Preliminary data analyses indicate that it is reasonable to consider the assumptions for one–way ANOVA satisfied. Use
Minitab to perform the required hypothesis test using the p–value approach.
49)
At the 0.025 significance level, do the data provide sufficient evidence to conclude that a
difference exists between the population means of the three different brands? The sample
data are given below.
Brand A
32
34
37
33
36
39
Brand B
27
24
33
30
Brand C
22
25
32
22
21
49)
Preliminary data analyses indicate that it is reasonable to consider the assumptions for one–way ANOVA satisfied.
Perform the required hypothesis test using the critical–value approach.
50)
A realtor wishes to compare the square footage of houses in 4 different cities, all of which
are priced approximately the same. The data are listed below. Can the realtor conclude that
the mean square footage in the four cities are equal? Use = 0.01.
City #1 City #2 City #3 City #4
2150 1650 1530 2400
1980 1540 1750 2350
2000 1690 1580 2600
2210 1780 1600 2150
1900 1500 2000
1670 2200
2350
50)
Preliminary data analyses indicate that it is reasonable to consider the assumptions for one–way ANOVA satisfied. Use
Minitab to perform the required hypothesis test using the p–value approach.
51)
At the 0.025 significance level, do the data provide sufficient evidence to conclude that a
difference exists between the population means of the four different brands? The sample
data are given below.
Brand A
17
20
21
22
21
Brand B
18
18
23
25
26
Brand C
21
24
25
26
29
29
Brand D
22
25
27
29
35
36
37
51)
Provide an appropriate response.
52)
A one–way ANOVA is being performed. Suppose that SST =129.7 and SSE =76.6. Find the
value of the third sum of squares, give its notation, state its name and the source of
variation it represents.
52)
53)
A one–way ANOVA is to be performed. The following sample data are obtained.
x1= 20, x2= 30, x3= 40
The common population standard deviation for the three populations is 2.5. Do you think
that the difference between the sample means could be due to variation within the
populations or does it seem clear that the difference between the sample means is due to a
difference between population means? Do you think that the null hypothesis would be
rejected? Explain your thinking.
53)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
54)
A one–way ANOVA is being performed. True or false: The null hypothesis will be rejected if SSE is
large relative to SSTR.
A)
True
B)
False
Find the required q–value.
55)
For a q–curve with parameters = 3 and = 8, find the q–value having area 0.01 to its right.
A)
15.6
B)
4.04
C)
8.85
D)
5.63
56)
For a q–curve with parameters = 5 and = 3, find q0.01 .
A)
5.32
B)
8.52
C)
4.11
D)
13.3
Provide an appropriate response.
57)
True or false: A one–way ANOVA test can be right–tailed, left–tailed, or two–tailed depending on
the alternative hypothesis.
A)
True
B)
False
58)
True or false: A Kruskal–Wallis test can be used to compare several population medians as well as
several population means.
A)
True
B)
False
Compute the value of the H test statistic.
59)
A Kruskall–Wallis test is to be performed to compare three population means. Independent
random samples are selected from three different populations. The sample data are given in the
table below.
A B C
21.6 33.8 35.0
24.3 23 29.7
17.1 18.3 31.6
17.6 16.8 25.7
19.7 28.2 18.8
18.3 32.9
33.8
A)
5.903
B)
8.166
C)
6.757
D)
4.718
Provide an appropriate response.
60)
A Tukey multiple comparison is performed to compare the means of 6 populations. How many
confidence intervals will be obtained?
A)
6
B)
30
C)
1
D)
15
Find the required q–value.
61)
For a q–curve with parameters = 10 and = 4, find the q–value having area 0.05 to its right.
A)
5.77
B)
4.33
C)
12.3
D)
7.83
Determine the specified calculation.
62)
Sample 1 Sample 2 Sample 3
4 2 3
5 4 5
8 3
6
F
A)
0.349
B)
0.954
C)
2.864
D)
1.048
Construct the one–way ANOVA table.
63)
A one–way ANOVA is to be performed. Independent random samples are selected from three
different populations. The sample data are given in the table below.
