Questions -
Q1. In a study of processes used to remove impurities from cellulose goods ("Optimization of Rope-Range Bleaching of Cellulosic Fabrics," Textile Research J., 1976: 493-496), the following data resulted from a 24 experiment involving the desizing process. The four factors were enzyme concentration (A), pH (B), temperature (C), and time (D).
|
Treatment
|
Enzyme (g/L)
|
pH
|
Temp. (oC)
|
Time (hr)
|
Starch % by Weight
|
|
1st Repl.
|
2nd Repl.
|
|
(1)
|
.50
|
6.0
|
60.0
|
6
|
9.72
|
13.50
|
|
a
|
.75
|
6.0
|
60.0
|
6
|
9.80
|
14.04
|
|
b
|
.50
|
7.0
|
60.0
|
6
|
10.13
|
11.27
|
|
ab
|
.75
|
7.0
|
60.0
|
6
|
11.80
|
11.30
|
|
c
|
.50
|
6.0
|
70.0
|
6
|
12.70
|
11.37
|
|
ac
|
.75
|
6.0
|
70.0
|
6
|
11.96
|
12.05
|
|
bc
|
.50
|
7.0
|
70.0
|
6
|
11.38
|
9.92
|
|
abc
|
.75
|
7.0
|
70.0
|
6
|
11.80
|
11.10
|
|
d
|
.50
|
6.0
|
60.0
|
8
|
13.15
|
13.00
|
|
ad
|
.75
|
6.0
|
60.0
|
8
|
10.60
|
12.37
|
|
bd
|
.50
|
7.0
|
60.0
|
8
|
10.37
|
12.00
|
|
abd
|
.75
|
7.0
|
60.0
|
8
|
11.30
|
11.64
|
|
cd
|
.50
|
6.0
|
70.0
|
8
|
13.05
|
14.55
|
|
acd
|
.75
|
6.0
|
70.0
|
8
|
11.15
|
15.00
|
|
bcd
|
.50
|
7.0
|
70.0
|
8
|
12.70
|
14.10
|
|
abcd
|
.75
|
7.0
|
70.0
|
8
|
13.20
|
16.12
|
a. Use Yates's algorithm to obtain sums of squares and the ANOVA table.
b. Do there appear to be arry second-,third--, or forth-order interaction effects present? Explain you reasoning. Which main effects appear to be significant?
Q2. The following data on power consumption in electric furnace heats (kW consumed per ton of melted product) resulted from a 24 factorial experiment with three replicates ("Studies on a 10-cwt Arc Furnace," J. of the Iron and Steel Institute, 1956: 22). The factors were nature of roof (A low/high), power setting (B, low/high), scrap used (C, tube/plate), and charge (D, 700lb/1000 lb).
|
Treatment
|
xijklm
|
|
Treatment
|
xijklm
|
|
(1)
|
866, 862, 800
|
|
d
|
988, 808, 650
|
|
a
|
946, 800, 840
|
|
ad
|
966, 976, 876
|
|
b
|
774, 834, 746
|
|
bd
|
702, 658, 650
|
|
ab
|
709, 789, 646
|
|
abd
|
784, 700, 596
|
|
c
|
1017, 990, 954
|
|
cd
|
922, 808, 868
|
|
ac
|
1028, 906, 977
|
|
acd
|
1056, 870, 908
|
|
bc
|
817, 783, 771
|
|
bcd
|
798, 726, 700
|
|
abc
|
829, 806, 691
|
|
abcd
|
752, 714, 714
|
Construct the ANOVA table, and test all hypothesis of interest using α = .01.
Construct the ANOVA table, and test all hypotheses of interest using α = .01.