Deck 17: Nonparametric Statistics

Question 1

The appropriate test for comparing the medians of two populations using ordinal-level data from two related samples is the Wilcoxon test.

Answer 1

True

Question 2

The HYPERLINK "http://www.statisticssolutions.com/mann-whitney-u-test" Mann-Whitney U-test is used to test whether three or more independent HYPERLINK "http://www.experiment-resources.com/sample-group.html" samples of observations are drawn from the same or identical distributions.

Answer 2

False

Question 3

The Mann-Whitney U test is implemented differently for small samples than for large samples.

Answer 3

True

Question 4

The methods of parametric statistics can be applied to nominal or ordinal data.

Question 5

To compare the means of two populations which cannot be assumed to be normally distributed and only ordinal-level data is available from two independent samples,instead of the t-test for independent samples we should use the Mann-Whitney U test.

Question 6

Statistical techniques based on assumptions about the population from which the sample data are selected are called parametric statistics.

Question 7

The nonparametric counterpart of the t test to compare the means of two independent populations is the Mann-Whitney U test.

Question 8

The appropriate test for comparing the means of two populations using ordinal-level data from two related samples is the Wilcoxon test and not the Mann-Whitney U test.

Question 9

The sampling distribution of R,the number of runs,in the one-sample runs test for randomness of the observations in a large sample is approximately normal if H₀ is true.

Question 10

The appropriate test for comparing the means of two populations using ordinal-level data from two independent samples is the Mann-Whitney U test.

Question 11

The HYPERLINK "http://www.statisticssolutions.com/mann-whitney-u-test" Mann-Whitney U-test requires that the two samples under consideration have the same number of observations.

Question 12

In the one-sample runs test for randomness of the observations in a large sample the sampling distribution of R,the number of runs,is approximately binomial.

Question 13

Nonparametric statistics are sometimes called distribution-dependent statistics.

Question 14

The Mann-Whitney U test is a generalization of the two sample t-test under the underlying assumptions of equality of variances.

Question 15

An advantage of nonparametric statistics is that the computations on nonparametric statistics are usually less complicated than those for parametric statistics,particularly for small samples.

Question 16

Nonparametric statistical techniques are based on fewer assumptions about the population and the parameters compared to parametric statistical techniques.

Question 17

A disadvantage of nonparametric statistics is that the probability statements obtained from most nonparametric tests are not exact probabilities.

Question 18

No assumptions on the distribution of the difference are needed for the use of the Wilcoxon matched-pairs signed rank.

Question 19

The nonparametric alternative to linear regression is the Kruskal-Wallis test.

Question 20

The one-sample runs test is a nonparametric test of randomness in the sample data.

Question 21

Charles Clayton monitors the daily performance of his investment portfolio by recording a "+" or a "-" sign to indicate whether the portfolio's value increased or decreased from the previous day. His record for the last eighteen business days is "- + + - - - + - - + + + + + + + + -". The number of runs in this sample is _________.

A) seven
B) six
C) four
D) three
E) one

Question 22

Statistical techniques based on fewer assumptions about the population and the parameters are called _______.

A) population statistics
B) parametric statistics
C) nonparametric statistics
D) chi-square statistics
E) correlation statistics

Question 23

Statistical techniques based on assumptions about the population from which the sample data are selected are called _______.

A) population statistics
B) parametric statistics
C) nonparametric statistics
D) chi-square statistics
E) correlation statistics

Question 24

The nonparametric counterpart of the t test to compare the means of two independent populations is the _______.

A) chi-square goodness of fit test
B) chi-square test of independence
C) Mann-Whitney U test
D) Wilcoxon test
E) Friedman test

Question 25

The one-sample runs test is a ______________________.

A) nonparametric test for statistical independence
B) parametric test for statistical independence
C) nonparametric test of randomness
D) nonparametric test for correlation
E) parametric test of sequences

Question 26

The nonparametric alternative to analysis of variance for a randomized block design is the Friedman test.

