Question 2 [15] Management at a large manufacturing plant is concerned about the output of a production line. It is thought that two factors affect output: shift, with levels day (8 am. to 4 pm), nightl (4 pm. to 12 pm.) and night2 (12 pm. to 8 am), and supervisor, with levels SI and S2. Each combination of shift and supervisor is replicated three times. The response variable is output. The following data were obtained: Shift Supervisor Day Night 1 Night 2 Total 570 480 470 SI 610 475 430 4650 625 540 450 480 625 630 $2 515 600 680 5235 465 580 660 Total 3265 3300 3320 a) Name as precisely as possible the design used in this experiment. (1) b) Given that SS Total = 108 812.50 and SS Interaction = 80 908.33, draw up an AN OVA table and hence test the three null hypotheses of interest. As far as is possible om the tables, give a p-value associated with each test. (11) c) Draw a graph to illustrate either the nature of the interaction among the factors, or the absence of interaction, depending on your answer in (b). (3)