Deck 17: Nonparametric Methods

Question 1

The Spearman's rho is equal to 0.18 and the sample size n = 7. The correct value of the test statistic to determine if it is significantly different from zero is

A) 0.409
B) 0.754
C) 0.875
D) 0.771
E) 2.42

Answer 1

A

Question 2

Consider the following to answer the question(s) below:
A paint manufacturer is interested in determining whether there is a difference in the median time it takes for two different brands of paint to dry once they have been applied to a wall surface. To test this, the company has selected a random sample of 5 walls and applied Brand 1, and another 5 walls and applied Brand 2. The following data reflect the actual drying time in hours:

Using Tukey's quick test to determine whether there is a difference in the two brands we can say that

A) The total of the values is 6 and we conclude there is no significant difference.
B) The total of the values is 6 and we conclude there is a significant difference.
C) The total of the values is 4 and we conclude there is no significant difference.
D) The total of the values is 4 and we conclude there is a significant difference.
E) None of the above are correct.

Answer 2

A

Question 3

Consumers were asked to "rate" the taste of three popular brands of yogurt that have been modified to include fibre. The data are shown in the table below. Are there differences in the results among the three brands?
a. What nonparametric method is appropriate for analyzing these data?
b. State the null and alternative hypotheses.
c. Perform the test and state your conclusion at α = 0.05.
d. If these data did satisfy the assumptions for performing ANOVA, what are the disadvantages of using this nonparametric method instead?

Answer 3

a. Kruskal-Wallis Test
b. H0: All three brands have the same distribution of customer rating.
HA: At least one brand has a different distribution from the others.
c.
H = 8.345. Critical χ2 = 5.991. Therefore we reject the null hypothesis and conclude that at least one brand has a different distribution from the others.
d. ANOVA would be more powerful. Using the Kruskal-Wallis instead of ANOVA, when the assumptions for the latter are satisfied, decreases the power of the test.

Question 4

Consider the following to answer the question(s) below:
A paint manufacturer is interested in determining whether there is a difference in the median time it takes for two different brands of paint to dry once they have been applied to a wall surface. To test this, the company has selected a random sample of 5 walls and applied Brand 1, and another 5 walls and applied Brand 2. The following data reflect the actual drying time in hours:

The sum of all the ranks for this test is

A) 55
B) 10
C) 25
D) 90
E) 45

Question 5

A particular additive is claimed to increase the fuel efficiency of hybrid vehicles. Eight hybrid cars are used to determine if there is a difference in fuel efficiency (l/100km) with and without the additive. The appropriate nonparametric method to use for these data is the

A) Kruskal-Wallis test
B) Kendall's tau test
C) Wilcoxon signed-rank test
D) Wilcoxon rank-sum test
E) Spearman's rho test

Question 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) reject the null hypothesis and conclude that the groups are not all the same
E) not reject the null hypothesis and conclude that the groups are all the same

Question 7

For the scatterplots shown below, indicate what about the data make nonparametric
methods appropriate for measuring the association between x and y.
a. b.

Question 8

A management professor was teaching a course in business leadership as part of an executive MBA program. She 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) Spearman's rho test
C) Wilcoxon signed-rank test
D) Wilcoxon rank-sum test
E) Friedman test

Question 9

Consumer ratings for three popular brands of yogurt are shown below. 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) indeterminate

Question 10

Suppose that 6 economists who work for the federal government and 7 university economists were asked to predict the percentage change in the Canada's GDP 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) The null hypothesis should be rejected and that there is a difference in predictions provided by the two groups of economists.
E) The null hypothesis should not be rejected and that there is not a difference in predictions provided by the two groups of economists

Question 11

The best tasting ice creams are generally high in fat content, which gives them a creamy texture. Four brands of ice cream were tested by consumers who graded their level of creaminess (A = very creamy to F = not creamy). Each brand was rated by a different group of consumers (the data are shown below). Are there differences in perceived creaminess among the four brands?
a. What nonparametric method is appropriate for analyzing these data?
b. State the null and alternative hypotheses.
c. Perform the test and state your conclusion at α = 0.10.
d. If these data did satisfy the assumptions for performing ANOVA, what are the disadvantages of using this nonparametric method instead?

