Chapter 22: Nonparametric Methods – Quiz A Name _________________
Use the following information for questions 1 through 4:
Six federal government economists and 7 university
economists graded the effectiveness of an economic
stimulus bill in terms of its ability to increase jobs over
the next two years. The grades are shown in the table
to the left.
22.2.2 Identify and/or perform an appropriate test.
1. What nonparametric method is appropriate to determine whether the two groups
differ in terms of their opinion?
22.2.1 Identify and/or perform an appropriate test.
2. Are the assumptions satisfied for applying this method? Explain.
22.2.3 Perform a Wilcoxon rank-sum test.
3. State the null and alternative hypotheses.
22.2.3 Perform a Wilcoxon rank-sum test.
4. Perform the test and state your conclusion at α = 0.10.
Use the following information for questions 5 through 8:
Consumers were asked to “rate” the taste of three
popular brands of yogurt that have been modified
to include fiber. The data are shown in the table
below. This data will be used to determine
whether there are differences in the results among
the three brands.
22.3.2 Identify and/or perform an appropriate test.
5. What nonparametric method is appropriate for analyzing these data?
22.3.5 Perform a Kruskal-Wallace test.
6. State the null and alternative hypotheses.
22.3.5 Perform a Kruskal-Wallace test.
7. Perform the test and state your conclusion at α = 0.05.
Government University
A- C
A B+
B+ B-
B- C+
B A-
A- B-
C
Activia Yoplait Dannon
4 2 5
5 2 4
3 2 3
2 1 3
4 1 4
22-2 Chapter 22 Nonparametric Methods
22.3.5 Perform a Kruskal-Wallace test.
8. If these data did satisfy the assumptions for performing ANOVA, what are the
disadvantages of using this nonparametric method instead?
22.8.2 Identify and/or perform an appropriate test.
9. For the scatterplot below, what about the data makes nonparametric methods
appropriate for measuring the association between x and y?
22.8.2 Identify and/or perform an appropriate test.
10. For the scatterplot below, what about the data makes nonparametric methods
appropriate for measuring the association between score 1 and score 2?
Quiz A 22-3
Chapter 22: Nonparametric Methods – Quiz A – Key
22-4 Chapter 22 Nonparametric Methods
Quiz A 22-5
22-6 Chapter 22 Nonparametric Methods
Chapter 23: Nonparametric Methods – Quiz B Name ____________________
Use the following information for questions 1 through 4:
Eight hybrid cars are used to determine if there is a difference in gas mileage (MPG) with
and without a particular additive. The data are shown below.
Hybrid Car MPG with
Additive
MPG without
Additive
1 20 18
2 22 20
3 24 20
4 25 26
5 29 22
6 26 22
7 20 22
8 28 24
22.4.2 Identify and/or perform an appropriate test.
1. What nonparametric method is appropriate for analyzing these data?
22.4.2 Identify and/or perform an appropriate test.
2. Are the assumptions satisfied for applying this method? Explain.
22.4.4 Perform a Wilcoxon signed-rank test.
3. State the null and alternative hypotheses.
22.4.4 Perform a Wilcoxon signed-rank test.
4. Perform the test and state your conclusion at α = 0.10.
Quiz B 22-7
Use the following information for questions 5 through 8:
The data below shows ratings for four brands of ice cream, each tested by a different
group of consumers. Ice cream was rated on the level of creaminess on a scale of 1 to 8
(1 = very creamy to 8 = not creamy). This data will be used to determine whether there
differences in perceived creaminess among the four brands.
Manning’s Ben &
Jerry’s Breyer’s Montdale’s
1 1 7 5
4 2 6 6
2 3 5 7
3 1 7 7
1 2 5 8
22.3.2 Identify and/or perform an appropriate test.
5. What nonparametric method is appropriate for analyzing these data?
22.3.5 Perform a Kruskal-Wallace test.
6. State the null and alternative hypotheses.
22.3.5 Perform a Kruskal-Wallace test.
7. Perform the test and state your conclusion at α = 0.10.
22.8.2 Identify and/or perform an appropriate test.
8. If these data did satisfy the assumptions for performing ANOVA, what are the
disadvantages of using this nonparametric method instead?
22-8 Chapter 22 Nonparametric Methods
Use the following information for questions 9 and 10:
Suppose that ten new smart phone models were evaluated by two consumer electronics
magazines (Popular Electronics and Electronics Now) from 1 (best) to 10 (worst) as
follows. How strong is the agreement between the two magazines?
Model Popular
Electronics
Electronics
Now
1 8 7
2 3 6
3 7 5
4 4 3
5 2 1
6 1 2
7 10 8
8 5 9
9 6 4
10 9 10
22.7.2 Identify and/or perform an appropriate test
9. Why can’t the Pearson correlation be used for these data?
22.7.9 Interpret and or calculate Spearman’s rho and Kendall’s tau.
10. The Spearman rho is 0.745. What does this tell us about the association?
Quiz B 22-9
Chapter 23: Nonparametric Methods – Quiz B – Key
22-10 Chapter 22 Nonparametric Methods
Quiz B 22-11
22-12 Chapter 22 Nonparametric Methods
Chapter 22: Nonparametric Methods Name___________________
Quiz C – Multiple Choice
22.1.1 Understand ranks and how to rank data values.
1. Which of the following statements is false regarding nonparametric methods?
A. Nonparametric methods are appropriate when we want to treat the data as ordinal.
B. Compared to the correlation coefficient r, Kendall’s tau is less affected by outliers
in the data.
