n
s
tx 2/
1
2
3
A B C D
t-Estimate: Mean
Acres
A17.17 Equal-variances t-test of µ1 − µ2
H0: µ1 – µ2 = 0
H1: µ1 – µ2 < 0
A17.18
A17.19
)pp(:H 210 −
= 0
)pp(:H 211 −
> 0
A17.20
A17.21
:H0
The two variables are independent
:H1
The two variables are dependent
=
−
=
15
1i i
2
ii
2
e
)ef(
A17.22 t-test of ρ or β1
:H
0
= 0
0:H1
2
r1
2n
rt −
−
=
A17.24 Unequal-variances t-test of µ1 − µ2
H0: µ1 – µ2 = 0
2
r1
2n
rt −
−
=
A17.26 t-test of ρ or β1
:H
0
= 0
0:H1
2
r1
2n
rt −
−
=
:H
0
A17.28 t-test of ρ or β1
:H
0
= 0
Case A17.1
Test of diameters:
Equal-variances t-test of
21 −
1
2
3
4
5
A B C
t-Test: Two-Sample Assuming Equal Variances
Metal Paclitaxel
Mean 3.01 3.00
Variance 0.0655 0.0667
Test of lengths
Equal-variances t-test of
21 −
1
2
3
4
5
A B C
t-Test: Two-Sample Assuming Equal Variances
Metal Paclitaxel
Mean 19.93 19.92
Variance 9.13 8.61
Inadequate blood flow
z-test of
21 pp −
(case 1)
0)pp(:H 210 =−
1
2
3
4
A B C D
z-Test: Two Proportions
Metal Paclitaxel
Sample Proportions 0.1196 0.0468
Blockage reoccurrence
z-test of
21 pp −
(case 1)
0)pp(:H 210 =−
)pp(:H 211 −
> 0
+−
−
=
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
Metal Paclitaxel
Sample Proportions 0.1120 0.0302
Death from cardiac causes
z-test of
21 pp −
(case 1)
)pp(:H 211 −
1
2
3
4
A B C D
z-Test: Two Proportions
Metal Paclitaxel
Sample Proportions 0.0475 0.0423
Death from blockage
z-test of
21 pp −
(case 1)
0)pp(:H 210 =−
21
1
2
3
4
A B C D
z-Test: Two Proportions
Metal Paclitaxel
Sample Proportions 0.0061 0.0076
Case A17.2 a Chi-squared test of a contingency table
:H0
The two variables are independent
:H1
The two variables are dependent
1
2
3
4
5
6
A B C D E F
Contingency Table
Age
Status 1 2 3 TOTAL
1509 354 4867
2611 413 51029
b z-estimate of p
n/)p
ˆ
1(p
ˆ
zp
ˆ2/ −
1
2
3
A B
z-Estimate: Proportion
Status
Sample Proportion 0.5806