1. Write out the treatment combinations for a 24 factorial experiment.
2. In the search for a lower-pollution synthetic fuel, researchers are experimenting with three different factors, each controlled at two levels, for the processing of such a fuel. Factor A is the concentration of corn extract at 5% and 10%, factor B is the concentration of an ethylene-based compound at 15% and 25%, and factor C is the distillation temperature at 120 °C and 150 °C.
The levels of undesirable emission of the fuel are shown in Table for three replications of each treatment; each level is randomly assigned to a treatment. The larger the level of emission, the worse the impact on the environment.
|
Treatment
|
Degree of Undesirable Emission Level (ppm)
|
|
(1)
|
30
|
24
|
26
|
|
a
|
18
|
22
|
24
|
|
b
|
30
|
32
|
25
|
|
ab
|
43
|
47
|
41
|
|
c
|
28
|
24
|
22
|
|
ac
|
54
|
49
|
46
|
|
bc
|
58
|
48
|
50
|
|
abc
|
24
|
20
|
22
|
(a) Find all of the main effects and the interaction effects.
(b) Find the sum of squares for each of the effects and the interaction effects.
(c) At the 5% level of significance, which effects are significant? Interpret your inferences.