ISyE 2028C Solution for HW#4
Problem #2:
The following table reports the investigation of the impact of different amount of dye
used on fabric color density.
Two plants are randomly selected among 10 plants owned by the
company for this investigation.
There are four replicates in each testing case.
Amount of Dye
Plant
0.33%
1%
3%
1
5.2, 6.0, 5.9, 5.9
12.3, 10.5, 12.4, 10.9
22.4, 17.8, 22.5, 18.4
2
6.5, 5.5, 6.4, 5.9
14.5, 11.8, 16.0, 13.6
29.0, 23.2, 29.7, 24.0
Answer the following questions.
(a)
What is the model for the data presented in the table?
(b)
What are the definitions of the sums of squares in terms of data notation?
Note that
there are several sums of squares.
(c)
What assumption(s) are needed to conduct an ANOVA test of whether the population
means from three different amounts of dye are the same?
Here, the mean is the
average of color densities.
(d)
What are the degrees of freedom for the sums of squares?
(e)
What is the formula of the Ftest in the end of the ANOVA table?
What are the degrees
of freedoms for the Fdistribution?
If α = 0.01, what is the Ftable value?
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 Spring '11
 x
 Yijk, color density, color density measurement

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