A product development engineer is interested in investigating the tensile streng

Question

A product development engineer is interested in investigating the tensile strength of a new synthetic fiber that will be used to make cloth for men's shirts. The engineer knows from previous experience that the strength is affected by the weight percent of cotton used on the blend of materials for the fiber. Consider the following table of results for this single factor experiment: Cotton Weight Percent Observations 15 20 25 30 15 12 18 18 19 19 18 19 23 17 12 14 19 25 Perform the usual 1-way ANOVA, but then use the method of orthogonal polynomials to decompose the treatment sum of squares into three separate sums of squares and test for linear, quadratic, and cubic ef- fects

Explanation / Answer

Suppose we have to test,

H0 : There is no significant difference in cotton weight percentage.

The ANOVA table is by using R- as

R-code:

y=c(7,7,15,11,9,12,17,12,18,18,14,18,18,19,19,19,25,22,19,23)
x=rep(c(15,20,25,30),c(5,5,5,5))
d=data.frame(y,x)
a=aov(y~x,d)
summary(a)

And the output is ,

> summary(a)
Df Sum Sq Mean Sq F value Pr(>F)   
x 1 353.4 353.4 45.98 2.37e-06 ***
Residuals 18 138.4 7.7
---
Signif. codes:  
0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
>

Here p-value is much less than 0.05 thus we reject H0 at 5% l.o.s.

And conclude that There is significant difference in cotton weight percentage.

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