Appendix 14
A14.1 One-way Analysis of variance
:H0
321 ==
:H1
At least two means differ
10
15
11
12
A B C D E F G
ANOVA
Source of Variation SS df MS F P-value F crit
Between Groups 91.43 2 45.72 1.09 0.3441 3.16
A14.2 t-test of
D
0:H D1
DD
DD
n/s
x
t−
=
1
2
3
4
5
6
A B C
t-Test: Paired Two Sample for Means
Price shown Price not shown
Mean 56.15 60.31
Variance 243.68 467.71
Observations 100 100
A14.3 Unequal-variances t-test of
21 −
0)(:H 210 =−
0)(:H 211 −
2
1
1
2
3
4
5
A B C
t-Test: Two-Sample Assuming Unequal Variances
Leftover Returned
Mean 61.71 70.57
Variance 48.99 203.98
A14.4 a z-test of
21 pp −
(case 1)
:H0
21 pp −
= 0
21 pp −
1
2
3
A B C D
z-Test: Two Proportions
Topiramate Placebo
b z-test of
21 pp −
(case 1)
:H0
21 pp −
= 0
1
2
3
4
5
A B C D
z-Test: Two Proportions
Topiramate Placebo
Sample Proportions 0.5091 0.1667
Observations 55 48
A14.5a Equal-variances t-test of
21 −
0)(:H 210 =−
1
2
3
4
5
A B C
t-Test: Two-Sample Assuming Equal Variances
Expenses MSA Expenses Regular
Mean 347.24 479.25
Variance 21043 21128
b z-test of
21 pp −
(case 1)
:H0
21 pp −
= 0
21 pp −
1
2
3
4
A B C D
z-Test: Two Proportions
Health MSA Health Regular
Sample Proportions 0.7619 0.7801
A14.6 a One-way analysis of variance
11
16
12
A B C D E F G
ANOVA
Source of Variation SS df MS F P-value F crit
Two-factor analysis of variance
23
24
25
A B C D E F G
ANOVA
Source of Variation SS df MS F P-value F crit
Sample 17024 117024 174.85 0.0000 3.87
A14.7 t-tests of
45 minutes:
:H0
= 45
:H1
< 45
n/s
x
t−
=
5
Standard Deviation 3.63
:H0
:H1
n/s
x
t−
=
1
2
3
4
A B C D
t-Test: Mean
45 minutes
Mean 41.75
:H0
:H1
x
t−
=
1
2
3
4
5
A B C D
t-Test: Mean
60 minutes
Mean 58.75
Standard Deviation 5.02
n/s
1
2
3
4
5
A B C D
t-Test: Mean
80 minutes
Mean 69.05
Standard Deviation 6.31
1
2
3
4
5
A B C D
t-Test: Mean
100 minutes
Mean 90.40
Standard Deviation 12.35
1
2
3
4
5
A B C D
t-Test: Mean
125 minutes
Mean 110.05
Standard Deviation 17.11
A14.8 Two-way analysis of variance
==210 :H
3
:H1
F = 5.29; p-value = .0084. There is sufficient evidence to infer that differences exist between the estimated repair
costs from different appraisers.
A14.9 One-way analysis of variance
:H0
321 ==
:H1
At least two means differ
10
15
11
A B C D E F G
ANOVA
Source of Variation SS df MS F P-value F crit
A14.10 z-test of
21 pp −
(case 2)
15.pp:H 210 −=−
15.pp:H 211 −−
2
22
1
11
2121
n
)p
ˆ
1(p
ˆ
n
)p
ˆ
1(p
ˆ
)pp()p
ˆ
p
ˆ
(
z−
+
−
−−−
=
1
2
3
4
A B C
z-Test: Two Proportions
Comm 1 Comm 2
Sample Proportions 0.268 0.486
A14.11 t-test of
D
D1 :H
< 0
DD
DD
n/s
x
t−
=
1
2
3
4
A B C
t-Test: Paired Two Sample for Means
Prior After
Mean 24.91 26.24
A14.12 Two-factor analysis of variance
29
30
31
32
A B C D E F G
ANOVA
Source of Variation SS df MS F P-value F crit
Sample 427.61 2 213.81 39.97 0.0000 3.06
Columns 20.17 1 20.17 3.77 0.0541 3.91
fitness.
A14.13 Equal-variances t-test of
21 −
0)(:H 210 =−
1
2
3
4
5
6
A B C
t-Test: Two-Sample Assuming Equal Variances
ABS speed No ABS speed
Mean 34.72 33.94
Variance 25.27 25.63
Observations 100 100
A14.14 One-way analysis of variance
10
11
A B C D E F G
ANOVA
Source of Variation SS df MS F P-value F crit
Multiple comparisons
1
2
A B C D E
Multiple Comparisons
A14.15 Equal-variances t-test of
21 −
0)(:H 210 =−
1
2
3
4
5
6
A B C
t-Test: Two-Sample Assuming Equal Variances
Echinacea Placebo
Mean 7.02 7.06
Variance 2.51 2.42
Observations 262 262
A14.16 Two-way analysis of variance
24
25
A B C D E F G
ANOVA
Source of Variation SS df MS F P-value F crit
F = 3.57, p-value = .0428. There is enough evidence to conclude that there are differences in waiting times between
the three resorts.
A14.17a There are 4 levels of ranks and 4 levels of faculties for a total of 16 treatments.
b
23
28
24
A B C D E F G
ANOVA
Source of Variation SS df MS F P-value F crit
F = 2.84, p-value = .0019. There is enough evidence to infer that at least two treatment means differ.
c Factor A (columns) is the faculty. The levels are business, engineering, arts, and science. Factor B (samples) is the
rank. The levels are professor, associate professor, assistant professor, and lecturer.
35
36
A B C D E F G
ANOVA
Source of Variation SS df MS F P-value F crit
A14.18 a z-estimate of p
Sample proportion 0.3569 Confidence Interval Estimate
Sample size 1328 0.357 ±0.026
Confidence level 0.95 Lower confidence limit 0.331
1
2
A B C D E
z-Estimate of a Proportion
b
Sample proportion 0.316 Confidence Interval Estimate
Sample size 1328 0.316 ±0.025
Confidence level 0.95 Lower confidence limit 0.291
1
2
A B C D E
z-Estimate of a Proportion
c t-estimate of µ
n
s
tx 2/
1
2
3
A B C D
t-Estimate: Mean
Dogs
d t-estimate of µ
n
s
tx 2/
1
2
3
A B C D
t-Estimate: Mean
Cats