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Appendix 13 A13.1 Equal-variances t-test of 1 2
H 0 : ( 1 2 ) 0 H 1 : ( 1 2 ) 0
t
( x 1 x 2 ) ( 1 2 ) 1 1 n1 n 2
s 2p
t = –5.09, p-value = 0. There is overwhelming evidence to conclude that there has been a decrease over the past three years. A13.2 a z-test of p1 p 2 (case 1)
H 0 : ( p1 p 2 ) 0 H 1 : ( p1 p 2 ) 0
z
( pˆ1 pˆ 2 ) 1 1 pˆ(1 pˆ) n1 n 2
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download full file at //testbankcafe.com 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 1 2
H 0 : ( 1 2 ) 0 H 1 : ( 1 2 ) 0
t
( x 1 x 2 ) ( 1 2 ) 1 1 n1 n 2
s 2p
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
pˆ(1 pˆ) n
pˆ z / 2
We estimate that between 34.23% and 52.50% of all customers who see the ad will make a purchase. d t-estimator of x t/2
s n
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download full file at //testbankcafe.com
We estimate that the mean amount spent by customers who see the ad and make a purchase lies between $90.22 and $104.55. A13.3 t-test of D
H0 : D 0 H1 : D 0 t
xD D sD / n D
t = .70, p-value = .2438. There is not enough evidence to conclude that the equipment is effective. A13.4 Frequency of accidents: z -test of p1 p 2 (case 1)
H 0 : ( p1 p 2 ) 0 H 1 : ( p1 p 2 ) 0
z
( pˆ1 pˆ 2 ) 1 1 pˆ(1 pˆ) n1 n 2
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download full file at //testbankcafe.com
z = .47, p-value = .32053. There is not enough evidence to infer that ABS-equipped cars have fewer accidents than cars without ABS. Severity of accidents Equal-variances t-test of 1 2
H 0 : ( 1 2 ) 0 H 1 : ( 1 2 ) 0
t
( x 1 x 2 ) ( 1 2 ) 1 1 n1 n 2
s 2p
Estimate of the difference between two means (equal-variances)
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download full file at //testbankcafe.com We estimate that the mean repair cost for non-ABS-equipped cars will be between $71 and $650 more than the mean repair cost for ABS-equipped cars. A13.5 Equal-variances t-test of 1 2
H 0 : ( 1 2 ) 0 H 1 : ( 1 2 ) 0
t
( x 1 x 2 ) ( 1 2 ) 1 1 n1 n 2
s 2p
t = –4.41, p-value = 0. There is enough evidence to infer that the discount plan works. A13.6 Speeds: Equal-variances t-test of 1 2
H 0 : ( 1 2 ) 0 H 1 : ( 1 2 ) 0
t
( x 1 x 2 ) ( 1 2 ) 1 1 n n 2 1
s 2p
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download full file at //testbankcafe.com
t = 1.07, p-value = .1424. There is not enough evidence to infer that speed bumps reduce speeds. Proper stops: Equal-variances t-test of 1 2
H 0 : ( 1 2 ) 0 H 1 : ( 1 2 ) 0
t
( x 1 x 2 ) ( 1 2 ) 1 1 n1 n 2
s 2p
t = –.84, p-value = .2021. There is not enough evidence to infer that speed bumps increase the number of proper stops. A13.7 t-estimator of
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download full file at //testbankcafe.com x t/2
s n
LCL = 3.93, UCL = 4.46. We estimate that on average tires are between 3.93 and 4.46 pounds per square inch below the recommended amount. 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. Gasoline consumption: LCL = .1(3.93) = .393, UCL = .1(4.46) = .446. We estimate that average gasoline consumption increases by between .393 and .446 gallons per mile. A13.8 t-test of D
H0 : D 0 H1 : D 0 t
xD D sD / n D
t = 3.73, p-value = .0002. There is enough evidence to infer that the law discourages bicycle use.
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download full file at //testbankcafe.com A13.9 z -test of p1 p 2 (case 1)
H 0 : ( p1 p 2 ) 0 H 1 : ( p1 p 2 ) 0
( pˆ1 pˆ 2 )
z
1 1 pˆ(1 pˆ) n1 n 2
z = .22, p-value = .4126. There is not enough evidence to indicate that Cardizem users are more likely to suffer headache and dizziness side effects than non-users. A13.10 t-test of
H 0 : 200 H 1 : 200 t
x s/
n
t = .96, p-value = .1711. There is not enough evidence to infer that the franchiser should build on this site. A13.11 Unequal-variances t-test of 1 2
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download full file at //testbankcafe.com H 0 : ( 1 2 ) 0 H 1 : ( 1 2 ) 0
t
( x 1 x 2 ) ( 1 2 ) s 12 s 22 n1 n 2
t = 14.06, p-value = 0. There is enough evidence to infer that quitting smoking results in weight gains. A13.12 F-test of 12 / 22
H 0 : 12 / 22 1 H1 : 12 / 22 1
F
s12 s 22
F = 3.87, p-value = 0. There is overwhelming evidence to infer that Brand B is superior to Brand A. A13.13 a z-test of p1 p 2 (case 1) (Success = 2)
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download full file at //testbankcafe.com H 0 : p1 p 2 = 0 H1 :
z
1 2 3 4 5 6 7 8 9 10 11
p1 p 2
0
( pˆ1 pˆ 2 ) 1 1 pˆ(1 pˆ) n1 n 2
A z-Test: Two Proportions
B
C
D
Male most Male less 0.5962 0.8077 52 52 0 -2.36 0.0092 1.6449 0.0184 1.96
Sample Proportions Observations Hypothesized Difference z Stat P(Z