Question

The percentage of hardwood concentration in raw pulp, the vat pressure, and the cooking time of the pulp are being investigated for their effects on the strength of paper. Three levels of hardwood concentration, three levels of pressure, and two cooking times are selected. A factorial experiment with two replicates is conducted, and the following data are obtained:

Percentage of Hardwood Concentration	Cooking Time 3.0 Hours				Cooking Time 4.0 Hours
	Pressure				Pressure
	400	500	650		400	500	650
2	196.6	197.7	199.8		198.4	199.6	200.6
	196	196	199.4		198.6	200.4	200.9
4	198.5	196	198.4		197.5	198.7	199.6
	197.2	196.9	197.6		198.1	198	199
8	197.5	195.6	197.4		197.6	197	198.5
	196.6	196.2	198.1		198.4	197.8	199.8

(a) Analyze the data and draw conclusions. Use ? = 0.05.

(b) Prepare appropriate residual plots and comment on the model’s adequacy.

(c) Under what set of conditions would you run the process? Why?

Answer 1

THE ANOVA for the fractional experiment is performed in the R stastistial software.

>tt<-read.Csv("clipboard",sep="\t")

>head(ttt)

Hardwood Cooking Pressure Strength

1 2 3 400 196.6

2 2 3 400 196.0

3 2 3 500 197.7

4 2 3 500 196.0

5 2 3 600 199.8

6 2 3 600 199.4

>tt$Hardwood <-as.factor(tt$ Hardwood)

>tt$Cooking <-as.factor(tt$Cooking)

>tt$Pressure <-as.factor(tt$Pressure)

>Strenght_aov <-aov(Strength~.,tt)

>summary(Strength_aov)

Df Sum Sq Mean Sq F value pr(>f)

Hardwood 28.84724.42366.91430.003392**

Cooking 121.777821.777834.03962.217e-06***

Presure 220.373910.186915.92261.937e-05***

Residucals 3019.19330.6398

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Signif.codes:0'****'0.001'**'0.01'*'0.05'.'0.1''1

Each of the factors is significant