# Quiz 16: Nonparametric Methods: Analysis of Ordinal Data

Statistics

84

All Questions

69

Multiple Choice

15

True False

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Essay

0

Short Answer

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Not Answered

Q 1

We can apply nonparametric tests to problems involving interval or ratio data.

Free

True False

True

Q 2

We can apply parametric tests,such as the t-test,to ordinal or ranked level of measurement.

Free

True False

False

Q 3

The Kruskal-Wallis one-way analysis of variance by ranks is especially appropriate to test whether three or more population means are equal if the data are measured with an ordinal scale and/or the populations are not normal.

Free

True False

True

Q 4

To apply the Kruskal-Wallis test,the samples selected from the populations must be dependent.

True False

Q 5

The Wilcoxon signed-rank test can replace the paired t-test when the assumptions for t cannot be met.

True False

Q 6

The Wilcoxon signed-rank test of differences requires that the data be at least ordinal scaled and that the two samples be related.

True False

Q 7

The sign test is an appropriate nonparametric test for dependent samples.

True False

Q 8

For small samples,the test statistic for the sign test is the z-statistic.

True False

Q 9

The Wilcoxon rank-sum test compares two dependent populations.

True False

Q 10

The Wilcoxon rank-sum test computes a z-test statistic.

True False

Q 11

The Wilcoxon rank-sum test includes a variable,W. It is the sum of the observed values from the larger sample.

True False

Q 12

Spearman's rank-order correlation coefficient may assume a value from −1 to +1.

True False

Q 13

A Spearman's rank-order correlation coefficient of 0.91 indicates a very weak relationship.

True False

Q 14

The alternate hypothesis states that the correlation between two populations is greater than zero. The test of significance is one-tailed.

True False

Q 15

The test statistic for the null hypothesis that the correlation among the ranks is equal to zero is a chi-square statistic.

True False

Q 16

A one-tailed sign test is used to test for differences between two populations at the 0.10 level of significance. There were nine plus signs and five minus signs. What is the decision regarding the null hypothesis?
A)Fail to reject the null hypothesis.
B)Reject the null hypothesis.
C)Neither reject nor fail to reject the null hypothesis.
D)Should have used a paired t-test.

Multiple Choice

Q 17

If a sign test is applied,what is the null hypothesis for a two-tailed test?
A)H

_{0}: π = 0.50 B)H_{0}: π is not equal to 0.50 C)H_{0}: π > 0.50 D)H_{0}: π < 0.50 Multiple Choice

Q 18

What is the test statistic for the sign test if the sample size is large?
A)Chi-square
B)Standard normal z
C)Binomial
D)Wilcoxon signed-rank

Multiple Choice

Q 19

To apply the large-sample procedure for the sign test,the sample size should be at least ________.
A)2
B)8
C)100
D)10

Multiple Choice

Q 20

To use the sign test with paired data,trials must ________.
A)be independent
B)be dependent
C)have three or more outcomes
D)have a probability of 0.50

Multiple Choice

Q 21

What is a null hypothesis for a one-tailed sign test?
A)H

_{0}: π = 0 B)H_{0}: π ≥ 1.00 C)H_{0}: π = 0.50 D)H_{0}: π ≤ 0.50 Multiple Choice

Q 22

What is the first step in applying the sign test?
A)Rank the paired data from high to low or vice versa.
B)Apply a correction factor to each observation.
C)Determine the sign of difference between each observed pair of data.
D)Determine the number of degrees of freedom.

Multiple Choice

Q 23

The decision rule for a small sample sign test is based on a(n)________.
A)binomial distribution
B)chi-square distribution
C)normal distribution
D)F-distribution

Multiple Choice

Q 24

Which statement is true when using the sign test and a large sample?
A)The chi-square value is applied to arrive at the degrees of freedom.
B)A normal distribution should be used to approximate a binomial distribution.
C)Wilcoxon z is the test statistic.
D)The F distribution is applied.

