STAT 3022, April 28, 2009
TA: Jinghan Meng
Homework 8 Solutions
Ex 13.14
(a)
Based on the given pvalue, all three eﬀects are signiﬁcant at
α
= 0
.
05.
(b)
In order to summarize the results, we would need to know the number of levels
for each factor(
I
and
J
) and the sample sizes in each cell (
n
ij
). We also would
want to know the sample cell means ¯
x
ij
so that we could interpret the signiﬁcant
main eﬀects and the nature of the interaction.
Ex 13.18
Pooling is reasonable, as the largest standard deviation is 2.16, the smallest is 1.42,
and 2
.
16
/
1
.
42 = 1
.
52
<
2. If we assume that all sample sizes in each cell (
n
ij
) were
equal, the pooled standard deviation is
s
p
=
v
u
u
t
∑
I
i
=1
∑
J
j
=1
(
n
ij

1)
s
2
ij
∑
I
i

1
∑
J
j

1
(
n
ij

1)
=
s
∑
I
i
=1
∑
J
j
=1
s
2
ij
I
×
J
=
r
(1
.
63)
2
+ (1
.
42)
2
+ (1
.
52)
2
+ (1
.
64)
2
+ (2
.
16)
2
+ (1
.
59)
2
2
×
3
= 1
.
6767
Ex 13.25
(a)
Here are the R codes to compute the mean and standard deviation for each of
the materialbytime combinations.
> ex13.25 < read.table("D:/PCText/ch13/ex13_025.txt",header=T)
> attach(ex13.25)
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 Spring '08
 Staff
 Standard Deviation, Variance, TA, Jinghan Meng

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