Appendix 13
A13.1 Equal-variances t-test of
21 −
0)(:H 210 =−
1
2
3
4
5
A B C
t-Test: Two-Sample Assuming Equal Variances
This Year 3 Years Ago
Mean 8.29 10.36
Variance 8.13 8.43
A13.2 a z-test of
21 pp −
(case 1)
0)pp(:H 210 =−
3
Sample proportion 0.4336 0.2414 P(Z<=z) one-tail 0.0024
z-Test of the Difference Between Two Proportions (Case 1)
Sample 1 Sample 2 z Stat 2.83
z = 2.83, p-value = .0024. There is enough evidence to infer that customers who see the ad are more likely to make a
purchase than those who do not see the ad.
b 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
Ad No Ad
Mean 97.38 92.01
Variance 621.97 283.26
Observations 49 21
t = .90, p-value = .1853. There is not enough evidence to infer that customers who see the ad and make a purchase
spend more than those who do not see the ad and make a purchase.
c z-estimator of p
n
)p
ˆ
1(p
ˆ
zp
ˆ2/
−
Sample size 113 0.4336 0.0914
Confidence level 0.95 Lower confidence limit 0.3423
1
2
A B C D E
z-Estimate of a Proportion
1
2
3
A B C D
t-Estimate: Mean
Ad
A13.3 t-test of
D
0:H D0 =
0:H D1
DD
DD
n/s
x
t−
=
1
2
3
4
5
A B C
t-Test: Paired Two Sample for Means
Before After
Mean 381.00 373.12
Variance 39001 40663
A13.4 Frequency of accidents: z -test of
21 pp −
(case 1)
0)pp(:H 210 =−
1
2
3
4
A B C D E
z-Test of the Difference Between Two Proportions (Case 1)
Sample 1 Sample 2 z Stat 0.47
Sample proportion 0.0840 0.0760 P(Z<=z) one-tail 0.3205
Severity of accidents 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
No ABS ABS
Mean 2075 1714
Variance 450,343 390,409
Observations 42 38
Sample size 42 38 Upper confidence limit 650
1
2
3
4
A B C D E F
t-Estimate of the Difference Between Two Means (Equal-Variances)
Sample 1 Sample 2 Confidence Interval Estimate
Mean 2075 1714 360.48 ±290
A13.5 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
Discount No Discount
Mean 13.06 18.22
Variance 30.26 38.13
Observations 50 50
A13.6 Speeds: Equal-variances t-test of
21 −
0)(:H 210 =−
1
2
3
4
5
A B C
t-Test: Two-Sample Assuming Equal Variances
Speeds Before Speeds After
Mean 31.74 31.42
Variance 4.50 4.41
Proper stops: Equal-variances t-test of
21 −
0)(:H 210 =−
1
2
3
4
5
A B C
t-Test: Two-Sample Assuming Equal Variances
Stops Before Stops After
Mean 7.82 7.98
Variance 1.83 1.84
A13.7 t-estimator of
1
2
3
A B C D
t-Estimate: Mean
PSI
Tire life: LCL = 100(3.93) = 393, UCL = 100(4.46) = 446. We estimate that the average tire life is decreased by
between 393 and 446 miles.
A13.8 t-test of
D
1
2
3
4
5
6
A B C
t-Test: Paired Two Sample for Means
Before After
Mean 28.94 26.22
Variance 61.45 104.30
Observations 50 50
A13.9 z -test of
21 pp −
(case 1)
0)pp(:H 210 =−
0)pp(:H 211 −
+−
−
=
21
21
n
1
n
1
)p
ˆ
1(p
ˆ
)p
ˆ
p
ˆ
(
z
1
2
3
4
A B C D
z-Test: Two Proportions
Cardizem Placebo
Sample Proportions 0.084 0.0797
A13.10 t-test of
200:H
200:H
1
0
=
n/s
x
t−
=
1
2
3
A B C D
t-Test: Mean
Pedestrians
A13.11 Unequal-variances t-test of
21 −
2
2
2
1
2
1
2121
n
s
n
s
)()xx(
t
+
−−−
=
1
2
3
4
5
A B C
t-Test: Two-Sample Assuming Unequal Variances
Quit Did not quit
Mean 2.04 0.72
Variance 2.05 1.40
A13.12 F-test of
2
2
2
1/
1/:H
2
2
2
10
=
1
2
3
4
5
A B C
F-Test Two-Sample for Variances
Brand A Brand B
Mean 145.95 144.78
Variance 16.45 4.25
A13.13 a z-test of
21 pp −
(case 1) (Success = 2)
21 pp −
1
2
3
4
A B C D
z-Test: Two Proportions
Male most Male less
Sample Proportions 0.5962 0.8077
z = –2.36, p-value = .0184. There is enough evidence that men’s choices are affected by the attractiveness of
women’s pictures
b z-test of
21 pp −
(case 1) (Success = 2)
21 pp −
1
2
3
4
A B C D
z-Test: Two Proportions
Female most Female less
Sample Proportions 0.7885 0.8269
z = –.50, p-value = .6188. There is not enough evidence to infer that women’s choices are affected by the
attractiveness of men’s pictures.
21 pp −
+−
−
=
21
21
n
1
n
1
)p
ˆ
1(p
ˆ
)p
ˆ
p
ˆ
(
z
1
2
3
A B C D
z-Test: Two Proportions
Exercisers Watchers
A13.15 a z-test of p
:H0
p = 104,320/425,000 = .245
:H1
p > .245
n
)p1(p
pp
ˆ
z−
−
=
1
2
3
A B C D
z-Test: Proportion
Deliver
z = 1.74, p-value = .0406. There is enough evidence to indicate that the campaign will increase home delivery sales.
b z-test of p
:H0
:H1