Multiple Choice

Q 25

When testing H

_{0}: Median equals $12.40 and the alternate hypothesis: Median does not equal $12.40,what is the critical value of z at the 10% level of significance? A)±1.96 B)±1.65 C)±2.33 D)±0.10 Multiple Choice

Q 26

A two-tailed test of hypothesis was conducted and 60 values were above the median. The computed z = 1.90. At the 0.05 level,what is the decision regarding the null hypothesis?
A)Reject the null hypothesis with a 0.05 Type I error rate.
B)Fail to reject the null hypothesis.
C)Reject the null hypothesis with a 0.025 Type I error rate.
D)None of these answers is correct.

Multiple Choice

Q 27

To determine whether four population means are equal,a sample from each population was selected at random. Using the Kruskal-Wallis test,H was computed to be 2.09. What is our decision at the 0.05 level of risk?
A)Fail to reject the null hypothesis because 0.05 < 2.09.
B)Fail to reject the null hypothesis because 2.09 < 7.815.
C)Reject the null hypothesis because 7.815 > 2.09.
D)Reject the null hypothesis because 2.09 > critical value of 1.96.

Multiple Choice

Q 28

What test is an appropriate substitute for the ANOVA procedure if the assumptions for ANOVA cannot be met?
A)z
B)t
C)Rank correlation
D)Kruskal−Wallis

Multiple Choice

Q 29

Which of the following tests is not a distribution-free test?
A)Rank correlation
B)Student's t
C)Kruskal-Wallis
D)Wilcoxon rank-sum

Multiple Choice

Q 30

This nonparametric test requires at least ordinal level data. It is used if the assumptions required for the paired t-test cannot be met. Which test is it?
A)Wilcoxon signed-rank
B)ANOVA
C)Rank correlation
D)Kruskal-Wallis

Multiple Choice

Q 31

Which of the following statements is true regarding the sign test?
A)It is based on the sign of the differences.
B)It is used with independent populations.
C)The chi-square is used as the test statistic.
D)The "T" statistic is the test statistic.

Multiple Choice

Q 32

What is the test statistic for Spearman's rank correlation?
A)t
B)z
C)F
D)Chi-square

Multiple Choice

Q 33

What is a requirement that must be met before the Kruskal-Wallis one-way analysis of variance by ranks test can be applied?
A)Populations must be normal or near normal.
B)Populations must be independent.
C)Population standard deviations must be equal.
D)Data must be at least interval level.

Multiple Choice

Q 34

The distribution of the sample statistic (H)for the Kruskal-Wallis test is approximately equal to the ________.
A)F-distribution
B)t-distribution
C)chi-square distribution
D)standard normal distribution

Multiple Choice

Q 35

For the coefficient of rank correlation,what scale is used to measure the data?
A)Nominal
B)Ordinal
C)Interval
D)Ratio

Multiple Choice

Q 36

Which of the following values of Spearman's (rho)indicates the strongest relationship between two variables?
A)-0.91
B)-0.05
C)+0.64
D)+0.89

Multiple Choice

Q 37

A data set has six values: 10,12,21,26,26,and 26. What ranks would be assigned to 26?
A)4,5,6
B)4,4,4
C)5,5,5
D)5.5,5.5,5.5

Multiple Choice

Q 38

For a given set of 12 ranked data values,the sum of the squared differences is 63.18. What is Spearman's coefficient of rank correlation for the data?
A)+0.7791
B)−0.7791
C)+0.2209
D)−0.2209

Multiple Choice

Q 39

A hypothesis test that rho is zero is conducted at the 5% level of significance. If Spearman's (rho)is 0.86 for a sample of 15 observations,what is the computed value of the t-statistic?
A)0.456
B)6.08
C)0.425
D)2.16

Multiple Choice

Q 40

A study was conducted on the percent of total advertising dollars spent by 10 local firms for advertising in the press and on cable television. Results were ranked with a resulting sum of squared differences equal to 128. What is Spearman's coefficient of rank correlation?
A)−0.871
B)+0.224
C)+0.234
D)−0.234

Multiple Choice

Q 41

A study was conducted on the percent of total advertising dollars spent by 10 local firms for advertising in the press and on cable television. Results were ranked with a resulting sum of squared differences equal to 128. What is the computed value of t?
A)0.719
B)0.804
C)1.339
D)0.650

