Refer to given Exercise. Factor A is the concentration of corn extract, factor B is the concentration of an ethylene-based compound, and factor C is the distillation temperature. Each factor will be controlled at two levels. Suppose the experimenter runs a 23-1 fractional factorial experiment, with the defining contrast being I= ABC. Using the data in Table, perform an analysis to determine the significance of effects. Which effects cannot be estimated? What is the alias structure? Comment on your inferences if the level of significance is 5%.
Exercise
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 levelis 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.