C. The Wilcoxon rank sum test is the nonparametric alternative to the paired t-test.
D. Spearman’s rho is always between -1 and 1.
E. The Friedman test is appropriate for a randomized block design.
22.2.2 Identify and/or perform an appropriate test.
2. A management professor divided her class of 10 executives into two equal sized
groups and used a different approach to teach about various leadership styles (case
study and online interactive). To compare the effectiveness of the two approaches,
the appropriate nonparametric procedure is the
A. Kruskal-Wallis test.
B. Kendall’s tau.
C. Wilcoxon signed-rank test.
D. Wilcoxon rank sum test.
E. Friedman test.
22.2.3 Perform a Wilcoxon rank-sum test.
3. Suppose that 6 economists who work for the federal government and 7 university
economists were asked to predict the percentage change in the U.S. GNP over the
three year period from January 2010 to January 2013. The Wilcoxon rank sum test
was used to determine if the two groups differ in their predictions. The value of the
test statistic was calculated to be 29.5. At α = 0.05, we can conclude that
A. the null hypothesis should be rejected.
B. the null hypothesis should not be rejected.
C. there is a difference in predictions provided by the two groups of economists.
D. both A and C.
E. both B and C.
Quiz C 22-13
22.3.5 Perform a Kruskal-Wallis test.
4. The best tasting ice creams are generally high in fat content, which gives them a
creamy texture. Four brands of ice cream (two national and two local) were tested by
consumers who rated how “creamy” they tasted on a 5-point Likert type scale (1 = not
creamy to 5 = very creamy). Each brand was rated by a different group of consumers.
The appropriate nonparametric method to use for these data is the
A. Kruskal-Wallis test.
B. Kendall’s tau.
C. Wilcoxon signed-rank test.
D. Wilcoxon rank sum test.
E. Spearman’s rho.
22.3.5 Perform a Kruskal-Wallis test.
5. Consumer ratings for three popular brands
of yogurt are shown in the table to the right.
Using the Kruskal-Wallis test to compare
ratings among brands, the calculated value for
the test statistic is
A. 8.345.
B. 12.315.
C. 4.995.
D. 2.635.
E. none of the above.
22.3.5 Perform a Kruskal-Wallis test.
6. Suppose the Kruskal-Wallis test was used to compare four groups. If the test statistic
value was found to be 9.545, using α = 0.05 we should
A. reject the null hypothesis.
B. not reject the null hypothesis.
C. conclude that the groups are all the same.
D. both A and C.
E. both B and C.
Activia Yoplait Dannon
4 2 5
5 2 4
3 2 3
2 1 3
4 1 4
22-14 Chapter 22 Nonparametric Methods
22.4.4 Perform a Wilcoxon Signed-Rank test.
7. Eight hybrid cars are used to determine if there is a difference in gas mileage (MPG)
with and without an additive claimed to increase the fuel efficiency. The appropriate
nonparametric method to use for these data is the
A. Kruskal-Wallis test.
B. Kendall’s tau.
C. Wilcoxon signed-rank test.
D. Wilcoxon rank sum test.
E. Spearman’s rho.
22.4.4 Perform a Wilcoxon Signed-Rank test.
8. Eight hybrid cars are used to determine if there is a difference in gas mileage (MPG)
with and without a particular additive. Using the appropriate nonparametric method,
the value of the calculated test statistic for the data shown below is
Hybrid Car MPG with
Additive
MPG without
Additive
1 20 18
2 22 20
3 24 20
4 25 26
5 29 22
6 26 22
7 20 22
8 28 24
A. 4
B. 5
C. 8
D. 30
E. 35
22.4.4 Perform a Wilcoxon Signed-Rank test.
9. Suppose the Wilcoxon signed-rank test was used on ten pairs of data. If the
calculated test statistic for a two tailed test was found to be 6, at α = 0.05 we can
conclude that the
A. null hypothesis should be rejected.
B. null hypothesis should not be rejected.
C. groups are the same.
D. both A and C.
E. both B and C.
Quiz C 22-15
22.7.6 Interpret and or calculate Spearman’s rho and Kendall’s tau.
10. Suppose that ten new smart phone models were evaluated by two consumer
electronics magazines from 1 (best) to 10 (worst). Spearman’s rho was calculated to
be -.45. We can say that there is
A. a high level of agreement between the two magazine rankings.
B. strong and positive association between the two magazine rankings.
C. an outlier in the data that affects the results.
D. a moderate level of disagreement between the two magazine rankings.
E. a rank of number 1 for the same smart phone in both magazines.
22-16 Chapter 22 Nonparametric Methods
Chapter 22: Nonparametric Methods – Quiz C – Key
Quiz D 22-17
Chapter 22: Nonparametric Methods Name___________________
Quiz D – Multiple Choice
22.2.2 Identify and/or perform an appropriate test.
1. Suppose that 6 federal government economists and 7 university economists were
asked to grade the effectiveness of an economic stimulus bill in terms of its ability to
increase jobs over the next two years. What nonparametric method is appropriate for
testing if the two groups differ in terms of their opinion?
