In an experiment conducted by the Mining Engineering Department at Virginia Tech to study a particular filtering system for coal, a coagulant was added to a solution in a tank containing coal and sludge, which was then placed in a recirculation system in order that the coal could be washed. Three factors were varied in the experimental process:
Factor A: percent solids circulated initially in the overflow
Factor B: flow rate of the polymer
Factor C: pH of the tank
The amount of solids in the underflow of the cleansing system determines how clean the coal has become. Two levels of each factor were used and two experimental runs were made for each of the 23 = 8 combinations. The response measurements in percent solids by weight in the underflow of the circulation system are as specified in the following table:
|
Treatment Combination
|
Response
|
|
Replication 1
|
Replication 2
|
|
(1)
|
4.65
|
5.81
|
|
A
|
21.42
|
21.35
|
|
B
|
12.66
|
12.56
|
|
ab
|
18.27
|
16.62
|
|
C
|
7.93
|
7.88
|
|
ac
|
13.18
|
12.87
|
|
bc
|
6.51
|
6.26
|
|
abc
|
18.23
|
17.83
|
Assuming that all interactions are potentially important, do a complete analysis of the data. Use P-values in your conclusion.