Question 27

A production run of 500 items resulted in 29 defectives items.A defective item is coded as 1 and a good item as 0.The following is an output from Minitab. Runs Test: Defects
Runs test for Defects
Runs above and below K = 0.058
The observed number of runs = 57
The expected number of runs = 55.636
29 observations above K,471 below
P-value = 0.574
The null hypothesis for a one-sample runs test is __________________.

A) successive items did not constitute a random sample.
B) successive items constituted a random sample
C) the proportion of defective items is 0.05
D) the proportion of defective items is 0.058
E) the distribution is binomial

Question 28

The alternative hypothesis for the Friedman test is that at least one treatment is different from at least one other treatment.

Question 29

The methods of parametric statistics require ________________.

A) interval or ratio data
B) nominal or ordinal data
C) large samples
D) small samples
E) qualitative data

Question 30

Charles Clayton monitors the daily performance of his investment portfolio by recording a "+" or a "-" sign to indicate whether the portfolio's value increased or decreased from the previous day. His record for the last eighteen business days is "- + + - - - + - - + + + - + + + + -". The number of runs in this sample is _________.

A) uncertain
B) four
C) five
D) nine
E) one

Question 31

Which of the following tests should be used to compare the means of two populations if the samples are independent?

A) Mann-Whitney test
B) Wilcoxon test
C) Runs test
D) Spearman's test
E) Kruskal-Wallis test

Question 32

The degree of association of two variables cannot be estimated when only ordinal-level data are available.

Question 33

The alternate hypothesis for a one-sample runs test is __________________.

A) "the observations in the sample are not cross-linked"
B) "the observations in the sample are correlated"
C) "the observations in the sample are not statistically independent"
D) "the observations in the sample are not randomly generated"
E) "the observations are not systematically generated"

Question 34

The Kruskal-Wallis test is an extension of the HYPERLINK "http://en.wikipedia.org/wiki/Mann%E2%80%93Whitney_U" \o "Mann-Whitney U" Mann-Whitney U test to 3 or more groups.

Question 35

Nonparametric statistics are sometimes called _______________.

A) nominal statistics
B) interval statistics
C) distribution-dependent statistics
D) distribution-free statistics
E) qualitative statistics

Question 36

The null hypothesis for a one-sample runs test is __________________.

A) "the observations in the sample are randomly generated"
B) "the observations in the sample are not correlated"
C) "the observations in the sample are statistically independent"
D) "the observations in the sample are cross-linked"
E) "the observations are systematically generated"

Question 37

Prior to computing a Friedman test,the data are ranked within each block from smallest to largest.

Question 38

Spearman rank correlation values,r_x,range between +1 and 0.

Question 39

A production run of 500 items resulted in 29 defectives items.A defective item is coded as 1 and a good item as 0.The following is an output from Minitab. Runs Test: Defects
Runs test for Defects
Runs above and below K = 0.058
The observed number of runs = 57
The expected number of runs = 55.636
29 observations above K,471 below
P-value = 0.574
Using α=0.1,the conclusion is __________________.

A) successive items did not constitute a random sample.
B) successive items constituted a random sample
C) do not reject the hypothesis that successive items constituted a random sample
D) reject the hypothesis that successive items constituted a random sample
E) the distribution is binomial

Question 40

When only ordinal-level data are available,Spearman's rank correlation rather than the Pearson product-moment correlation coefficient must be used to analyze the association between two variables.

Question 41

The Kruskal-Wallis test is to be used to determine whether there is a significant difference in the satisfaction rating (alpha = 0.05)between three brands of boxed cake mix.Shoppers were asked to rate their satisfaction on various attributes and an aggregate satisfaction score ranging from 1-50 was computed.The following data were obtained: For this test,how many degrees of freedom should be used?

A) 3
B) 2
C) 4
D) 8
E) 1

Question 42

A Kruskal-Wallis test is to be performed. There will be four categories,and alpha is chosen to be 0.10.The critical chi-square value is _______.

A) 6.251
B) 2.706
C) 7.779
D) 4.605
E) 3.234

Question 43

In the Wilcoxon test of the differences between two populations,the value z statistic was calculated to be 1.80.If the level of significance is 0.10,which of the following decisions is appropriate?

