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APPM 4/5570
Solutions to Problems from Section 9.1 and 9.2
3. Test statistic
Z
=
X

Y

5000
r
S
2
1
n
1
+
S
2
2
n
2
=
42
,
500

40
,
400

5000
q
2200
2
45
+
1900
2
45
≈ 
6
.
69
The rejection region is the upper tail area under the
z
curve above the value
2
.
33.
Conclusion: The test statistic is defnitely not in there or even close! We Fail to
reject
H
0
in Favor oF
H
a
at 0
.
01 level oF signifcance or at any almost other level!
The data does not at all suggest that the premium brand has a true average
tread liFe that is at least 5
,
000 more than that For the economy brand.
The Pvalue For this problem is approximately 1
.
000.
7. Let
μ
1
be the true mean boredom proneness rating For males and let
μ
2
be the
true mean boredom proneness rating For Females.
Hypotheses:
H
0
:
μ
1

μ
2
= 0
H
a
:
μ
1

μ
2
>
0
Test Statistic:
Z
=
X

Y

5000
r
S
2
1
n
1
+
S
2
2
n
2
=
10
.
40

9
.
26

0
q
4
.
83
2
97
+
4
.
68
2
148
≈
1
.
83
Rejection Region: The rejection region is the upper tail area under the
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This note was uploaded on 01/23/2011 for the course APPM 5440 at Colorado.
 '08
 staff

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