c.
at least two population locations are the same.
d.
at least two population locations differ.
62. The Kruskal-Wallis test is a nonparametric alternative to:
a.
ANOVA F-test.
b.
Student-t test for matched pairs.
c.
Student-t test for independent samples.
d.
None of these choices.
63. The nonparametric counterpart of the parametric one-way analysis of variance F-test is the:
a.
Kruskal-Wallis test.
b.
Friedman test.
c.
Wilcoxon rank sum test.
d.
Wilcoxon signed rank sum test.
64. In a Kruskal-Wallis test, there are four samples and the value of the test statistic is calculated as H =
8.79. The most accurate statement that can be made about the p-value is that:
a.
it is greater than 0.10.
b.
it is greater than 0.05 but smaller than 0.10.
c.
it is greater than 0.05.
d.
it is greater than 0.025 but smaller than 0.05.
65. Suppose there is interest in comparing the locations of response times for three independent groups
learning new specific task. The appropriate nonparametric procedure is the:
a.
Wilcoxon rank sum test.
b.
Wilcoxon signed rank test.
c.
Kruskal-Wallis test.
d.
None of these choices.
66. Which of the following distributions approximate Kruskal-Wallis test statistic H when the problem
objective is to compare k populations (k > 2) where the sample sizes are greater than or equal to 5?
a.
normal distribution
b.
chi-squared distribution
c.
Student t-distribution
d.
None of these choices.
67. The Kruskal-Wallis test statistic can be approximated by a chi-squared distribution with k − 1 degrees
of freedom (where k is the number of populations) whenever the sample sizes are all greater than or
equal to:
a.
5
b.
10
c.
30
d.
None of these choices.
68. The Kruskal-Wallis test is always:
a.
one-tail.
b.
two-tail.
c.
used with one sample.
d.
used when the populations are normally distributed.
69. The Friedman test applies to which situation?
a.
When the problem objective is to compare two or more populations.
b.
The data are either ordinal or interval but not nominal.
c.
The data are generated from a randomized block experiment.
d.
All of these choices are true.
70. The nonparametric counterpart of the randomized block model of the analysis of variance is the:
a.
Kruskal-Wallis test.
b.
Friedman test.
c.
Wilcoxon rank sum test.
d.
Wilcoxon signed rank sum test.
71. A nonparametric method to compare two or more populations, when the samples are matched pairs
and the data are either ordinal or interval but not normal, is the:
a.
Wilcoxon signed rank sum test.
b.
sign test.
c.
Friedman test.
d.
Kruskal-Wallis test.
72. In a Friedman test for comparing three populations, provided that there are five blocks, the test statistic
is calculated as Fr = 6.594. Then, the most accurate statement that can be made about the p-value is:
a.
p-value < 0.025
b.
.05 < p-value < .10
c.
.025 < p-value < .05
d.
p-value > .10
73. The Friedman test is always:
a.
one-tail with > in the alternative hypothesis.
b.
one-tail with < in the alternative hypothesis.
c.
two-tail
d.
None of these choices.
74. In a Friedman test for comparing four populations, provided that there as eight blocks, the test statistic
is calculated as Fr = 10.98. If the test is conducted at the 5% significance level, the conclusion and
p-value will be:
a.
reject the null hypothesis, and 0.01 < p–value < 0.025.
b.
reject the null hypothesis, and p-value > 0.025.
c.
do not reject the null hypothesis, and 0.025 < p-value < 0.05.
d.
do not reject the null hypothesis, and p-value > 0.05.
75. To apply the Friedman test to determine whether the locations of two or more populations are the
same, the samples must be:
a.
from a randomized block experiment.
b.
from normal populations.
c.
independent.
d.
All of these choices are true.
76. The test statistic Fr for the Friedman test has what distribution?
a.
approximate normal distribution
b.
approximate chi-squared distribution
c.
F-distribution
d.
None of these choices.
77. The Kruskal-Wallis test compares the locations of ____________________ populations.
78. The data for analysis by a Kruskal-Wallis test are either ordinal or interval, but they do not have a(n)
____________________ distribution.
79. The alternative hypothesis of the Kruskal-Wallis test is that ____________________ population
locations differ.
80. If the rank sums for each sample are similar, the test statistic H for the Kruskal-Wallis test will be
____________________. As a result, you ____________________ (do/do not) reject H0.
81. For sample sizes greater than or equal to 5, the test statistic H has an approximate
____________________ distribution.
82. The Kruskal-Wallis test is always one tailed. The inequality sign in the alternative hypothesis is
always ____________________.
