Download Chapter 8

Chapter 8
Interval Estimates For Proportions,
Mean Differences And Proportion
Differences
Figure 8.1 The Sampling Distribution of p
for Our Small-Scale Illustration
p
f(
p)
0.0
1/6 = .167
.5
4/6 = .667
1.0
1/6 = .167
1.00
Figure 8.2
A Bar Chart Showing the
Sampling Distribution of p
P( p )
.667
.167
0
.5
1.0
Sample Proportion of
Favorable Responses
p
The Sampling Distribution of the
Sample Proportion
The sampling distribution of the sample
proportion is the probability distribution of
all possible values of the sample
proportion, p , when a sample of size n is
taken from a particular population.
Standard Deviation of the Sampling (8.1)
Distribution of the Sample Proportion
p 
 (1   )
n
Figure 8.3 The Sampling Distribution of
the Sample Proportion
p 
m
 (1   )
n
p
Interval Estimate for a
Population Proportion
pz
 (1   )
n
(8.2)
Interval Estimate for a
Population Proportion using
the Estimated Standard Error
p(1  p)
pz
n
(8.3)
Determining Sample Size for
(8.4)
Estimating a Population Proportion
 z ( )(1   ) 
n= 

E


2
The Sampling Distribution of the
Sample Mean Difference
The sampling distribution of the sample mean
difference is the probability distribution of all
possible values of the sample mean difference,
x1 - x 2 , when a sample of size n1 is taken from
one population and a sample of size n2 is taken
from another.
Standard Deviation of the Sampling (8.5)
Distribution of the Sample Mean Difference

x1 - x 2
=
 12
n1

 22
n2
Figure 8.4 The Sampling Distribution of
Sample Mean Difference
 x x 
1
m1 – m2
2
 12
n1

 22
n2
x1  x2
Estimating the Difference Between (8.6)
the Means of Two Populations
( x1  x2 )  z
1
2
n1

2
2
n2
Estimating the Difference between the
Means of Two Populations:
Large Sample Sizes, Population Standard
Deviations are Unknown
2
1
2
2
s s
(x1  x 2 )  z

n1 n 2
(8.7)
Pooled Sample Standard Deviation (8.8)
s pooled
(n1-1 )s  (n 2 -1 )s

n1  n2 -2
2
1
2
2
Estimating the Difference between (8.9)
Means of Two Populations:
Small Sample Sizes, Population Standard
Deviations are Unknown but equal
( x1  x2 )  t
2
pooled
s
n1

2
pooled
s
n2
The Sampling Distribution of the
Sample Proportion Difference
The sampling distribution of the sample
proportion difference is the probability
distribution of all possible values of the
sample proportion difference, p1 - p 2 , when
a sample of size n1 is taken from one
population and a sample of size n2 is taken
from another.
Standard Deviation of the
(8.10)
Sampling Distribution of the Sample
Proportion Difference
 p1  p2 
  1 1   1     2 1   2 
n1
n2
Figure 8.5 The Sampling Distribution of
Sample Proportion Difference
 p1  p2 
1 – 2
  1 1   1     2 1   2 
n1
n2
p1  p2
Estimating the Difference between (8.11)
Two Population Proportions
1 (1  1 )  2 (1   2 )
( p1  p2 )  z

n1
n2
Estimating the Difference between (8.12)
Two Population Proportions,
p s replace s
p1 (1  p1 ) p2 (1  p2 )
( p1  p2 )  z

n1
n2
Estimating the Difference in (8.13)
Two Population Means: Matched Samples
 sd 
d  t 

 n
Standard Deviation of Matched
Sample Differences
sd =
2
(
d

d
)
 i
n 1
(8.14)