Obtain sums of squares and the ANOVA table

Assignment Help Applied Statistics

Reference no: EM131899630

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
Treatment	Enzyme (g/L)	pH	Temp. (^oC)	Time (hr)	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	x_ijklm	Treatment	x_ijklm
(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.

Reference no: EM131899630

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