Two controllable factors, temperature and pressure, are each kept at three levels to determine their impact on the ductility of an alloy being produced. The temperature levels are 150, 250, and 300 °C, respectively. Pressure is controlled at 50, 100, and 150 kg/cm2. Each of the nine treatments is replicated five times. The ductility of the produced alloy is shown in Table 12-43. The higher the value, the more ductile the alloy.
(a) Test whether the interaction effects between temperature and pressure are significant at the 5% level of significance.
(b) What are the desirable settings of the process temperature and pressure if a ductile alloy is preferred?
(c) Find a 90% confidence interval for the mean ductility when the process temperature is set at 150 °C and the pressure at 150 kg/cm2.
(d) Find a 95% confidence interval for the difference in mean ductility for a process temperature of 250 °C and pressure of 150 kg/cm2 versus a process temperature of 300 °C and pressure of 100 kg/cm2.
|
Temperature(C°)
|
Pressure (kg/cm2)
|
|
50
|
100
|
150
|
|
150
|
50
|
44
|
75
|
|
65
|
49
|
80
|
|
70
|
52
|
81
|
|
73
|
40
|
76
|
|
68
|
45
|
82
|
|
|
|
|
|
|
250
|
40
|
25
|
86
|
|
45
|
30
|
88
|
|
56
|
20
|
82
|
|
50
|
33
|
81
|
|
52
|
34
|
76
|
|
|
|
|
|
|
300
|
72
|
62
|
60
|
|
60
|
71
|
62
|
|
75
|
65
|
55
|
|
73
|
68
|
52
|
|
70
|
72
|
50
|