Question 12

Consider the following to answer the question(s) below:
A paint manufacturer is interested in determining whether there is a difference in the median time it takes for two different brands of paint to dry once they have been applied to a wall surface. To test this, the company has selected a random sample of 5 walls and applied Brand 1, and another 5 walls and applied Brand 2. The following data reflect the actual drying time in hours:

The appropriate nonparametric method to use for these data is the

A) Wilcoxon rank-sum test
B) Kruskal-Wallis test
C) Kendall's tau test
D) Spearman's rho test
E) Wilcoxon signed-rank test

Question 13

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

A) The null hypothesis should be rejected and that the groups are not all the same.
B) The null hypothesis should not be rejected and that the groups are not all the same.
C) The groups are the same.
D) The null hypothesis should be rejected and that the groups are the same.
E) The null hypothesis should not be rejected and that the groups are the same.

Question 14

Suppose the Wilcoxon signed-rank test was used on seven pairs of data. If the calculated test statistic for a two-tailed test was found to be 5, at α = 0.05 we can conclude that

A) The null hypothesis should not be rejected and that the groups are all the same.
B) The null hypothesis should be rejected and that the groups are not all the same.
C) The null hypothesis should not be rejected and that the groups are not all the same.
D) The null hypothesis should be rejected and that the groups are all the same.
E) The groups are different.

Question 15

Suppose that 6 economists who work for the federal government and 7 university economists were asked to grade the effectiveness of the federal government's stimulus bill in terms of its ability to increase jobs over the next two years. The grades are shown below. Do the two groups differ in terms of their opinion?
a. What nonparametric method is appropriate for analyzing these data?
b. Are the assumptions satisfied for applying this method? Explain.
c. State the null and alternative hypotheses.
d. Perform the test and state your conclusion at α = 0.10.

Question 16

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 -0.45. We can say that

A) There is a high level of agreement between the two magazine rankings.
B) The association between the two magazine rankings is strong and positive.
C) There is an outlier in the data that affects the results.
D) The association between the two magazine ratings is moderate and negative.
E) Both magazines had the same smart phone ranked as number 1.

Question 17

The Wilcoxon signed-rank test is used to test which of the following types of hypotheses?

A) It is used to test hypotheses involving the median of paired samples.
B) It is used to test hypotheses involving three or more population medians.
C) It is used to test hypotheses involving the variances of two or more populations.
D) It is used to test hypotheses involving the variances of paired samples.
E) It is used to test hypotheses involving two or more population proportions.

Question 18

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, Spearman's rho 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.

Question 19

Which of the following is not an advantage of the Spearman's Rank Correlation over the correlation coefficient r?

A) It requires the Linearity condition to hold.
B) It is not significantly affected by outliers.
C) It is not altered by re-expressing the data using functions such as logarithms.
D) It does not require the Linearity condition to hold.
E) It can be used when only ranks are known.

Question 20

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 test
C) Wilcoxon signed-rank test
D) Wilcoxon rank-sum test
E) Spearman's rho test

Question 21

Consider the following to answer the question(s) below:
Assume that a Kruskal-Wallis test is being conducted to determine whether or not the medians of three populations are equal. The sum of rankings and the sample size for each group are below.
Group 1 Group 2 Group 3
T1 = 60 T2 = 36 T3 = 24
n1 = 6 n2 = 5 n3 = 4
What is the critical value for α = 0.05?

A) 5.9915
B) 0.1026
C) 7.3778
D) 7.8147
E) 9.34884

Question 22

Consider the following to answer the question(s) below:
Assume that a Kruskal-Wallis test is being conducted to determine whether or not the medians of three populations are equal. The sum of rankings and the sample size for each group are below.
Group 1 Group 2 Group 3
T1 = 60 T2 = 36 T3 = 24
n1 = 6 n2 = 5 n3 = 4
What is the correct value of the test statistic?

A) 2.16
B) 7.81
C) 48.68
D) 12.59
E) 15.69

Question 23

Consider the following to answer the question(s) below:
Assume that a Kruskal-Wallis test is being conducted to determine whether or not the medians of three populations are equal. The sum of rankings and the sample size for each group are below.
Group 1 Group 2 Group 3
T1 = 60 T2 = 36 T3 = 24
n1 = 6 n2 = 5 n3 = 4
At α = 0.05

A) We fail to reject the null hypothesis and conclude the groups come from the same distribution.
B) We reject the null hypothesis and conclude the groups come from the same distribution.
C) We reject the null hypothesis.
D) We fail to reject the null hypothesis.
E) We reject the null hypothesis and conclude the groups do not come from the same distribution.