n
)p1(p
pp
ˆ
z−
−
=
1
2
3
4
5
A B C D
z-Test: Proportion
Deliver
Sample Proportion 0.2825
Observations 400
A13.16 t-tests of
D
a
D0 :H
= 40
1
2
3
4
5
6
A B C
t-Test: Paired Two Sample for Means
SAT after SAT before
Mean 1235 1162
Variance 37970 28844
Observations 40 40
t = 2.98, p-value = .0024. There is enough evidence to conclude that the ETS claim is false.
b
D0 :H
= 110
1
2
3
4
5
6
A B C
t-Test: Paired Two Sample for Means
SAT after SAT before
Mean 1235 1162
Variance 37970 28844
Observations 40 40
A13.17a t-test of
1
2
3
4
5
A B C D
t-Test: Mean
Potatoes
Mean 985.3
Standard Deviation 49.2
b t-estimator of
1
2
3
A B C D
t-Estimate: Mean
Potatoes
Estimate of the total
A13.18
F-test F = 1.05, p-value = .6509. Use equal-variances
A13.19
:H0
21 pp −
= 0
:H1
21 pp −
≠ 0
A19.20
:H0
21 pp −
= 0
:H1
21 pp −
≠ 0
A13.21
:H0
21 pp −
= 0
:H1
21 pp −
A13.22
:H0
21 pp −
= 0
:H1
21 pp −
≠ 0
A13.23
A13.24
A13.25
A13.26
:H0
21 pp −
= 0
:H1
21 pp −
> 0
A13.27
F = 1.26, p-value = .0101 Use Unequal-variances t-test
intention to vote.
A13.28
A13.29
:H0
21 pp −
= 0
:H1
21 pp −
> 0
Success = 1
A13.30
Case A13.1 California Verbal Learning Test (CVLT) scores
Equal-variances t-test of
21 −
1
2
3
4
5
A B C
t-Test: Two-Sample Assuming Equal Variances
User Nonuser
Mean 71.53 69.66
Variance 82.64 49.71
t = 1.16, p-value = .1246.
Logical Memory Test (LMT) score
+
−−−
=
21
2
p
2121
n
1
n
1
s
)()xx(
t
1
2
3
4
5
A B C
t-Test: Two-Sample Assuming Equal Variances
User Nonuser
Mean 57.67 56.64
Variance 27.24 28.98
Conclusion of both tests: There is not enough evidence to conclude that HRT helps improve cognitive performance
among women over 75.
Case A13.2 a z-estimator of p
1
A B
z-Estimate: Proportion
b z-estimator of p
1
2
3
A B
z-Estimate: Proportion
Modify
Sample Proportion 0.6466
:H0
21 pp −
= 0
:H1
21 pp −
< 0
+−
−
=
21
21
n
1
n
1
)p
ˆ
1(p
ˆ
)p
ˆ
p
ˆ
(
z
1
2
3
4
5
A B C D
z-Test: Two Proportions
LSES HSES
Sample Proportions 0.1521 0.6732
Observations 447 153
d z-test of
21 pp −
(case 1)
:H0
21 pp −
= 0
:H1
21 pp −
+−
−
=
21
21
n
1
n
1
)p
ˆ
1(p
ˆ
)p
ˆ
p
ˆ
(
z
1
2
3
4
5
A B C D
z-Test: Two Proportions
LSES HSES
Sample Proportions 0.1588 0.4641
Observations 447 153
Case A13.3 a z-test of p (success = 1, vote “No“)
:H0
p = .5
:H1
p > .5
n
)p1(p
pp
ˆ
z−
−
=
1
2
3
4
A B C D
z-Test: Proportion
Planned vote
Sample Proportion 0.5382
b z-estimator
21 pp −
(success = 2, vote “Yes”)
2
22
1
11
2/21 n
)p
ˆ
1(p
ˆ
n
)p
ˆ
1(p
ˆ
z)p
ˆ
p
ˆ
(−
+
−
−
1
2
A B C D
z-Estimate: Two Proportions
LCL = .4123, UCL = .5397. We estimate that the difference between French-speaking and English-speaking
Quebecers in their support for separation lies between 41.23% and 53.97%.