STAT 420
Examples #3
Spring 2009
1.
Assume that the distributions of Y
1
and Y
2
are
N
(
µ
1
,
σ
2
)
and
N
(
µ
2
,
σ
2
)
,
respectively. Given the
n
1
= 6 observations of Y
1
,
65, 68, 67, 66, 71, 68
and the
n
2
= 8 observations of Y
2
,
68, 70, 67, 71, 70, 72, 73, 69
test
H
0
:
µ
1
=
µ
2
vs.
H
1
:
µ
1
≠
µ
2
using the ANOVA
F
test. Use a 5%
level of significance. What can you say about the p-value of this test?
Recall:
n
1
= 6,
n
2
= 8,
1
y
= 67.5,
2
y
= 70,
2
1
s
= 4.3,
2
2
s
= 4,
2
pooled
s
=
4.125, H
0
:
µ
1
=
µ
2
t
test statistic:
t
= –
2.279.
t
0.025
(
12
)
= 2.179.
J =
2
. N =
n
1 +
n
2 = 6 + 8 =
14
.
14
965
14
7085.676
...
2
2
1
1
===
⋅⋅
⋅
⋅
⋅
+
+++
N
J
J
ynynyn
y
=
68.92857
.
SSB =
(
)
(
)
(
)
2 2
2
2
2
1
1
...
yynyynyyn
J
J−++−+−
⋅⋅⋅
= 6
⋅
(
67.5 – 68.92857
)
2 + 8
⋅
(
70 – 68.92857
)
2 =
21.42857
.
MSB =
1
21.42857
1
SSB =
−
J
=
21.42857
.