Sample 1 Sample 2 Sample 3
9 6 7
4 5 9
7 3 6
4 4 8
Construct the one–way ANOVA table for the data.
A)
216.00 8.00 1.44
930.00 3.33
11 46.00
24
B)
218.00 9.00 2.15
928.00 3.11
11 46.00 4.18
C)
318.00 6.00 1.93
928.00 3.11
12 46.00
D)
218.00 9.00 2.89
928.00 3.11
11 46.00
Compute the sum of squares.
64)
A one–way ANOVA is to be performed. Independent random samples are selected from four
different populations. The sample data are given in the table below.
Sample 1 Sample 2 Sample 3 Sample 4
2 2 3 6
7 1 5 7
1 1 8
812
7
Compute the treatment sum of squares, SSTR.
A)
123.3
B)
150.0
C)
425.3
D)
75.3
Provide an appropriate response.
65)
A Tukey multiple comparison is performed to compare the means of four populations. The sample
sizes are 8, 9, 5, and 8. Determine the parameters and for the appropriate q–curve.
A)
= 3, =26
B)
= 3, =29
C)
= 4, =26
D)
= 4, =29
Find the required q–value.
66)
For a q–curve with parameters = 2 and = 14, find q0.01 .
A)
4.21
B)
34.8
C)
3.03
D)
15.4
Fill in the missing entries in the partially completed one–way ANOVA table.
67)
Source df SS MS = SS/df F–statistic
Treatment 24
Error 29 4.8
Total 33
A)
Source df SS MS = SS/df F–statistic
Treatment 424 6.00 1.25
Error 29 139.2 4.8
Total 33 163.2
B)
Source df SS MS = SS/df F–statistic
Treatment 424 6.00 1.25
Error 29 139.2 4.8
Total 33 5.8
C)
Source df SS MS = SS/df F–statistic
Treatment 62 24 0.39 0.08
Error 29 139.2 4.8
Total 33 163.2
D)
Source df SS MS = SS/df F–statistic
Treatment 424 6.00 0.80
Error 29 139.2 4.8
Total 33 163.2
26
Determine the specified calculation.
68)
Sample 1 Sample 2 Sample 3 Sample 4 Sample 5
610 410 8
913 10 912
612 911
11 8 9
9
SSE
A)
10.778
B)
46
C)
43.111
D)
3.538
D)
Find the required q–value.
69)
For a q–curve with parameters = 6 and = 7, find q0.05 .
A)
4.74
B)
5.92
C)
9.24
D)
5.36
D)
Determine the specified calculation.
70)
Sample 1 Sample 2 Sample 3
6 2 4
5 4 4
7 4
6
MSTR
A)
14
B)
7
C)
0.667
D)
4
D)
Provide an appropriate response.
71)
True or false: A variable with an F–distribution can take nonnegative values only.
A)
False
B)
True
Fill in the missing entries in the partially completed one–way ANOVA table.
72)
Source df SS MS = SS/df F–statistic
Treatment 28.7
Error 25 4.2
Total 29
A)
Source df SS MS = SS/df F–statistic
Treatment 428.7 0.27 0.064
Error 25 105.0 4.2
Total 29 133.7
B)
Source df SS MS = SS/df F–statistic
Treatment 4 28.7 7.18 1.71
Error 25 105.0 4.2
Total 29 76.3
C)
Source df SS MS = SS/df F–statistic
Treatment 4 28.7 7.18 1.71
Error 25 105.0 4.2
Total 29 133.7
D)
Source df SS MS = SS/df F–statistic
Treatment 4 28.7 7.18 0.59
Error 25 105.0 4.2
Total 29 133.7
Find the required F–value.
73)
An F–curve has df = (6, 20). Find the F–value having area 0.10 to its right.
A)
7.40
B)
3.87
C)
2.09
D)
2.84
Find the required q–value.
74)
For a q–curve with parameters = 5 and = 20, find q0.05 .
