Inferences Based on Two Samples:
Confidence Intervals and
Tests of Hypothesis
Chapter 7
7.2
a.
1
x
μ
=
μ
1
= 12
1
1
1
4
64
x
n
σ
σ
=
=
= .5
b.
2
x
μ
=
μ
2
= 10
2
2
2
3
64
x
n
σ
σ
=
=
= .375
c.
1
2
x
x
μ
−
=
μ
1
−
μ
2
= 12
−
10 = 2
1
2
2
2
2
2
1
2
1
2
4
3
2
64
64
64
x
x
n
n
σ
σ
σ
−
=
+
=
+
=
5
= .625
d.
Since
n
1
≥
30 and
n
2
≥
30, the sampling distribution of
1
2
x
x
−
is approximately normal by
the Central Limit Theorem.
7.4
Assumptions about the two populations:
1.
Both sampled populations have relative frequency distributions that are approximately
normal.
2.
The population variances are equal.
Assumptions about the two samples:
The samples are randomly and independently selected from the population.
7.6
a.
2
p
s
=
2
2
1
1
2
2
1
2
(
1)
(
1)
(25
1)120
(25
1)100
5280
2
25
25
2
48
n
s
n
s
n
n
−
+
−
−
+
−
=
=
+
−
+
+
= 110
b.
2
p
s
=
(20
1)12
(10
1)20
408
20
10
2
28
−
+
−
=
+
−
= 14.5714
c.
2
p
s
=
(6
1).15
(10
1).2
2.55
6
10
2
14
−
+
−
=
+
−
= .1821
d.
2
p
s
=
(16
1)3000
(17
1)2500
85,000
16
17
2
31
−
+
−
=
+
−
= 2741.9355
e.
2
p
s
falls near the variance with the larger sample size.
Inferences Based on Two Samples: Confidence Intervals and Tests of Hypothesis
201

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