A) Reject the null hypothesis
B) Do not reject the null hypothesis
C) Indeterminate without the sample size
D) Indeterminate without all of the data
E) Inconclusive

Question 44

A Mann-Whitney U test was performed to determine if there were differences in the average compute time for Dallas residents versus Atlanta residents.The travel time for 22 commuters in Dallas was compared to the travel time for 28 commuters in Atlanta.The U statistic was calculated to be 58.0 based on the sample sizes of 22 and 28.What is the z value for this test?

A) 51.17
B) 308
C) 0.117
D) -4.88
E) -2.44

Question 45

In the Wilcoxon test of the differences between two populations,the value z statistic was calculated to be 1.80.If the level of significance is 0.05,which of the following decisions is appropriate?

A) Reject the null hypothesis
B) Do not reject the null hypothesis
C) Indeterminate without the sample size
D) Indeterminate without all of the data
E) Inconclusive

Question 46

The Wilcoxon test was used on 16 pairs of data.The total of the ranks (T)were computed to be 76 (for + ranks)and 60 (for - ranks).The z value for this test is _____.

A) -0.41
B) -0.02
C) 0.02
D) 16
E) -0.041.

Question 47

Which of the following tests should be used to compare the means of three populations if the sample data is ordinal?

A) one-way analysis of variance
B) Kruskal-Wallis test
C) Wilcoxon test
D) Mann-Whitney test
E) Friedman test

Question 48

Suppose a research uses the Mann-Whitney test to determine if there is a difference in the volume of text messages sent by a high school student living in a rural area versus an urban area during the month of December.Eight rural high school students and 9 urban high school students were included in the study. If,among all 17,the U statistic is 29,n₁=8 and n₂ = 9 what is the the conclusion at α=0.05 is __________

A) reject the hypothesis that the number of text messages sent in December is identical
B) do not reject the hypothesis that the number of text messages sent in December is identical.
C) reject the hypothesis that the average number of text messages is identical.
D) do not reject the hypothesis that the average number of text messages is identical.
E) accept the hypothesis that the number of text messages sent in December identical.

Question 49

Which of the following tests might be used to compare the means of two populations if the samples are related?

A) Mann-Whitney test
B) Wilcoxon test
C) Runs test
D) Spearman's test
E) Kruskal-Wallis test

Question 50

The Kruskal-Wallis test is to be used to determine whether there is a significant difference in the satisfaction rating (alpha = 0.05)between three brands of boxed cake mix.Shoppers were asked to rate their satisfaction on various attributes and an aggregate satisfaction score ranging from 1-50 was computed.The following data were obtained: For this situation,the critical (table)chi-square value is _______.

A) 15.507
B) 7.815
C) 9.488
D) 5.991
E) 3.991

Question 51

A Kruskal-Wallis test is to be performed. There will be five categories,and alpha is chosen to be 0.01.The critical chi-square value is _______.

A) 15.086
B) 13.277
C) 7.779
D) 9.236
E) 8.987

Question 52

A Mann-Whitney U test was performed to determine if there were differences in the cost of tuition at a Texas state university versus an Oklahoma state university.The total cost,including room,board,and books for 24 freshman attending a Texas university were computed and compared to the total cost for 20 Oklahoma state university students.The U statistic was calculated to be 38.78 based on the sample sizes of 24 and 20.What is the z value for this test?

A) 0.133
B) -4.74
C) 240
D) 42.43
E) 8.75

Question 53

The nonparametric alternative to the one-way analysis of variance is the _______.

A) chi-square goodness of fit test
B) Kruskal-Wallis test
C) Mann-Whitney U test
D) Wilcoxon test
E) Friedman test

Question 54

The null hypothesis in the Kruskal-Wallis test is _______.

A) all populations are identical
B) all sample means are different
C) x and y are not correlated
D) the mean difference is zero
E) all populations are not identical

Question 55

In a Wilcoxon matched-pairs signed rank test with 20 matched-pairs of observations,the observed value of the ?T statistic based on sample data is 76.33.The corresponding observed z-value is ___________.

A) −1.79
B) −2.07
C) −1.70
D) −1.59
E) −1.07

Question 56

The nonparametric counterpart of the t test to compare the means of two related samples is the _______.

