Chapter 14
14.1a
555
)20(5)15(5)10(5
x++
++
=
= 15
ANOVA Table
Source Degrees of Freedom Sum of Squares Mean Squares F
Treatments
21k =−
SST = 250
2
250
1k
SST =
−
= 125
50
125
MSE
MST =
= 2.50
ANOVA Table
Source Degrees of Freedom Sum of Squares Mean Squares F .
Treatments
21k =−
SST = 500
2
500
1k
SST =
−
= 250
50
250
MSE
MST =
= 5.00
Error
27kn =−
SSE = 1350
50
27
1350
kn
SSE ==
−
__________________________________________
ANOVA Table
Source Degrees of Freedom Sum of Squares Mean Squares F
ANOVA Table
Source Degrees of Freedom Sum of Squares Mean Squares F
14.3 a
34.35
18111410
)40(18)33(11)35(14)30(10
x=
+++
+++
=
Source Degrees of Freedom Sum of Squares Mean Squares F
Treatments
31k =−
SST = 737.9
0.246
3
9.737
1k
SST ==
−
60.24
00.10
0.246
MSE
MST ==
Error
49kn =−
SSE = 490.0
00.10
49
0.490
kn
SSE ==
−
ANOVA Table
Source Degrees of Freedom Sum of Squares Mean Squares F
c No change
14.4
==210 :H
3
:H1
At least two means differ.
Rejection region:
26.4FFF 9,2,05.kn,1k, ==−−
Finance Marketing Management
ANOVA table
Source Degrees of Freedom Sum of Squares Mean Squares F .
Treatments
21k =−
SST = 26.00
00.13
2
00.26
1k
SST ==
−
82.4
69.2
00.13
MSE
MST ==
69.2
25.24
14.5
==210 :H
3
:H1
At least two means differ.
Rejection region:
36.6FFF 15,2,01.kn,1k, ==−−
SSE =
=− 2
jj s)1n(
(6 –1)(1.87) + (6 – 1)(2.30) + (6 – 1)(1.47) = 28.17
ANOVA table
Source Degrees of Freedom Sum of Squares Mean Squares F .
14.6
==210 :H
3
:H1
At least two means differ.
Rejection region:
89.3FFF 12,2,05.kn,1k, ==−−
BA BSc BBA
Mean 3.94 4.78 5.76
=− 2
jj s)1n(
ANOVA table
Source Degrees of Freedom Sum of Squares Mean Squares F .
14.7
==210 :H
3
:H1
At least two means differ.
Rejection region:
10.5FFF 12,2,025.kn,1k, ==−−
SST =
−2
jj )xx(n
= 5(6.4 – 9.2)
2
+ 5(10.4 – 9.2)
2
+ 5(10.8 – 9.2)
2
= 59.2
SSE =
=− 2
jj s)1n(
(5 –1)(48.3) + (5 – 1)(16.3) + (5 – 1)(37.7) = 409.2
ANOVA table
Source Degrees of Freedom Sum of Squares Mean Squares F .
14.8
==210 :H
3
:H1
At least two means differ.
Rejection region:
07.4FFF 8,3,05.kn,1k, ==−−
IBM Dell HP Other
2
2
2
ANOVA table
Source Degrees of Freedom Sum of Squares Mean Squares F .
8
kn
−
F = .81, p-value = .5224. There is not enough evidence to conclude that there are differences in age between the
computer brands.
==210 :H
3
:H1
ANOVA table
Source Degrees of Freedom Sum of Squares Mean Squares F .
Treatments
31k =−
SST = 430.95
65.143
3
95.430
1k
SST ==
−
83.2
70.50
65.143
MSE
MST ==
Error
77kn =−
SSE = 3903.57
70.50
77
57.3903
kn
SSE ==
−
14.10a
==210 :H
3
4
=
:H1
At least two means differ.
Rejection region:
68.2FFF 116,3,05.kn,1k, =−−
Grand mean = 101.0
Source Degrees of Freedom Sum of Squares Mean Squares F .
Treatments
31k =−
SST = 8,464
821,2
3
464,8
1k
SST ==
−
94.2
0.961
821,2
MSE
MST ==
Error
116kn =−
SSE = 111,480
0.961
116
480,111
kn
SSE ==
−
14.11
==210 :H
3
4
=
:H1
At least two means differ.
Rejection region:
61.2FFF 275,3,05.kn,1k, =−−
Grand mean = 218.0
ANOVA table
Source Degrees of Freedom Sum of Squares Mean Squares F .
Treatments
31k =−
SST = 45,496
165,15
3
496,45
1k
SST ==
−
66.14
034,1
165,15
MSE
MST ==
14.12
==210 :H
3
4
=
5
=
:H1
At least two means differ.