A)
5.51
B)
4.23
C)
4.45
D)
5.29
Fill in the missing entries in the partially completed one–way ANOVA table.
75)
Source df SS MS = SS/df F–statistic
Treatment 21.1
Error 26 3.3
Total 30
A)
Source df SS MS = SS/df F–statistic
Treatment 421.1 5.28 1.60
Error 26 0.13 3.3
Total 30 21.23
B)
Source df SS MS = SS/df F–statistic
Treatment 421.1 5.28 1.60
Error 26 85.8 3.3
Total 30 64.70
C)
Source df SS MS = SS/df F–statistic
Treatment 421.1 5.28 1.60
Error 26 85.8 3.3
Total 30 106.9
D)
Source df SS MS = SS/df F–statistic
Treatment 421.1 5.28 0.63
Error 26 85.8 3.3
Total 30 106.9
Find the required F–value.
76)
An F–curve has df = (9, 3). Find the F–value having area 0.005 to its right.
A)
43.88
B)
8.72
C)
8.81
D)
3.86
Provide an appropriate response.
77)
A one–way ANOVA is performed to compare the means of three populations. The sample sizes are
9, 12, and 13. Determine the degrees of freedom for the F–statistic.
A)
(31, 33)
B)
(2, 31)
C)
(3, 31)
D)
(2, 33)
Find the required F–value.
78)
An F–curve has df = (8, 15). Find the F–value having area 0.05 to its right.
A)
3.22
B)
2.64
C)
6.81
D)
4.67
Compute the value of the H test statistic.
79)
A Kruskall–Wallis test is to be performed to compare four population means. Independent random
samples are selected from four different populations. The sample data are given in the table below.
A B C D
190 107 97 146
182 125 133 163
151 172 142 96
176 200 114 110
114 190 189 183
195 101
A)
18.905
B)
4.327
C)
9.918
D)
3.647
80)
A Kruskall–Wallis test is to be performed to compare three population means. Independent
random samples are selected from three different populations. The sample data are given in the
table below.
A B C
42 94 38
51 60 45
70 75 57
35 83 79
30 55 64
A)
219.3
B)
2619.62
C)
12.4
D)
5.46
Determine the specified calculation.
81)
Sample 1 Sample 2 Sample 3 Sample 4 Sample 5
410 11 10 8
813 11 912
612 911
11 8 9
9
SSTR
A)
2.308
B)
30
C)
54.5
D)
13.625
82)
Sample 1 Sample 2 Sample 3
5 2 6
7 4 5
9 2
4
MSE
A)
15.472
B)
25.417
C)
4.236
D)
7.736
Find the required F–value.
83)
An F–curve has df = (15, 24). Find the F–value having area 0.025 to its right.
A)
2.70
B)
3.29
C)
2.11
D)
2.44
84)
For an F–curve with df = (12, 15), find F0.10 .
A)
2.10
B)
2.02
C)
4.01
D)
3.67
Provide an appropriate response.
85)
True or false: An F–curve is symmetrical about 0 and extends indefinitely in both directions,
approaching, but never touching, the horizontal axis as it does so.
A)
True
B)
False
Compute the sum of squares.
86)
A one–way ANOVA is to be performed. Independent random samples are selected from four
different populations. The sample data are given in the table below.
Sample 1 Sample 2 Sample 3 Sample 4
3 5 3 5
2 6 5 8
1 1 8
8 9
7
Compute the error sum of squares, SSE.
A)
104.8
B)
62.7
C)
107.0
D)
44.3
Fill in the missing entries in the partially completed one–way ANOVA table.
87)
Source df SS MS = SS/df F–statistic
Treatment 22.2
Error 23 4
Total 27
A)
Source df SS MS = SS/df F–statistic
Treatment 422.2 5.55 1.39
Error 23 92.0 4
Total 27 114.2
B)
Source df SS MS = SS/df F–statistic
Treatment 422.2 5.55 1.39
Error 23 92.0 4
Total 27 69.8
C)
Source df SS MS = SS/df F–statistic
Treatment 50 22.2 0.44 0.111
Error 23 92.0 4
Total 27 70.0
D)
Source df SS MS = SS/df F–statistic
Treatment 422.2 0.44 9.09
Error 23 92.0 4
Total 27 114.2
Determine the specified calculation.