Multiple Choice

Q 42

A study was conducted on the percent of total advertising dollars spent by 10 local firms for advertising in the press and on cable television. Results were ranked with a resulting sum of squared differences equal to 128. What is the sum of the differences in ranks?
A)128
B)100
C)0
D)1

Multiple Choice

Q 43

The following are the ratings (0 to 4)given by 12 individuals for two possible new flavors of soft drinks. Wilcoxon rank-sum is to be used. What is the sum of the ranks for flavor #1?
A)144
B)139
C)156
D)153

Multiple Choice

Q 44

The following are the ratings (0 to 4)given by 12 individuals for two possible new flavors of soft drinks. Wilcoxon rank-sum is to be used. What is the sum of the ranks for flavor #2?
A)153
B)139
C)144
D)156

Multiple Choice

Q 45

The following are the ratings (0 to 4)given by 12 individuals for two possible new flavors of soft drinks. Wilcoxon rank-sum is to be used. What is W,if flavor #1 is identified as population 1?
A)153
B)156
C)144
D)139

Multiple Choice

Q 46

The following are the ratings (0 to 4)given by 12 individuals for two possible new flavors of soft drinks. Wilcoxon rank-sum is to be used. What is the z-test statistic?
A)−0.3464
B)0.3464
C)8.6602
D)0.2807

Multiple Choice

Q 47

The following are the ratings (0 to 4)given by 12 individuals for two possible new flavors of soft drinks. Wilcoxon rank-sum is to be used. At the 0.05 level of significance,what is the decision?
A)Fail to reject null hypothesis; critical value is ±1.65.
B)Fail to reject null hypothesis; critical value is ±1.96.
C)Reject null hypothesis; critical value is 0.1732.
D)Reject null hypothesis; critical value is 0.3464.

Multiple Choice

Q 48

Twenty economists were sampled and asked to predict if the national economy would improve during the next 12 months. Eleven of the economists predicted an increase,two economists predicted no change,and seven economists predicted a decrease in the economy. Conduct a hypothesis test at the 0.10 significance level to determine if the majority of economists predict an increase. The null hypothesis is ________.
A)H

_{0}: π = 0.5 B)H_{0}: π ≠ 0.5 C)H_{0}: π ≤ 0.5 D)H_{0}: π ≥ 0.5 Multiple Choice

Q 49

Twenty economists were sampled and asked to predict if the national economy would improve during the next 12 months. Eleven of the economists predicted an increase,two economists predicted no change,and seven economists predicted a decrease in the economy. Conduct a hypothesis test at the 0.10 significance level to determine if the majority of economists predict an increase. The correct analysis would be a ________.
A)sign test based on the binomial distribution
B)sign test based on the standard normal distribution
C)chi-square test
D)Wilcoxon signed-rank test

Multiple Choice

Q 50

Twenty economists were sampled and asked to predict if the national economy would improve during the next 12 months. Eleven of the economists predicted an increase,two economists predicted no change,and seven economists predicted a decrease in the economy. Conduct a hypothesis test at the 0.10 significance level to determine if the majority of economists predicts an increase. The test statistic is ________.
A)0.224
B)1.179
C)1.707
D)0.179

Multiple Choice

Q 51

Twenty economists were sampled and asked to predict if the national economy would improve during the next 12 months. Eleven of the economists predicted an increase,two economists predicted no change,and seven economists predicted a decrease in the economy. Conduct a hypothesis test at the 0.10 significance level to determine if the majority of economists predicts an increase. Based on the analysis,we would conclude that ________.
A)the economists predict an increase in the economy
B)the economists predict a decrease in the economy
C)the economists predict no change in the economy
D)no conclusion can be reached

Multiple Choice

Q 52

A nonparametric test ________.
A)assumes that the populations are normally distributed
B)assumes that the populations have equal standard deviations
C)makes no assumptions about the population distributions
D)assumes that the populations follow a standard normal distribution

Multiple Choice

Q 53

A nonparametric test requires that the data can be ________.
A)ranked
B)summed
C)graphed
D)transformed