Rejection region:
48.3FFF 120,4,01.kn,1k, ==−−
Grand mean = 173.3
ANOVA table
Source Degrees of Freedom Sum of Squares Mean Squares F .
Treatments
41k =−
SST = 17,251
6.312,4
4
251,17
1k
SST ==
−
32.3
5.299,1
6.312,4
MSE
MST ==
c The histograms are approximately bell-shaped with similar sample variances.
14.13
==210 :H
3
4
=
:H1
At least two means differ.
Rejection region:
61.2FFF 297,3,05.kn,1k, =−−
Grand mean = 16.11
ANOVA table
Source Degrees of Freedom Sum of Squares Mean Squares F .
F = 19.83, p-value = 0. There is enough evidence to infer that there are differences exist between the four groups.
14.14
==210 :H
3
:H1
At least two means differ.
Rejection region:
15.3FFF 57,2,05.kn,1k, =−−
ANOVA table
Source Degrees of Freedom Sum of Squares Mean Squares F .
14.15
==210 :H
3
:H1
At least two means differ.
Rejection region:
07.3FFF 297,2,05.kn,1k, =−−
Grand mean = 5.48
ANOVA table
Source Degrees of Freedom Sum of Squares Mean Squares F .
F = 1.73, p-value = .1783. There is not enough evidence of a difference between the three departments.
14.16
==210 :H
3
4
=
:H1
At least two means differ.
Rejection region:
68.2FFF 116,3,05.kn,1k, =−−
Grand mean = 77.39
ANOVA table
Source Degrees of Freedom Sum of Squares Mean Squares F .
14.17
==210 :H
3
:H1
At least two means differ.
SSE =
−2
jj s)1n(
= (50 –1)(48.23) + (50 – 1)(54.54) + (50 – 1)(33.85) = 6,695
ANOVA table
Source Degrees of Freedom Sum of Squares Mean Squares F .
147
kn
−
F = 13.95, p-value = 0. There is sufficient evidence to conclude that the leaf sizes differ between the 3 groups.
b Nicotine: Rejection region:
06.3FFF 147,2,05.kn,1k, =−−
Grand mean = 13.00
−2
jj s)1n(
ANOVA table
Source Degrees of Freedom Sum of Squares Mean Squares F .
F = 101.47, p-value = 0. There is sufficient evidence to infer that the amounts of nicotine differ between the 3
groups.
Grand mean = 36.23
ANOVA table
Source Degrees of Freedom Sum of Squares Mean Squares F .
F = 25.60, p-value = 0. There is sufficient evidence to infer that the ages of the four groups of cereal buyers differ.
b Incomes: Rejection region:
61.2FFF 291,3,05.kn,1k, =−−
Grand mean = 39.97
ANOVA table
Source Degrees of Freedom Sum of Squares Mean Squares F .
F = 7.37, p-value = .0001. There is sufficient evidence to conclude that incomes differ between the four groups of
cereal buyers.
c Education: Rejection region:
61.2FFF 291,3,05.kn,1k, =−−
Grand mean = 11.98
ANOVA table
Source Degrees of Freedom Sum of Squares Mean Squares F .
Treatments
31k =−
SST =21.71
24.7
3
71.21
1k
SST ==
−
82.1
97.3
24.7
MSE
MST ==
14.19
==210 :H
3
:H1
At least two means differ.
Rejection region:
15.3FFF 57,2,05.kn,1k, =−−
ANOVA table
Source Degrees of Freedom Sum of Squares Mean Squares F .
Treatments
21k =−
SST = 5,011
506,2
2
011,5
1k
SST ==
−
41.3
0.735
506,2
MSE
MST ==
14.20
==210 :H
3
:H1
At least two means differ.
ANOVA table
Source Degrees of Freedom Sum of Squares Mean Squares F .
14.21
==210 :H
3
:H1
At least two means differ.
14.22 Reading
==210 :H
3
:H1
At least two means differ.
Mathematics
==210 :H
3
:H1
At least two means differ.
Science
==210 :H
3
:H1
At least two means differ.
14.23
==210 :H
3
:H1
At least two means differ.
14.24
==210 :H
3
:H1
At least two means differ.
14.25
==210 :H
3
:H1
At least two means differ.
14.26
==210 :H
3
:H1
At least two means differ.
14.27
==210 :H
3
:H1
At least two means differ.
14.28
==210 :H
3
:H1
At least two means differ.
14.29
==210 :H
3
:H1
At least two means differ.
14.30
==210 :H
3
:H1
At least two means differ.
14.31
==210 :H
3
:H1
At least two means differ.
14.32 H0:μ1 = μ 2= μ3 = μ4 = μ5
H1: At least two means differ.
14.33
==210 :H
3
:H1
At least two means differ.
14.34
43210 :H ===
:H1
At least two means differ.
14.35
==210 :H
3
:H1
At least two means differ.