivity E(y), assuming that the relationship between E(y) and incentive x1 is first order.

b. Fit the model, and graph the prediction equations for the traditional and disciplined plants.

c. Do the data provide sufficient evidence to indicate that the rate of increase in worker productivity is different for disciplined and traditional plants? Test at a = .10.