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Solution to HW12:
Problem 1:
a)
It appears that brand A and B might have the same mean, or perhaps B and C, but it appears that brand
A and C have different means.
b)
By rule of thumb, ratio of the largest variance to the smallest variance is
2
1.619835
1
.
1
4
.
1
2
2
<
=
, so we
are okay to pool.
c)
:
H
:
H
a
3
2
1
0
⇔
=
=
μ
they are not equal.
32
.
10
20
20
10
8
.
10
20
2
.
10
20
6
.
9
10
3
2
1
3
3
2
2
1
1
=
+
+
×
+
×
+
×
=
+
+
+
+
=
n
n
n
X
n
X
n
X
n
X
2
3
3
2
2
2
2
1
1
Trt
)
(
)
(
)
(
SS
X
X
n
X
X
n
X
X
n
−
+
−
+
−
=
2
2
2
10.32)

(10.8
20
10.32)

(10.2
20
10.32)

(9.6
10
×
+
×
+
×
=
0.08
1
=
with
2
1
3
=
−
=
df
75.44
)
1
(
)
1
(
)
1
(
SS
2
3
3
2
2
2
2
1
1
=
−
+
−
+
−
=
s
n
s
n
s
n
E
47
3
3
2
1
=
−
+
+
=
n
n
n
df
3.195056
F
3.139979
47
/
2
/
0.05,2,47
=
<
=
=
SSE
SS
F
Trt
We fail to reject the null hypothesis and conclude there is no significant evidence of inequality between
two means.
d)
0.1178672
44
.
75
08
.
10
08
.
10
2
=
+
=
+
=
=
Trt
SS
SSE
SSE
SST
SSE
R
e) A and C are significant different as they have the largest difference in mean. In fact, if you test the equality
of
A
and
C
, you will reject the null hypothesis.
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 Spring '08
 Wherly
 Statistics, Variance

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