Exam
Name___________________________________
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
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.
1)
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
1)
2)
Four different types of fertilizers are used on raspberry plants. The number of raspberries
on each randomly selected plant is given below. Test the claim that the type of fertilizer
makes no difference in the mean number of raspberries per plant. Use = 0.01.
Fertilizer 1 Fertilizer 2 Fertilizer 3 Fertilizer 4
6 8 6 3
5 5 3 5
7 5 4 3
6 5 3 4
7 5 2 4
6 6 3 5
2)
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.
3)
Random samples of four different models of cars were selected and the gas mileage of each
car was measured. The results are shown below.
Model A
23
25
24
26
Model B
28
26
29
30
Model C
30
28
32
27
Model D
25
26
25
28
Test the claim that the four different models have the same population mean. Use a
significance level of 0.05.
3)
4)
A consumer magazine wants to compare the lifetimes of ballpoint pens of three different
types. The magazine takes a random sample of pens of each type in the following table.
Brand 1
260
218
184
219
Brand 2
181
240
162
218
Brand 3
238
257
241
213
Do the data indicate that there is a difference in mean lifetime for the three brands of
ballpoint pens? Use = 0.01.
4)
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.
5)
A consumer magazine wants to compare the lifetimes of ballpoint pens of three different
types. The magazine takes a random sample of pens of each type in the following table.
Brand 1
260
218
184
219
Brand 2
181
240
162
218
Brand 3
238
257
241
213
Do the data indicate that there is a difference in mean lifetime for the three brands of
ballpoint pens? Use = 0.01.
5)
Provide an appropriate response.
6)
List the basic properties of F–curves.
6)
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.
7)
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
15
25
21
23
22
20
Brand B
20
17
22
23
Brand C
21
22
20
19
18
Brand D
15
15
14
23
22
28
28
7)
8)
At the 0.01 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
44
47
44
40
39
Brand B
30
32
34
36
38
40
42
Brand C
28
27
31
32
36
8)
Provide an appropriate response.
9)
When performing a one–way ANOVA, two of the assumptions required are that the
populations be normally distributed and that the populations have equal standard
deviations. What rule of thumb can be used to assess the equal–standard deviations
assumption? What other method can be used to assess the normality and equal–standard
deviations assumptions?
9)
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.
10)
A medical researcher wishes to try three different techniques to lower blood pressure of
patients with high blood pressure. The subjects are randomly selected and assigned to one
of three groups. Group 1 is given medication, Group 2 is given an exercise program, and
Group 3 is assigned a diet program. At the end of six weeks, each subject’s blood pressure
is recorded. Test the claim that there is no difference among the means. Use = 0.05.
Group 1 Group 2 Group 3
984
12 212
11 5 4
15 3 6
13 4 9
808
10)
Provide an appropriate response.
11)
A one–way ANOVA is being performed. Suppose that SST =144.3 and SSE =71.8. Find the
value of the third sum of squares, give its notation, state its name and the source of
variation it represents.
11)
12)
For an F–curve with df = (8, 3), find the F–value having area 0.05 to its right and illustrate
your answer with a sketch.
12)
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.
13)
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
15
25
21
23
22
20
Brand B
20
17
22
23
Brand C
21
22
20
19
18
Brand D
15
15
14
23
22
28
28
13)
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.
14)
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
14)
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.
15)
The data below represent the weight losses for people on three different exercise programs.
Exercise A
2.5
8.8
7.3
9.8
5.1
Exercise B
5.8
4.9
1.1
7.8
1.2
Exercise C
4.3
6.2
5.8
8.1
7.9
At the 1% significance level, does it appear that a difference exists in the true mean weight
loss produced by the three exercise programs?
15)
Explanation:
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.
16)
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
16)
Explanation:
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.
17)
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 1780 1530 2400
1980 1540 1600 2350
2210 1690 1580 2600
2000 1650 1750 2150
1900 1500 2000
1670 2200
2350
17)
Provide an appropriate response.
18)
A one–way ANOVA is to be performed. Independent random samples are taken from two
populations. The sample data are depicted in the dotplot below. Is it reasonable to
conclude that the difference between the sample means is due to a difference between the
population means and not to variation within the populations? Do you think the null
hypothesis would be rejected? Explain your thinking.
18)
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.
19)
At the 0.01 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
44
47
44
40
39
Brand B
30
32
34
36
38
40
42
Brand C
28
27
31
32
36
19)
Provide an appropriate response.
20)
A one–way ANOVA is being performed. Suppose that SST =82.1 and SSTR =55.6. Find
the value of the third sum of squares, give its notation, state its name and the source of
variation it represents.
20)
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.
