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Ch. 22  Two Population Proportions for Large Samples
Def’n: Two samples drawn from two populations are independent
if the selection of one
sample from one population does not affect the selection of the second sample from the
second population.
Otherwise, the samples are dependent
.
Notation: Two samples require appropriate subscripts.
e.g.
p
1
and
p
2
,
n
1
and
n
2
Properties of the Sampling Distribution of
2
1
ˆ
ˆ
p
p
−
:
If the random samples on which
1
ˆ
p
and
2
ˆ
p
are based are selected independently of one
another, then
1.
2
1
ˆ
ˆ
2
1
p
p
p
p
−
=
−
µ
2.
2
2
2
1
1
1
2
ˆ
2
ˆ
2
ˆ
ˆ
)
1
(
)
1
(
2
1
2
1
n
p
p
n
p
p
p
p
p
p
−
+
−
=
+
=
−
σ
and
2
ˆ
ˆ
ˆ
ˆ
2
1
2
1
p
p
p
p
−
−
=
3. If both
n
1
&
n
2
are large (i.e. if
n
1
p
1
≥
15,
n
1
(1 –
p
1
)
≥
15,
n
2
p
2
≥
15, &
n
2
(1 –
p
2
)
≥
15),
then
1
ˆ
p
and
2
ˆ
p
each have a sampling distribution that is (approximately) normal.
This
implies that the sampling distribution of
2
1
ˆ
ˆ
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 Winter '10
 PaulCartledge

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