A) chi-square goodness of fit test
B) chi-square test of independence
C) Mann-Whitney U test
D) Wilcoxon test
E) Friedman test

Question 57

Suppose a research uses the Mann-Whitney test to determine if there is a difference in the volume of text messages sent by a high school student living in a rural area versus an urban area during the month of December.Eight rural high school students and 9 urban high school students were included in the study. If,among all 17,the sum of the ranks W₁ produced from the rural high school students is 72,the U statistic is __________

A) 29
B) 45
C) 90
D) 36
E) 43

Question 58

Many "Before and after" types of experiments should be analyzed using _______.

A) chi-square goodness of fit test
B) Kruskal-Wallis test
C) Mann-Whitney U test
D) Wilcoxon test
E) Friedman test

Question 59

Suppose a research uses the Mann-Whitney test to determine if there is a difference in the volume of text messages sent by a high school student living in a rural area versus an urban area during the month of December.Eight rural high school students and 9 urban high school students were included in the study. If,among all 17,the sum of the ranks W₂ produced from the urban high school is 88,the U test statistic is _____________

A) 29
B) 45
C) 90
D) 43
E) 20

Question 60

The Wilcoxon test was used on 18 pairs of data.The total of the ranks (T)were computed to be 111 (for + ranks)and 60 (for - ranks).The z value for this test is ____.

A) -1.11
B) -0.05
C) -0.07
D) 0.033
E) 2.22

Question 61

Correlation coefficients may be computed for parametric and nonparametric data. If the data are nonparametric,which of the following should be used?

A) Pearson correlation coefficient
B) Spearman correlation coefficient
C) Gaussian correlation coefficient
D) De Moivre correlation coefficient
E) Gossett correlation coefficient

Question 62

Correlation coefficients may be computed for parametric and nonparametric data. If the data are interval data,which of the following should be used?

A) Pearson correlation coefficient
B) Spearman correlation coefficient
C) Gaussian correlation coefficient
D) De Moivre correlation coefficient
E) Gossett correlation coefficient

Question 63

A quality control supervisor wishes to determine whether the following measurements are random: For this purpose,the supervisor computes the median of the thirty observations above and compares each measurement to the median to perform a runs test.She determines the number of runs and finds that the corresponding z score is ______.

A) 1.506
B) −1.506
C) 1.706
D) −1.706
E) −1.676

Question 64

Performance records for 18 salespersons are selected to investigate whether compensation methods are a significant motivational factor.
A Kruskal-Wallis test performed with $\alpha$ = 0.01 will result in a decision to _____.

A) reject the null hypothesis
B) reject the alternate hypothesis
C) do not reject the null hypothesis
D) do no reject the alternate hypothesis
E) do nothing

Question 65

Personnel specialist,Steve Satterfield,is assessing a new supervisor's ability to follow company standards for evaluating employees. Steve has the new supervisor rate five hypothetical employees on a scale of one to ten. He is interested in how the new supervisor's ratings correlate with company norms for these benchmark cases. The Spearman rank correlation coefficient is ___________.

A) 0.80
B) 0.85
C) 0.90
D) 0.95
E) 1.00

Question 66

A local pediatrician office is interested in the 'no-show' appointment count for each of the 4 pediatricians.'No-show' appointments represent lost revenues because the physician is idle when
Patients do not show for their scheduled appointments.Using the data in the table below and an
Alpha of .10,what is the null hypothesis?

A) The physicians differ in the no-show rates.
B) The no show rates differ by day of week
C) The no show rate between physician is equal
D) The no show rate between days of the week is equal
E) The no show rates are dependent upon both day of week and physician.

Question 67

A local pediatrician office is interested in the 'no-show' appointment count for each of the 4 pediatricians.'No-show' appointments represent lost revenues because the physician will be
Idle when patients do not show for their scheduled appointments.Using the data in the table
Below and an alpha of .10,what is the critical value of χ²?

A) 4.61
B) 6.25
C) 7.78
D) 13.28
E) 15.09

Question 68

A local pediatrician office is interested in the 'no-show' appointment count for each of the 4 pediatricians.'No-show' appointments represent lost revenues because the physician will be
Idle when patients do not show for their scheduled appointments.Using the data in the table
Below and an alpha of .10,what is the appropriate decision?

