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Math/Stat 423/523
Spring 2006
Solution Key
Exam 2
1.
An experiment was carried out to study the effects of factors A, B and C.
The
ANOVA table and interaction plot are given below.
Source
DF
SS
MS
F
P
A
1
17.36
17.36
31.31
0.000
B
2
21.86
10.93
19.71
0.000
C
2
8.37
4.19
7.55
0.004
A*B
2
1.06
0.53
0.96
0.406
A*C
2
3.20
1.60
2.91
0.082
B*C
4
6.51
1.63
2.94
0.050
A*B*C
4
2.08
0.52
0.94
0.463
Error
18
9.98
0.55
Total
35
70.42
The full model fit to data is:
X
ijkl
=
μ
+
α
i
+
β
j
+
χ
k
+
γ
ij
AB
+
γ
ik
AC
+
γ
jk
BC
+
γ
ijk
ABC
+
ε
ijkl
a.
Fill in the missing entries in the ANOVA table.
[6 pts]
b.
Test the hypothesis H
0
: {
γ
ik
AC
=0 for all i, k} versus H
a
: {H
0
is false} at the
α
=.05
level.
[7 pts]
Test Statistic = ___f=2.91___
Reject Region = ___{f > F
.05,2,18
= 3.55}__
Circle one:
Retain
c.
Compute the value of R
2
in this analysis
.
Does this number suggest a good fit of
the model to the data?
Explain briefly.
[6 pts]
%
8
.
85
42
.
70
98
.
9
1
R
2
=

=
This is a high R
2
that indicates a good fit of the model to the data.
d.
Based on the numerical results, what smaller model may adequately describe the
data?
Give a onesentence explanation for your answer
.
[6 pts]
X
ijkl
=
μ
+
α
i
+
β
j
+
χ
k
+
γ
jk
BC
+
ε
ijkl
Factors A, B, C, and the interaction between B and C are judged significant at the .05
level.
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View Full Document2.
An experiment was performed to determine the effect of four different chemicals on
the strength of a fabric.
Five fabric samples were randomly selected, and a
completely randomized block design (block = {fabric sample}) was run by testing
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 Spring '06
 Pascual
 Factors

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