# Quiz 16: Nonparametric Methods: Analysis of Ordinal Data

Statistics

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Q 3Q 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.

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Q 5Q 5

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

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Q 6Q 6

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

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Q 11Q 11

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

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Q 14Q 14

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

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Q 15Q 15

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

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Q 16Q 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.

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Q 17Q 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 < 0.50Free

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Q 18Q 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

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Q 19Q 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

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Q 20Q 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

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Q 21Q 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 ≤ 0.50Free

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Q 22Q 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.

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Q 23Q 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

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Q 24Q 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.

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Q 25Q 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)±0.10Free

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Q 26Q 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.

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Q 27Q 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.

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Q 28Q 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

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Q 29Q 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

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Q 30Q 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

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Q 31Q 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.

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Q 33Q 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.

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Q 34Q 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

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Q 35Q 35

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

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Q 36Q 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

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Q 37Q 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

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Q 38Q 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

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Q 39Q 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

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Q 40Q 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

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Q 41Q 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

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Q 42Q 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

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Q 43Q 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

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Q 44Q 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

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Q 45Q 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

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Q 46Q 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

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Q 47Q 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.

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Q 48Q 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 ≥ 0.5Free

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Q 49Q 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

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Q 50Q 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

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Q 51Q 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

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Q 52Q 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

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Q 53Q 53

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

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Q 54Q 54

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

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Q 55Q 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

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Q 56Q 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

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Q 57Q 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

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Q 58Q 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

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Q 59Q 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.

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Q 60Q 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.

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Q 61Q 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.

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Q 62Q 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

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Q 63Q 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

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Q 64Q 64

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

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Q 65Q 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

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Q 66Q 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

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Q 67Q 67

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

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Q 68Q 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

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Q 69Q 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

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Q 70Q 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

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Q 71Q 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

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Q 72Q 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

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Q 73Q 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

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Q 74Q 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

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Q 75Q 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

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Q 76Q 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

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Q 77Q 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

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Q 78Q 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

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Q 79Q 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

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Q 80Q 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 = 0.5Free

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Q 81Q 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

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Q 82Q 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

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Q 83Q 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

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Q 84Q 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

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