Multiple Choice

Q 54

A sign test cannot be applied when the data are ________.
A)nominal
B)ordinal
C)interval
D)ratio

Multiple Choice

Q 55

In the Wilcoxon signed-rank test,the ranks are ________.
A)assigned to paired observation with a difference of zero
B)assigned for each sample
C)assigned the sign (either positive or negative)of the difference between a pair of observations
D)all positive in sign

Multiple Choice

Q 56

To test the hypothesis,the Wilcoxon signed-rank test uses a ________.
A)z-statistic
B)T-test statistic
C)chi-square statistic
D)student's t-statistic

Multiple Choice

Q 57

Using the following data,the Wilcoxon signed-rank hypothesis test is used to test the hypothesis that there is no difference between the Before and After populations. What are the sum of the ranks?
A)4 and 6
B)5
C)17
D)6 and −11

Multiple Choice

Q 58

Using the following data,the Wilcoxon signed-rank hypothesis test is used to test the hypothesis that the test results of a treatment after training are greater than the test results before the treatment. What is the sum of the ranks?
A)41
B)28
C)19 and −7
D)6 and 15

Multiple Choice

Q 59

Using the following data,the Wilcoxon signed-rank hypothesis test is used to test the hypothesis that the test results of a treatment after training are greater than the test results before the treatment. The Wilcoxon critical value is 3 for n = 7 with a 0.05 significance level. What decision should be made regarding the null hypothesis?
A)Reject the null hypothesis and conclude that After is greater than Before.
B)Reject the null hypothesis and conclude that Before is greater than After.
C)Fail to reject the null hypothesis.
D)Reject the null hypothesis and conclude that there is no difference between the Before and After.

Multiple Choice

Q 60

Using the following data,the Wilcoxon signed-rank hypothesis test is used to test the hypothesis that the test results of a treatment after training are greater than the test results before the treatment. The Wilcoxon critical value is 3 for n = 7 with a 0.05 significance level. What decision should be made regarding the null hypothesis?
A)Reject the null hypothesis and conclude that the After is greater than Before.
B)Reject the null hypothesis and conclude that the Before is greater than After.
C)Fail to reject the null hypothesis.
D)Reject the null hypothesis and conclude that there is no difference between the Before and After.

Multiple Choice

Q 61

When the paired observations are equal in a Wilcoxon signed-rank test hypothesis ________.
A)observations are removed from the analysis.
B)the ranks are averaged.
C)a zero is assigned to the difference and retained in the analysis.
D)observations are removed from the analysis and n is not changed.

Multiple Choice

Q 62

In the Kruskal-Wallis test,the degrees of freedom are ________.
A)the total number of observations less one
B)the total number of observations
C)the number of populations less one
D)each sample size less one

Multiple Choice

Q 63

In the Kruskal-Wallis test for the following data,what is the sum of the ranks for Sample 1?
A)9
B)163
C)3
D)23

Multiple Choice

Q 64

In the Kruskal-Wallis test for the following data,what are the degrees of freedom?
A)8
B)2
C)6
D)3

Multiple Choice

Q 65

In the Kruskal-Wallis test for the following data,what is the sum of the ranks for Sample 3?
A)9
B)80
C)3
D)23

Multiple Choice

Q 66

In the Kruskal-Wallis test for the following data,what is the sum of the ranks for Sample 1?
A)61.5
B)163
C)6
D)253

Multiple Choice

Q 67

In the Kruskal-Wallis test for the following data,what are the degrees of freedom?
A)5
B)2
C)16
D)15

Multiple Choice

Q 68

In the Kruskal-Wallis test for the following data,what is the sum of the ranks for Sample 3?
A)57
B)80
C)4
D)210

Multiple Choice

Q 69

In a Kruskal-Wallis test,the null hypothesis states equality among five different populations. The sample size for each population exceeds five. What is the critical value for the test using a 0.05 significance level?
A)1.960
B)5.05
C)9.488
D)2.776

Multiple Choice

Q 70

For the rank correlation coefficient,what test statistic is used to test the null hypothesis that the correlation is zero?
A)Chi-square
B)Student's t-statistic
C)z-statistic
D)H