88)
Sample 1 Sample 2 Sample 3 Sample 4 Sample 5
610 11 10 8
10 13 8 9 12
612 911
11 8 9
9
MSTR
A)
2.859
B)
37.167
C)
27.278
D)
6.819
Fill in the missing entries in the partially completed one–way ANOVA table.
89)
Source df SS MS = SS/df F–statistic
Treatment 21.1
Error 22 3.3
Total 26
A)
Source df SS MS = SS/df F–statistic
Treatment 48 21.1 5.28 306.91
Error 22 0.15 3.3
Total 26 21.25
B)
Source df SS MS = SS/df F–statistic
Treatment 421.1 5.28 1.60
Error 22 72.6 3.3
Total 26 51.5
C)
Source df SS MS = SS/df F–statistic
Treatment 421.1 5.28 1.60
Error 22 72.6 3.3
Total 26 93.7
D)
Source df SS MS = SS/df F–statistic
Treatment 421.1 5.28 0.63
Error 22 72.6 3.3
Total 26 93.7
Find the required F–value.
90)
For an F–curve with df = (24, 30), find F0.01 .
A)
1.67
B)
2.58
C)
1.64
D)
2.47
Find the required q–value.
91)
For a q–curve with parameters = 5 and = 11, find the q–value having area 0.01 to its right.
A)
5.99
B)
6.55
C)
5.31
D)
5.97
Find the required F–value.
92)
For an F–curve with df = (15, 60), find F0.005 .
A)
2.57
B)
1.84
C)
2.16
D)
3.48
Provide an appropriate response.
93)
True or false: In a one–way ANOVA, if the null hypothesis is rejected, we conclude that the
population means are all different (i.e., no two of the population means are equal).
A)
False
B)
True
Determine the specified calculation.
94)
Sample 1 Sample 2 Sample 3
6 2 3
6 4 5
6 3
4
SSE
A)
7.667
B)
10.333
C)
1.278
D)
5.167
Provide an appropriate response.
95)
A researcher is considering performing a Kruskal–Wallis test to compare four population means
and wants to determine whether the assumptions are met. Independent samples of sizes 7, 6, 3, and
8 are selected from the four populations. The variable under consideration has a uniform
distribution on each of the four populations. Which, if any, of the assumptions for the
Kruskal–Wallis test is violated?
A)
The assumption that all sample sizes should be 5 or greater
B)
The assumption that the populations should have the same shape
C)
None of the assumptions is violated.
D)
The assumption that the populations should be normally distributed
96)
A Tukey multiple comparison is being performed. True or false, the family confidence level is
larger than the individual confidence level?
A)
True
B)
False
Compute the sum of squares.
97)
A one–way ANOVA is to be performed. Independent random samples are selected from three
different populations. The sample data are given in the table below.
Sample 1 Sample 2 Sample 3
3 8 6
2 5 8
9 2
2
Compute the total sum of squares, SST.
A)
266.0
B)
1800
C)
66.0
D)
291.0
Find the required q–value.
98)
For a q–curve with parameters = 2 and = 24, find the q–value having area 0.05 to its right.
A)
2.92
B)
5.18
C)
6.11
D)
6.19
Provide an appropriate response.
99)
A researcher is considering performing a Kruskal–Wallis test to compare four population means
and wants to determine whether the assumptions are met. Independent samples of sizes 7, 6, 10,
and 8 are selected from the four populations. The variable under consideration has a normal
distribution on each of the four populations. The standard deviations of the populations are 2.5,
3.2, 8.6, and 11.7. Which, if any, of the assumptions for the Kruskal–Wallis test is violated?
A)
The assumption that the sample sizes are all 8 or greater
B)
The assumption that the populations have the same shape
C)
None of the assumptions is violated.
D)
The assumption of equal standard deviations