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 x1 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 20 bonus per casting, three a 30 bonus, and three a 40 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) 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 x1 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 20 bonus per casting, three a 30 bonus, and three a 40 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)