Question 1

Which of the following is not true about the Spearman's rho compared with the correlation coefficient r?

Accepted Answer

A)  Spearman's rho is not sensitive to violations of the Linearity condition. 
B)  Spearman's rho is not significantly affected by outliers. 
C)  Spearman's rho can be smaller than - 1 and greater than 1. 
D)  Spearman's rho can be used for data with bends and outliers. 
E)  It can be used when only ranks are known. 
A)  Spearman's rho is not sensitive to violations of the Linearity condition. 
B)  Spearman's rho is not significantly affected by outliers. 
C)  Spearman's rho can be smaller than - 1 and greater than 1. 
D)  Spearman's rho can be used for data with bends and outliers. 
E)  It can be used when only ranks are known. C

Question 2

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

Accepted Answer

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

Question 3

Eight hybrid cars are used to determine if there is a difference in fuel consumption (l/100 km) with and without a particular additive. The data are shown below.
 
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.

Accepted Answer

a. Wilcoxon signed-rank test.
b. Yes. The data are appropriately paired. We assume that the cars are randomly selected and both distributions are symmetric.
c. Let the difference be d = With Additive - Without Additive.
H0: The median difference in (l/100km) with and without the additive is zero.   HA: The median difference in (l/100km) with and without the additive is not zero.   d.
   We get T- = 32.5 and T+ = 3.5, therefore the test statistic value is 3.5. The critical value from the table W2 is 6. We reject the null hypothesis and conclude that the median difference in (l/100 km) with and without the additive is different from zero. Thus, there is a difference in fuel consumption (l/100 km) with and without a particular additive.

Question 4

We use Spearman's Rank Correlation to find whether there is a strong association between two variables. We find that the Spearman's rho is equal to 0.18 for the sample size n = 7. The correct value of the test statistic to determine whether two variables are dependent on each other is

Accepted Answer

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

Question 5

Consider the following to answer the question(s) below:
Assume that a Kruskal-Wallis test is being conducted to determine whether or not all groups come from the same distribution.
 
-What is the correct value of the test statistic?

Accepted Answer

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

Question 6

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

Accepted Answer

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. 
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 7

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

Accepted Answer

A)  the null hypothesis should not be rejected and there is no evidence that the median of the differences differs from zero. 
B)  the null hypothesis should be rejected and that the groups are not all the same. 
C)  the alternative hypothesis should not be rejected and the median of the differences is not zero. 
D)  as T = 5 > Tcr = 2, we support the alternative hypothesis. 
E)  the groups are different, as T = 5 > Tcr = 2. 
A)  the null hypothesis should not be rejected and there is no evidence that the median of the differences differs from zero. 
B)  the null hypothesis should be rejected and that the groups are not all the same. 
C)  the alternative hypothesis should not be rejected and the median of the differences is not zero. 
D)  as T = 5 > Tcr = 2, we support the alternative hypothesis. 
E)  the groups are different, as T = 5 > Tcr = 2.

Question 8

Consider the following to answer the question(s) below:
A paint manufacturer is interested in determining whether there is a difference in 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

Accepted Answer

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

Question 9

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?

Accepted Answer

a. Kruskal-Wallis Test.
b. H0: All four

Question 10

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 (case study and online interactive) to teach about various leadership styles. To compare the effectiveness of the two approaches, the appropriate nonparametric procedure is the

Accepted Answer

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

Question 11

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

Accepted Answer

A)  the null hypothesis should be rejected and the median of the differences is not zero. 
B)  the null hypothesis should not be rejected and the median of the differences is zero. 
C)  we know that the groups are the same. 
D)  the alternative hypothesis should be rejected and there is no difference between the pairs. 
E)  all groups are the same, as T = 6 < Tcrt = 8. 
A)  the null hypothesis should be rejected and the median of the differences is not zero. 
B)  the null hypothesis should not be rejected and the median of the differences is zero. 
C)  we know that the groups are the same. 
D)  the alternative hypothesis should be rejected and there is no difference between the pairs. 
E)  all groups are the same, as T = 6 < Tcrt = 8.

Question 12

Consider the following to answer the question(s) below:
Assume that a Kruskal-Wallis test is being conducted to determine whether or not all groups come from the same distribution.
 
-At α = 0.05,

Accepted Answer

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 that at least one group has the different distribution from the others. 
C)  we support the alternative hypothesis. 
D)  as H = 2.16 < χcrt2 = 5.991, we fail to reject the alternative hypothesis. 
E)  as H = 2.16 < χcrt2 = 5.991, we reject the null hypothesis and conclude the groups do not come from the same distribution. 
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 that at least one group has the different distribution from the others. 
C)  we support the alternative hypothesis. 
D)  as H = 2.16 < χcrt2 = 5.991, we fail to reject the alternative hypothesis. 
E)  as H = 2.16 < χcrt2 = 5.991, we reject the null hypothesis and conclude the groups do not come from the same distribution.

Question 13

Which of the following statements is false regarding nonparametric methods?

Accepted Answer

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. 
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 14

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?

