1
2
3
4
5
6
7
8
9
10
11
12
13
14
A
B
C
t-Test: Two-Sample Assuming Equal Variances
Speeds Before
Speeds After
Mean
31.74
31.42
Variance
4.50
4.41
Observations
100
100
Pooled Variance
4.45
Hypothesized Mean Difference
0
df
198
t Stat
1.07
P(T<=t) one-tail
0.1424
t Critical one-tail
1.6526
P(T<=t) two-tail
0.2849
t Critical two-tail
1.9720
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
2
1
μ
−
μ
0
)
(
:
H
2
1
0
=
μ
−
μ
0
)
(
:
H
2
1
1
<
μ
−
μ
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
+
μ
−
μ
−
−
=
2
1
2
p
2
1
2
1
n
1
n
1
s
)
(
)
x
x
(
t
1
2
3
4
5
6
7
8
9
10
11
12
13
14
A
B
C
t-Test: Two-Sample Assuming Equal Variances
Stops Before
Stops After
Mean
7.82
7.98
Variance
1.83
1.84
Observations
100
100
Pooled Variance
1.83
Hypothesized Mean Difference
0
df
198
t Stat
-0.84
P(T<=t) one-tail
0.2021
t Critical one-tail
1.6526
P(T<=t) two-tail
0.4042
t Critical two-tail
1.9720
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
μ
n
s
t
x
2
/
α
±

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1
2
3
4
5
6
7
A
B
C
D
t-Estimate: Mean
PSI
Mean
4.20
Standard Deviation
1.93
LCL
3.93
UCL
4.46
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
μ
0
:
H
D
0
=
μ
0
:
H
D
1
>
μ
D
D
D
D
n
/
s
x
t
μ
−
=
1
2
3
4
5
6
7
8
9
10
11
12
13
14
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
Pearson Correlation
0.87
Hypothesized Mean Difference
0
df
49
t Stat
3.73
P(T<=t) one-tail
0.000
t Critical one-tail
1.677
P(T<=t) two-tail
0.000
t Critical two-tail
2.010
t = 3.73, p-value = .0002. There is enough evidence to infer that the law discourages bicycle use.
A13.9 z -test of
2
1
p
p
−
(case 1)
0
)
p
p
(
:
H
2
1
0
=
−