21)
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
21)
22)
Random samples of four different models of cars were selected and the gas mileage of each
car was measured. The results are shown below.
Model A
23
25
24
26
Model B
28
26
29
30
Model C
30
28
32
27
Model D
25
26
25
28
Test the claim that the four different models have the same population mean. Use a
significance level of 0.05.
22)
Provide an appropriate response.
23)
In the context of a one–way ANOVA, explain what is meant by variation between samples
and variation within samples.
23)
24)
For an F–curve with df = (10, 20), find the F–value having area 0.01 to its right and
illustrate your answer with a sketch.
24)
25)
Describe the null and alternate hypotheses for one–way ANOVA. Give an example.
25)
26)
A one–way ANOVA is to be performed. Independent random samples are taken from two
populations. The sample data are depicted in the dotplot below. Is it reasonable to
conclude that the difference between the sample means is due to a difference between the
population means and not to variation within the populations? Do you think the null
hypothesis would be rejected? Explain your thinking.
26)
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.
27)
The data below represent the weight losses for people on three different exercise programs.
Exercise A
2.5
8.8
7.3
9.8
5.1
Exercise B
5.8
4.9
1.1
7.8
1.2
Exercise C
4.3
6.2
5.8
8.1
7.9
At the 1% significance level, does it appear that a difference exists in the true mean weight
loss produced by the three exercise programs?
27)
Provide an appropriate response.
28)
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.
28)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Compute the sum of squares.
29)
29)
A)
239.6
B)
14.6
C)
75.1
D)
34.0
Find the required F–value.
30)
30)
A)
8.81
B)
3.86
C)
43.88
D)
8.72
Provide an appropriate response.
31)
31)
A)
True
B)
False
32)
32)
A)
False
B)
True
Find the required F–value.
33)
33)
A)
2.84
B)
2.01
C)
1.77
D)
3.70
34)
34)
A)
2.09
B)
7.40
C)
2.84
D)
3.87
Determine the specified calculation.
35)
35)
A)
3.167
B)
19
C)
4.611
D)
9.222
Construct the one–way ANOVA table.
36)
36)
13
A)
388.53 29.51 0.95
12 377.47 31.46
15 466.00 31.07
B)
488.53 22.13 0.70
12 377.47 31.46
16 466.00
C)
388.53 29.51 0.94
12 377.47 31.46
15 466.00
D)
398.53 32.84 1.07
12 367.47 30.62
15 466.00
Provide an appropriate response.
37)
37)
A)
True
B)
False
Determine the specified calculation.
38)
38)
A)
5.667
B)
18.333
C)
9.167
D)
0.944
39)
39)
A)
0.521
B)
0.174
C)
5.763
D)
1.921
Fill in the missing entries in the partially completed one–way ANOVA table.
40)
40)
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 29 133.7
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 76.3
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
Compute the sum of squares.
41)
41)
A)
1800
B)
240.0
C)
265.0
D)
40.0
Fill in the missing entries in the partially completed one–way ANOVA table.
42)
42)
A)
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
B)
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
C)
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
D)
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
43)
43)
A)
Source df SS MS = SS/df F–statistic
Treatment 422 5.50 1.83
Error 22 66.0 3
Total 26 44
B)
Source df SS MS = SS/df F–statistic
Treatment 48 22 10.33
Error 22 66.0 3
Total 26 88.0
C)
Source df SS MS = SS/df F–statistic
Treatment 422 5.50 1.83
Error 22 66.0 3
Total 26 88.0
D)
Source df SS MS = SS/df F–statistic
Treatment 422 0.33 0.11
Error 22 66.0 3
Total 26 88.0
Provide an appropriate response.
44)
44)
A)
(33, 35)
B)
(2, 35)
C)
(3, 33)
D)
(2, 33)
Determine the specified calculation.
45)
45)
A)
7
B)
3.667
C)
22
D)
14
D)
Fill in the missing entries in the partially completed one–way ANOVA table.
46)
46)
A)
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
B)
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
C)
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
D)
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)
Provide an appropriate response.
47)
47)
A)
True
B)
False
48)
48)
A)
False
B)
True
49)
49)
A)
False
B)
True
50)
50)
A)
True
B)
False
Construct the one–way ANOVA table.
51)
51)
A)
218.00 9.00 2.75
918.00 2.00
11 36.00 3.27
20
B)
318.00 6.00 3.00
918.00 2.00
12 36.00
C)
216.00 8.00 1.80
920.00 2.22
11 36.00
D)
218.00 9.00 4.50
918.00 2.00
11 36.00
Determine the specified calculation.
52)
52)
A)
2.111
B)
7.778
C)
12.667
D)
15.556
Compute the sum of squares.