Accepted Answer

a. Kruskal-Wallis Test
b. H0: All three

Question 15

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 2013 to January 2016. 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

Accepted Answer

A)  the null hypothesis should be rejected. 
B)  the alternative hypothesis should not be rejected. 
C)  there is a difference in predictions provided by the two groups of economists. 
D)  since TL= 28 < 29.5 < TU = 56, we can conclude that two groups of economists have different predictions. 
E)  the null hypothesis should not be rejected; there is no significant difference in predictions provided by the two groups of economists. 
A)  the null hypothesis should be rejected. 
B)  the alternative hypothesis should not be rejected. 
C)  there is a difference in predictions provided by the two groups of economists. 
D)  since TL= 28 < 29.5 < TU = 56, we can conclude that two groups of economists have different predictions. 
E)  the null hypothesis should not be rejected; there is no significant difference in predictions provided by the two groups of economists.

Question 16

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

Accepted Answer

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)  the total of the values is 9 and we conclude there is a significant difference. 
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)  the total of the values is 9 and we conclude there is a significant difference.

Question 17

Consider the following to answer the question(s) below:
Assume that a Kruskal-Wallis test is being conducted to determine whether or not all groups come from the same distribution.
 
-What is the critical value for α = 0.05?

Accepted Answer

A)  5.991 
B)  7.815 
C)  7.378 
D)  12.838 
E)  9.348 
A)  5.991 
B)  7.815 
C)  7.378 
D)  12.838 
E)  9.348

Question 18

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.

Accepted Answer

a. Wilcoxon rank-sum / Mann-Whitney test

Question 19

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

Accepted Answer

A)  8.345. 
B)  12.315. 
C)  4.995. 
D)  2.635. 
E)  402.760. 
A)  8.345. 
B)  12.315. 
C)  4.995. 
D)  2.635. 
E)  402.760.

Question 20

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

Accepted Answer

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

Which of the following is not true about the Spearman's rho compared with the correlation coefficient r?

We use Spearman's Rank Correlation to find whether there is a strong association between two variables. We find that the Spearman's rho is equal to 0.18 for the sample size n = 7. The correct value of the test statistic to determine whether two variables are dependent on each other is

Consider the following to answer the question(s) below: Assume that a Kruskal-Wallis test is being conducted to determine whether or not all groups come from the same distribution. -What is the correct value of the test statistic?

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

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

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

Consider the following to answer the question(s) below: Assume that a Kruskal-Wallis test is being conducted to determine whether or not all groups come from the same distribution. -At α = 0.05,

Which of the following statements is false regarding nonparametric methods?

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

Consider the following to answer the question(s) below: Assume that a Kruskal-Wallis test is being conducted to determine whether or not all groups come from the same distribution. -What is the critical value for α = 0.05?

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 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

Data

Surveys and Sampling

Displaying and Describing Categorical Data

Displaying and Describing Quantitative Data

Scatterplots, Association, and Correlation

Introduction to Linear Regression

Randomness and Probability

Random Variables and Probability Distributions

Sampling Distributions

Confidence Intervals for Proportions

Testing Hypotheses About Proportions

Confidence Intervals and Hypothesis Tests for Means

Comparing Two Means

Design of Experiments and Analysis of Variance Anova

Inference for Counts: Chi-Square Tests

Inference for Regression

Understanding Regression Residuals

Multiple Regression

Building Multiple Regression Models

Time Series Analysis

Decision Making and Risk

Quality Control

Exploring and Collecting Data

Understanding Probability Distributions and Statistical Inference

Exploring Relationships Among Variables

Using Statistics for Decision Making

Filters

Exam 17: Nonparametric Methods

Which of the following is not true about the Spearman's rho compared with the correlation coefficient r?

We use Spearman's Rank Correlation to find whether there is a strong association between two variables. We find that the Spearman's rho is equal to 0.18 for the sample size n = 7. The correct value of the test statistic to determine whether two variables are dependent on each other is

Consider the following to answer the question(s) below: Assume that a Kruskal-Wallis test is being conducted to determine whether or not all groups come from the same distribution. -What is the correct value of the test statistic?

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

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

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

Consider the following to answer the question(s) below: Assume that a Kruskal-Wallis test is being conducted to determine whether or not all groups come from the same distribution. -At α = 0.05,

Which of the following statements is false regarding nonparametric methods?

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

Consider the following to answer the question(s) below: Assume that a Kruskal-Wallis test is being conducted to determine whether or not all groups come from the same distribution. -What is the critical value for α = 0.05?

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 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

Data

Surveys and Sampling

Displaying and Describing Categorical Data

Displaying and Describing Quantitative Data

Scatterplots, Association, and Correlation

Introduction to Linear Regression

Randomness and Probability

Random Variables and Probability Distributions

Sampling Distributions

Confidence Intervals for Proportions

Testing Hypotheses About Proportions

Confidence Intervals and Hypothesis Tests for Means

Comparing Two Means

Design of Experiments and Analysis of Variance Anova

Inference for Counts: Chi-Square Tests

Inference for Regression

Understanding Regression Residuals

Multiple Regression

Building Multiple Regression Models

Time Series Analysis

Decision Making and Risk

Quality Control

Exploring and Collecting Data

Understanding Probability Distributions and Statistical Inference

Exploring Relationships Among Variables

Using Statistics for Decision Making

Filters