1. In order to investigate the relationship between work productivity and salary incentive for two plants: disciplined and traditional, the productivity y per worker was measured. The incentive was the amount * of bonus (in cents per casting) paid for all casting produced. Nine workers were selected from each plant, and three were assigned to receive a 20g bonus per casting, three a 30g bonus, and three a 40g bonus. The productivity data for the 18 workers are saved in CASTING.TXT file. a. Write a model for mean productivity E(y), assuming that the relationship between E(y) and incentive x] is first order. (2) b. Fit the model and the prediction equations for the traditional and disciplined plants. (4) 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 = 0.10. (4)STYLE INCENTIVE CASTINGS SDUMMY INC_SDUM Traditional 20 1435 Traditional 20 1512 Traditional 20 1491 Disciplined 20 1575 20 Disciplined 20 1512 20 Disciplined 20 1488 20 Traditional 30 1583 Traditional 30 1529 Traditional 30 1610 Disciplined 30 1635 30 Disciplined 30 1589 30 Disciplined 30 1661 30 Traditional 40 1601 Traditional 40 1574 Traditional 40 1636 Disciplined 40 1645 40 Disciplined 40 1616 40 Disciplined 40 1689 40