14.76
==210 :H
3
4
=
:H1
At least two means differ.
Rejection region:
1bkn,1k,
FF +−−−
12,3,01.
F=
= 5.95
SST =
8.53])3.82.8()3.88.10()3.80.8()3.82.6[(5)x]T[x(b 2222
k
1j
2
j=−+−+−+−=−
=
ANOVA Table
Source Degrees of Freedom Sum of Squares Mean Squares F
Treatments 3 53.8 17.93 1.65
14.77 ANOVA Table
Source Degrees of Freedom Sum of Squares Mean Squares F
Treatments 2 204.2 102.11 4.54
==210 :H
:H1
==210 :H
=
14.78 ANOVA Table
Source Degrees of Freedom Sum of Squares Mean Squares F
Treatments 2 7,131 3,566 123.36
1bkn,1k,
FF +−−−
14.79 ANOVA Table
Source Degrees of Freedom Sum of Squares Mean Squares F
Treatments 2 10.26 5.13 .86
==210 :H
Rejection region:
1bkn,1k,
FF +−−−
= 38,2,05.
F
3.23
F = .86, p-value = .4313. There is not enough evidence to conclude that there are differences in sales ability between
the holders of the three degrees.
b
==210 :H
…
20
=
14.80 ANOVA Table
Source Degrees of Freedom Sum of Squares Mean Squares F
Treatments 3 4,206 1,402 21.16
==210 :H
3
4
:H1
F = 21.16, p-value = 0. There is sufficient evidence to conclude that differences in completion times exist between
the four forms.
b
==210 :H
…
30
=
:H1
14.81
==210 :H
3
=
4
=
5
=
6
=
7
:H1
At least two means differ.
ANOVA Table
Source Degrees of Freedom Sum of Squares Mean Squares F
14.82 ANOVA Table
Source Degrees of Freedom Sum of Squares Mean Squares F
Treatments 4 1,406.4 351.6 10.72
==210 :H
3
4
5
:H1
==210 :H
36
=
14.83
==210 :H
3
=
4
:H1
At least two means differ.
ANOVA Table
Source Degrees of Freedom Sum of Squares Mean Squares F
Treatments 3 563.82 187.9 15.06
14.84
==210 :H
3
:H1
At least two means differ.
14.85
==210 :H
3
:H1
At least two means differ.
14.86
==210 :H
3
4
=
:H1
At least two means differ.
14.87
==210 :H
3
4
=
:H1
At least two means differ.
14.88 ANOVA Table
Source Degrees of Freedom Sum of Squares Mean Squares F
Factor A 2 1,560 780 5.86
14.89 ANOVA Table
Source Degrees of Freedom Sum of Squares Mean Squares F
Factor A 3 203 67.67 .72
14.90 ANOVA Table
30
4.91 ANOVA Table
36
14.92 ANOVA Table
42
23
24
25
A B C D E F G
ANOVA
Source of Variation SS df MS F P-value F crit
Sample 5.33 1 5.33 1.23 0.2995 5.32
29
30
31
A B C D E F G
ANOVA
Source of Variation SS df MS F P-value F crit
Sample 177.25 2 88.63 9.99 0.0012 3.55
35
36
A B C D E F G
ANOVA
Source of Variation SS df MS F P-value F crit
14.93 ANOVA Table
42
14.94 a There are 12 treatments.
b There are two factors, tax form and income group.
c There are a = 4 forms and b = 3 income groups.
14.95 a Detergents and temperatures
b The response variable is the whiteness score.
c There are a = 5 detergents and b = 3 temperatures.
35
36
A B C D E F G
ANOVA
Source of Variation SS df MS F P-value F crit
28
29
30
31
A B C D E F G
ANOVA
Source of Variation SS df MS F P-value F crit
Sample 6719 2 3359.4 4.11 0.0190 3.08
14.96 a Factor A is the drug mixture and factor B is the schedule.
b The response variable is the improvement index.
c There are a = 4 drug mixtures and b = 2 schedules.
30
14.97 a There are 2 factors—class configuration and time period.
b The response variable is the number of times students ask and answer questions.
c There are 2 levels of class configuration and 3 levels of time period.
29
30
A B C D E F G
ANOVA
Source of Variation SS df MS F P-value F crit
23
24
25
A B C D E F G
ANOVA
Source of Variation SS df MS F P-value F crit
Sample 14.40 1 14.40 0.57 0.4548 4.15
ANOVA
Source of Variation SS df MS F P-value F crit
Sample 13.33 1 13.33 1.58 0.2203 4.26
14.98
14.99
42
14.100
36
23
24
25
A B C D E F G
ANOVA
Source of Variation SS df MS F P-value F crit
Sample 16.04 1 16.04 14.74 0.0005 4.11
35
36
37
A B C D E F G
ANOVA
Source of Variation SS df MS F P-value F crit
Sample 0.000309 3 0.000103 0.66 0.5798 2.90
29
30
31
A B C D E F G
ANOVA
Source of Variation SS df MS F P-value F crit
Sample 211.78 2 105.89 21.04 0.0000 3.22
14.102
==210 :H
3
=
4
:H1
At least two means differ.
14.103a
==210 :H
3
=
4
=
5
:H1
At least two means differ.
29
30
31
A B C D E F G
ANOVA
Source of Variation SS df MS F P-value F crit
Sample 2118.4 2 1059.22 24.48 0.0000 3.17