10.4 Proportions - Outcome 10.4 Using the sampling...

Hypothesis Tests
Statistical Inference
About Means and
Proportions with Two
Populations

BUQU 1230

Esther Tiessen
Outcome 10.4—
Using the sampling
distribution
of , be able to
develop interval
estimates and
conduct hypothesis
tests about the
difference between
two population
proportions.
p
1
- p
2

Hypothesis Tests
Two Populations
Statistical inference about the difference between
two population:
ü
means (σ1 and σ2 known)
ü
means (σ1 and σ2 unknown)
ü
means (matched samples)
 proportions

Hypothesis Tests
Two Populations
Statistical inference about the difference between
two population:
ü
means (σ1 and σ2 known)
ü
means (σ1 and σ2 unknown)
ü
means (matched samples)
 proportions
z -Test:Two-Sample for Proportions

Hypothesis Tests

difference between 2 population proportions:
D = p 1– p 2

to make inferences about D,
◦
take independent simple random samples from 2
populations
◦
use sampling distribution of

if n1 . p1 , n1 .(1 – p1 ), n2 . p2 , n2 .(1 – p2 ) are all ≥ 5, then
sampling distribution of can be approximated by
normal distribution

mean is D = p 1– p 2
Statistical Inference about the Difference
between Two Population Proportions
d = p
1
- p
2
d = p
1
- p
2

Hypothesis Tests

difference between 2 population proportions:
D = p 1– p 2

to make inferences about D,
◦
take independent simple random samples from 2
populations
◦
use sampling distribution of

if n1 . p1 , n1 .(1 – p1 ), n2 . p2 , n2 .(1 – p2 ) are all ≥ 5, then
sampling distribution of can be approximated by
normal distribution

mean is D = p 1– p 2
Statistical Inference about the Difference
between Two Population Proportions
d = p
1
- p
2
d = p
1
- p
2
Use for
both
interval
estimation
and
hypothesis
testing

Hypothesis Tests

difference between 2 population proportions:
D = p 1– p 2

sampling distribution of
Statistical Inference about the Difference
between Two Population Proportions
d = p
1
- p
2

Hypothesis Tests
Statistical Inference about the Difference
between Two Population Proportions
Population Proportion
parameter
p
point estimator
standard error
margin of error
interval estimate
p
σ
x
=
p 1 - p
( 29
n
z
α 2
p 1 - p
( 29
n
p ± z
α 2
p 1 - p
( 29
n
Recall from
chapter 8

Hypothesis Tests
Statistical Inference about the Difference
between Two Population Proportions
Population Proportion
Difference Between 2
Population Proportions
parameter
p D = p 1 – p 2
point estimator
standard error
margin of error
interval estimate
p
d = p
1
- p
2
σ
x
=
p 1 - p
( 29
n
σ
d
=
p
1
1 - p
1
( 29
n
1
+
p
2
1 - p
2
( 29
n
2
z
α 2
p 1 - p
( 29
n
z
α 2
p
1
1 - p
1
( 29
n
1
+
p
2
1 - p
2
( 29
n
2
p ± z
α 2
p 1 - p
( 29
n
d ± z
α 2
p
1
1 - p
1
( 29
n
1
+
p
2
1 - p
2
( 29
n
2

Hypothesis Tests
Statistical Inference about the Difference
between Two Population Proportions
Population Proportion
Difference Between 2
Population Proportions
parameter
p D = p 1 – p 2
point estimator
standard error
margin of error
interval estimate
p
d = p
1
- p
2
σ
x
=
p 1 - p
( 29
n
σ
d
=
p
1
1 - p
1
( 29
n
1
+
p
2
1 - p
2
( 29
n
2
z
α 2
p 1 - p
( 29
n
z
α 2
p
1
1 - p
1
( 29
n
1
+
p
2
1 - p
2
( 29
n
2
p ± z
α 2
p 1 - p
( 29
n
d ± z