83. When the Kruskal-Wallis test is used to test for a difference between two populations, it will produce
the same outcome as the two-tail Wilcoxon ____________________ test.
84. In the case of comparing two population locations, the Kruskal-Wallis test can only determine whether
a difference in locations exists. To determine which population has a higher location requires the use
of the Wilcoxon ____________________ test.
85. The Friedman test compares the locations of ____________________ populations where the data are
generated from a randomized block experiment.
86. The Friedman test compares the locations of two or more populations where the data are generated
from a randomized ____________________ experiment.
87. The data for analysis by a Friedman test are either ordinal or interval, but they do not have a(n)
____________________ distribution.
88. The alternative hypothesis of the Friedman test is that ____________________ population locations
differ.
89. If the test statistic Fr for the Friedman test is ____________________, we do not reject H0.
90. The test statistic Fr for the Friedman test has an approximate ____________________ distribution.
91. The Friedman test is always one tailed. The inequality sign in the alternative hypothesis is always
____________________.
92. When the Friedman test is used to test for a difference between two populations, it will produce the
same outcome as the ____________________ test.
93. In the case of comparing two population locations, the Friedman test can only determine whether a
difference exists. To determine which population, for example, has a higher location requires the use
of the ____________________ test.
Song Ratings
A music critic wanted to determine whether or not music listeners of different age groups evaluate a
song differently. With this objective, he commissioned a survey that asked people their ratings of the
most popular songs. The rating categories were: 1 = terrible, 2 = fair, 3 = good, and 4 = excellent. Each
respondent was also asked to categorize his or her age as either: 1 = teenager, 2 = young adult (20-34),
3 = middle age (35-50), and 4 = over 50.
The results are shown below.
Song Ratings
Teenager
Young Adult
Middle Age
Senior
3
2
3
3
4
3
2
4
3
3
1
4
3
2
2
3
3
2
2
3
4
1
3
4
2
3
1
4
4
2
4
3
94. {Song Ratings Narrative} Which test can the movie critic use in this situation?
95. {Song Ratings Narrative} Does this data provide sufficient evidence to infer at the 5% significance
level that there are differences in ratings among the different age categories?
96. {Song Ratings Narrative} What statement can be made about the p-value for this test?
97. {Song Ratings Narrative} Explain how to use the p-value for testing the hypotheses.
Advertisement
In a Kruskal-Wallis test to determine whether differences exist among three different advertisements,
the following statistics were obtained: T1 = 884, n1 = 20, T2 = 756, n2 = 28, T3 = 1061, n3 = 25.
98. {Advertisement Narrative} Conduct the test at the 5% significance level.
99. {Advertisement Narrative} What is the most accurate statement that can be made about the p-value of
this test?
100. {Advertisement Narrative} Explain how to use the p-value for testing the hypotheses.
Customers’ Ages
The marketing manager of a Hot Dog Stand chain is in the process of examining some of the
demographic characteristics of her customers. In particular, she would like to investigate the belief that
the ages of the customers of hot dogs, fast-food hamburger, and fast-food chicken restaurants are
different. To test this belief, the ages of eight randomly selected customers from each restaurant type
were recorded and listed below. From previous analysis we know that the ages are not normally
distributed.
Customers’ Ages
Hot Dogs
Hamburger
Chicken
23
26
25
19
20
28
25
18
36
17
35
23
36
33
39
25
25
27
28
19
38
31
17
31
101. {Customers’ Ages Narrative} Does this data provide enough evidence at the 10% significance level to
infer that there are differences in ages among the customers of the three restaurant types?
102. {Customers’ Ages Narrative} Using the appropriate statistical table, what statement can be made about
the p-value for this test?
103. {Customers’ Ages Narrative} Explain how to use the p-value for testing the hypotheses?
104. The data below are drawn from four independent populations:
Sample
1
2
3
4
13
15
18
9
9
10
15
10
16
15
17
6
12
14
18
6
15
13
8
Test at the 1% significance level to determine whether the population locations differ.
Assessments of TV Shows
Because of the cost of producing television shows and the profits associated with successful shows,
television network executives are keenly interested in public opinion. A network has recently
developed three comedy series. The pilot of each series is shown in to 10 randomly selected people
who evaluate each show on a 9-point scale where 1 = terrible and 9 = excellent. The results are shown
below.