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Chapter 10. Hypothesis Tests for Proportions, Mean Differences and Proportion Differences. Figure 10.1 The Sampling Distribution of the Sample Proportion. =. p. = = . 024. p = .06. - PowerPoint PPT Presentation
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Chapter 10
Hypothesis Tests for Proportions, Mean Differences and Proportion
Differences
Figure 10.1 The Sampling Distribution of the Sample Proportion
= n
)1(
p
p
Figure 10.2 The “Null” Sampling Distribution
100
)94.1(06. p
p.06
=
= .024
Figure 10.3 Setting a Boundary on the Null Sampling Distribution
p.06
REJECT H0
zzc = 1.65
= .05
Test Statistic for a (10.1)
Sample Proportion
n
p
)1(
zstat =
Figure 10.4 Showing the Sample Result on the Null Sampling Distribution
zstat = 2.08
= .11.06
REJECT H0
zzc = 1.65
pp
Figure 10.5 Identifying the Critical p
p
zzc = 1.65
.06c = .099
REJECT H0
Figure 10.6 Computing the p-value
p
z 0 z = 2.08
= .06
p-value=.0188 .4812
p
Figure 10.7 The Sampling Distribution of the Sample Mean Difference
=2
22
1
21
nn
21 xx
21 xx
Figure 10.8 The “Null” Sampling Distribution
21 xx 0
Figure 10.9 Setting Boundaries on the Null
Sampling Distribution
21 xx
0
REJECT H0
z zcl = -1.96
REJECT H0
zcu = +1.96
/2 = .025/2 = .025
Test Statistic (10.2) ( values are known)
2
22
1
21
21 0)(
nn
xx
zstat =
Figure 10.10 Showing zstat on the Null Sampling Distribution
REJECT H0
z zcl = -1.96
REJECT H0
zcu = +1.96
zstat = 2.51
0
Estimated Standard Error of the (10.3)Sampling Distribution of Mean Differences (large samples)
2
22
1
21
n
s
n
s
21 xx s =
Test Statistic for Large Samples, (10.4) values unknown
21
0)( 21
xxs
xx
zstat =
Test Statistic for Small Samples, (10.5)
values unknown
21
0)( 21
xxs
xx
tstat =
Pooling Sample (10.6) Standard Deviations
( ) ( )n s n s
n n1 1
22 2
2
1 2
1 1
2
spooled =
Estimated Standard Error of the (10.7) Sampling Distribution of the Sample Mean Difference (small samples)
2
2
1
2 ss
nnpooledpooled
21 xxs =
1. Pool the sample standard deviations:
2. Estimate the standard error (standard deviation) of the sampling distribution:
3. Calculate the test statistic:
tstat =
Calculating tstat
2
2
1
2 ss
nnpooledpooled 21 xxs =
( ) ( )n s n s
n n1 1
22 2
2
1 2
1 1
2
Spooled =
21
0)( 21
xxs
xx
Figure 10.11 The Sampling Distribution of the Sample Proportion Difference
2
22
1
11 )1()1(
nn
21 pp =
21 pp
Figure 10.12 The “Null” Sampling Distribution
21 pp
0
Figure 10.13 Setting the Boundary on the Null Sampling Distribution
21 pp
0zzc = 2.33
0
REJECT H0
= .01
The Test Statistic (10.8)
21 pp
21 0)(
ppz stat
Pooling the Sample Proportions (10.9)
pn p n p
n npooled
1 1 2 2
1 2
Estimated Standard Error (10.10) of the Null Sampling Distribution
21pp
)1()1(21 n
pp
n
pps pooledpooledpooledpooled
Figure 10.14 Showing zstat on the Null Sampling Distribution
0
REJECT H0
zzc = 2.33 0
zstat = .877
21 pp
Test Statistic for Matched (10.11)
Samples Case
ns
d
d
0 tstat =
Standard Deviation of the (10.12)
Sample Mean Differences
1
)( 2
n
dd isd =