A. Wilcoxon Rank-Sum
B. Wilcoxon Signed-Rank
C. Spearman’s rho
D. Kruskal Wallis
E. Kendall’s tau
22.2.3 Perform a Wilcoxon Rank-Sum test.
2. Suppose that 6 federal government economists and
7 university economists were asked to grade the
effectiveness of an economic stimulus bill in terms
of its ability to increase jobs over the next two
years. The grades are shown in the table to the
right. Using the appropriate nonparametric
method, the calculated value of the test statistic is
A. T1 = 62.5.
B. T1 = 30.
C. T1 = 54.
D. T1 = 28.5.
E. None of the above.
Government University
A- C
A B+
B+ B-
B- C+
B A-
A- B-
C
22-18 Chapter 22 Nonparametric Methods
22.7.2 Identify and/or perform an appropriate test.
3. Based on the scatterplot shown below, what makes a nonparametric method more
appropriate than the Pearson correlation for measuring the association between the
two variables?
A. Nonlinearity
B. These variables are not quantitative.
C. The presence of an outlier.
D. Both A and B.
E. All of the above.
22.7.2 Identify and/or perform an appropriate test.
4. Suppose that ten new smart phone models were evaluated by two consumer
electronics magazines (Popular Electronics and Electronics Now) from 1 (best) to 10
(worst) as shown below. Why is the Spearman rho more appropriate than the Pearson
correlation for these data?
A. The relationship is nonlinear.
B. The data are ordinal.
C. The data are not paired.
D. Both B and C.
E. All of the above.
Quiz D 22-19
22.3.5 Perform a Kruskal-Wallis test.
5. Four brands of ice cream was each tested by a different group of consumers and rated
on the level of creaminess on a scale of 1 to 8 (1 = very creamy to 8 = not creamy).
This data will be used to determine whether there differences in perceived creaminess
among the four brands. Using the Kruskal-Wallis test, the value of H is
Manning’s Ben &
Jerry’s Breyer’s Montdale’s
1 1 7 5
4 2 6 6
2 3 5 7
3 1 7 7
1 2 5 8
A. 14.51
B. 22.10
C. 6.351
D. 5.999
E. None of the above.
22.3.5 Perform a Kruskal-Wallis test.
6. Ratings were collected for four brands of ice cream, each tested by a different group
of consumers. Ice cream was rated on the level of creaminess on a scale of 1 to 8 (1 =
very creamy to 8 = not creamy). This data will be used to determine whether there
differences in perceived creaminess among the four brands. What would be the
critical value for the Kruskal-Wallis test at α = 0.10.
A. 14.51
B. 22.10
C. 6.251
D. 5.999
E. None of the above.
22.3.5 Perform a Kruskal-Wallis test.
7. The data below shows ratings for four brands of ice cream, each tested by a different
group of consumers. Ice cream was rated on the level of creaminess on a scale of 1 to
8 (1 = very creamy to 8 = not creamy). This data will be used to determine whether
there differences in perceived creaminess among the four brands. Using the Kruskal-
Wallis test, the value of H is 14.51. Using the Kruskal-Wallis test, at α = 0.10 we
would conclude that
A. the null hypothesis should be rejected.
B. the null hypothesis should be accepted.
C. there is no difference in creaminess among the brands.
D. Both A and C.
E. Both B and C.
22-20 Chapter 22 Nonparametric Methods
22.7.2 Identify and/or perform an appropriate test.
8. Based on the scatterplot shown below, what makes a nonparametric method more
appropriate than the Pearson correlation for measuring the association between the
two variables?
A. Nonlinearity
B. These variables are not quantitative.
C. The presence of an outlier.
D. Both A and B.
E. All of the above.
22.4.4 Perform a Wilcoxon Signed-Rank test.
9. Suppose that ten new smart phone models were evaluated by two consumer
electronics magazines (Popular Electronics and Electronics Now) from 1 (best) to 10
(worst). To determine if there is difference in the rankings between the two
magazines, the appropriate nonparametric method is
A. Wilcoxon Rank-Sum
B. Wilcoxon Signed-Rank
C. Spearman’s rho
D. Kruskal Wallis
E. Kendall’s tau
22.5.2 Identify and/or perform an appropriate test.
10. The nonparametric alternative to the randomized block design is the
A. Kruskal-Wallis test.
B. Kendall’s tau.
C. Wilcoxon Rank Sum test.
D. Friedman test.
E. Mann-Whitney test.
Quiz D 22-21
Chapter 22: Nonparametric Methods – Quiz D – Key