A) Reject the null hypothesis and conclude at least one physician differs in the no-show rates.
B) Reject the null hypothesis and conclude the no show rates differ by day of week
C) Fail to reject the null hypothesis and conclude there is not enough evidence to demonstrate the no show rate between physician is equal
D) Fail to reject the null hypothesis and conclude there is not enough evidence to show the no show rate between days of the week is equal
E) Reject the null hypothesis and conclude the no show rates are dependent upon both day of week and physician.

Question 69

A quality control supervisor wishes to determine whether the following measurements are random: For this purpose,the supervisor computes the median of the thirty observations above and compares each measurement to the median.She determines that the number of runs is ______.

A) 9
B) 10
C) 11
D) 12
E) 13

Question 70

The nonparametric alternative to analysis of variance for a randomized block design is the _______.

A) chi-square test
B) Kruskal-Wallis test
C) Mann-Whitney U test
D) Wilcoxon test
E) Friedman test

Question 71

What is the Spearman rank correlation coefficient for the following set of data?

A) -10.2
B) -2.35
C) 0.65
D) 0.50
E) 0.05

Question 72

Performance records for 18 salespersons are selected to investigate whether compensation methods are a significant motivational factor.
A Kruskal-Wallis test is to be performed with $\alpha$ = 0.01. The null hypothesis is _______.

A) Group 1 = Group 2 = Group 3
B) Group 1 $\neq$ Group 2 $\neq$ Group 3
C) Group 1 $\ge$ Group 2 $\ge$ Group 3
D) Group 1 $\le$ Group 2 $\le$ Group 3
E) Group 1 $\le$ Group 2 ≥ Group 3

Question 73

Two stock analysts rank five investment portfolios for overall performance and risk. The Spearman rank correlation coefficient is ___________.

A) 0.80
B) 0.20
C) 0.05
D) 0.95
E) 1.00

Question 74

The Spearman correlation coefficient is calculated for a set of data on two variables,x and y. It appears that as the rank of x increases,the rank of y is decreasing. We would expect the Spearman correlation coefficient to be ________.

A) equal to zero
B) positive
C) negative
D) greater than 5
E) greater than 1

Question 75

A quality control supervisor wishes to determine whether the following measurements are random: For this purpose,the supervisor computes the median of the thirty observations above,and finds it is ______.Then she compares each measurement to the median and assigns an "L" to it if it is below the median and a "U" if it is above the median.She determines that the number of Ls and Us are ______ and ______,respectively.

A) 66.8; 12; 18
B) 67; 12; 18
C) 67.5; 18; 12
D) 67; 18; 12
E) 67.5; 12; 18

Question 76

A perfect Spearman correlation of +1 or −1 between two variables indicates

A) a perfect linear relationship between the two variables
B) a perfect monotone function of the two variables.
C) the Pearson correlation is 1
D) the Pearson correlation is +1 or -1
E) the two variables are not related.

Question 77

Performance records for 18 salespersons are selected to investigate whether compensation methods are a significant motivational factor.
A Kruskal-Wallis test is to be performed with $\alpha$ = 0.01.The calculated K value is _______.

A) 15.086
B) 1.715
C) 7.779
D) 9.210
E) 8.657

Question 78

Performance records for 18 salespersons are selected to investigate whether compensation methods are a significant motivational factor.
A Kruskal-Wallis test is to be performed with $\alpha$ = 0.01. The critical chi-square value is _______.

A) 15.086
B) 13.277
C) 7.779
D) 9.210
E) 8.657

Question 79

A local pediatrician office is interested in the 'no-show' appointment count for each of the 4 pediatricians.'No-show' appointments represent lost revenues because the physician will be
Idle when patients do not show for their scheduled appointments.Using the data in the table
Below and an alpha of .10,what is the observed value of χ²?

A) 85.68
B) 75.0
C) 13.68
D) 10.68
E) 23.45

Question 80

What is the Spearman rank correlation coefficient for the following set of data?

A) -0.20
B) 1.00
C) 0.20
D) 0.80
E) -1.20