Multiple Choice

Q 71

If Spearman's rank correlation statistic is −0.91 with a sample size of 10,what is the test statistic value to test the hypothesis that the rank correlation coefficient is zero?
A)−6.2080
B)6.2080
C)1.960
D)2.262

Multiple Choice

Q 72

For a given set of 12 ranked data values,the sum of the squared differences is 63.18. What is the test statistic value to test the hypothesis that the rank correlation coefficient is zero?
A)0.221
B)0.673
C)0.779
D)0.327

Multiple Choice

Q 73

A hypothesis test that a rank correlation coefficient is zero is conducted at the 5% level of significance. If the correlation coefficient is 0.50 for a sample of 15 observations,what is the computed value of the t-statistic?
A)0.456
B)6.08
C)2.082
D)2.2361

Multiple Choice

Q 74

A hypothesis test that rho is zero is conducted at the 5% level of significance. If Spearman's (rho)is 0.75 for a sample of 15 observations,what is the computed value of the t-statistic?
A)0.456
B)4.088
C)4.391
D)2.236

Multiple Choice

Q 75

A hypothesis test that rho is zero is conducted at the 5% level of significance. If Spearman's (rho)is 0.50 for a sample of 15 observations,what is the critical value?
A)±2.160
B)±2.131
C)±1.771
D)±1.753

Multiple Choice

Q 76

Which of the following tests would not be an example of a nonparametric method?
A)Sign test
B)t-test
C)Kruskal-Wallis test
D)Wilcoxon signed-rank test

Multiple Choice

Q 77

A sign test is a ________.
A)parametric method used to determine the differences between two related observations
B)nonparametric method based on the sign of a difference between two related observations
C)nonparametric method that uses the chi-square distributions as the test statistic
D)parametric method for determining the differences between related observations where distribution dependent tests are used

Multiple Choice

Q 78

A nonparametric equivalent of a version of the ANOVA test,which tests the hypothesis that several population means are equal,is known as the ________.
A)Wilcoxon ranked-sum test
B)Spearman's coefficient of rank correlation
C)Kruskal-Wallis test
D)sign test

Multiple Choice

Q 79

The Spearman coefficient of rank correlation is a ________.
A)measure of correlation used to determine whether several population means are equal
B)measure of the association between sets of ranked data
C)measure of correlation based on the sign of a difference between two related observations
D)goodness-of-fit test used to test for normality

Multiple Choice

Q 80

Twenty-five college seniors were given two brands of organic hamburgers to sample: Burger A and Burger B. Four students preferred Burger A and 21 preferred Burger B. A statistician wants to determine if one of the burgers is preferred over the other. The null hypothesis for this scenario is ________.
A)H

_{0}: μ = 5.0 B)H_{0}: π = 5.0 C)H_{0}: μ = 0.5 D)H_{0}: π = 0.5 Multiple Choice

Q 81

Twenty-five college seniors were given two brands of organic hamburgers to sample: Burger A and Burger B. Four students preferred Burger A and 21 preferred Burger B. A statistician wants to determine if one of the burgers is preferred over the other. To test the null hypothesis,which of the following probability distributions is used?
A)Poisson
B)Chi-square
C)Standard normal
D)Binomial

Multiple Choice

Q 82

Fifty-five voters from a sample of 80 indicated that they favored casino gambling in their city. The city council is interested in finding out whether or not there is a significant difference between the proportions of those favoring and not favoring casino gambling in their community. μ in this scenario is ________.
A)55
B)80
C)40
D)25

Multiple Choice

Q 83

Fifty-five voters from a sample of 80 indicated they favored casino gambling in their city. The city council is interested in finding out whether there is a significant difference between the proportions of those favoring and not favoring casino gambling in their community. σ in this scenario is ________.
A)8.94
B)3.42
C)4.47
D)7.42

Multiple Choice

Q 84

Fifty-five voters from a sample of 80 indicated that they favored casino gambling in their city. The city council is interested in finding out whether there is a significant difference between the proportions of those favoring and not favoring casino gambling in their community. The test statistic is ________.
A)0.50
B)3.71
C)80
D)3.24

Multiple Choice