53)
53)
A)
36.2
B)
67.0
C)
86.2
D)
30.8
Find the required F–value.
54)
54)
A)
2.47
B)
1.67
C)
1.64
D)
2.58
Provide an appropriate response.
55)
55)
A)
(3, 69)
B)
(4, 66)
C)
(3, 66)
D)
(66, 69)
Determine the specified calculation.
56)
56)
A)
2.051
B)
26.667
C)
43.333
D)
10.833
Find the required F–value.
57)
57)
A)
2.02
B)
3.67
C)
4.01
D)
2.10
Provide an appropriate response.
58)
58)
A)
True
B)
False
Find the required F–value.
59)
59)
A)
2.57
B)
3.48
C)
1.84
D)
2.16
Fill in the missing entries in the partially completed one–way ANOVA table.
60)
60)
A)
Source df SS MS = SS/df F–statistic
Treatment 322.97 7.66 11.16
Error 20 13.72 0.686
Total 23 36.69
B)
Source df SS MS = SS/df F–statistic
Treatment 322.97 1.15 1.68
Error 20 13.72 0.686
Total 23 36.69
C)
Source df SS MS = SS/df F–statistic
Treatment 322.97 1.67 2.43
Error 20 13.72 0.686
Total 23 36.69
D)
Source df SS MS = SS/df F–statistic
Treatment 322.97 7.66 11.16
Error 20 13.72 0.686
Total 23 9.25
61)
61)
A)
Source df SS MS = SS/df F–statistic
Treatment 5 20.5 4.10 0.95
Error 29 113.1 3.9
Total 34 133.6
B)
Source df SS MS = SS/df F–statistic
Treatment 520.5 4.10 1.05
Error 29 113.1 3.9
Total 34 133.6
C)
Source df SS MS = SS/df F–statistic
Treatment 520.5 4.10 1.05
Error 29 113.1 3.9
Total 34 92.6
D)
Source df SS MS = SS/df F–statistic
Treatment 520.5 0.18 0.046
Error 29 113.1 3.9
Total 34 133.6
Compute the sum of squares.
62)
62)
A)
80.0
B)
19.3
C)
136.5
D)
369.3
Find the required F–value.
63)
63)
A)
6.33
B)
4.10
C)
3.29
D)
4.56
64)
64)
A)
2.11
B)
2.44
C)
3.29
D)
2.70
65)
65)
A)
2.64
B)
3.22
C)
4.67
D)
6.81
66)
66)
A)
2.90
B)
1.99
C)
2.62
D)
4.86
Fill in the missing entries in the partially completed one–way ANOVA table.
67)
67)
A)
Source df SS MS = SS/df F–statistic
Treatment 424 6.00 0.80
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 33 163.2
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 1.25
Error 29 139.2 4.8
Total 33 5.8
68)
68)
A)
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
B)
Source df SS MS = SS/df F–statistic
Treatment 422.2 0.44 9.09
Error 23 92.0 4
Total 27 114.2
C)
Source df SS MS = SS/df F–statistic
Treatment 422.2 5.55 1.39
Error 23 92.0 4
Total 27 114.2
D)
Source df SS MS = SS/df F–statistic
Treatment 422.2 5.55 1.39
Error 23 92.0 4
Total 27 69.8
Compute the sum of squares.
69)
69)
A)
98.0
B)
153.0
C)
128.0
D)
4550
Determine the specified calculation.
70)
70)
A)
2.667
B)
19.611
C)
34.667
D)
4.903
Compute the sum of squares.
71)
71)
A)
67.5
B)
5.5
C)
73.0
D)
230.5
Determine the specified calculation.
72)
72)
A)
41.333
B)
74.667
C)
5.744
D)
10.333
73)
73)
A)
0.212
B)
0.688
C)
1.453
D)
4.724
Fill in the missing entries in the partially completed one–way ANOVA table.
74)
74)
A)
Source df SS MS = SS/df F–statistic
Treatment 424.1 6.03 1.88
Error 30 96.0 3.2
Total 34 120.1
B)
Source df SS MS = SS/df F–statistic
Treatment 424.1 6.03 0.53
Error 30 96.0 3.2
Total 34 120.1
C)
Source df SS MS = SS/df F–statistic
Treatment 424.1 0.38 482.00
Error 30 96.0 3.2
Total 34 120.1
D)
Source df SS MS = SS/df F–statistic
Treatment 424.1 6.03 1.88
Error 30 96.0 3.2
Total 34 24.21
Determine the specified calculation.
75)
75)
A)
3.744
B)
25.333
C)
48.667
D)
6.333
Answer Key
Testname: C13
32
Answer Key
Testname: C13
33
Answer Key
Testname: C13
Answer Key
Testname: C13