Nonparametric Statistics Test Bank Docx Chapter.17

CHAPTER 17

NONPARAMETRIC STATISTICS

CHAPTER LEARNING OBJECTIVES

1. Use both the small-sample and large-sample runs tests to determine whether the order of observations in a sample is random. The runs test is a nonparametric test of randomness. It is used to determine whether the order of sequence of observations in a sample is random. A run is a succession of observations that have a particular characteristic. If data are truly random, neither a very high number of runs nor a very small number of runs is likely to be present.

2. Use both the small-sample and large-sample cases of the Mann-Whitney U test to determine if there is a difference in two independent populations. The Mann-Whitney U test is a nonparametric version of the t test of the means from two independent samples. When the assumption of normally distributed data cannot be met or if the data are only ordinal in level of measurement, the Mann-Whitney U test can be used in place of the t test. The Mann-Whitney U test—like many nonparametric tests—works with the ranks of data rather than the raw data.

3. Use both the small-sample and large-sample cases of the Wilcoxon matched-pairs signed rank test to compare the differences in two related samples. The Wilcoxon matched-pairs signed rank test is used as an alternative to the t test for related measures when assumptions cannot be met and/or if the data are ordinal in measurement. In contrast to the Mann-Whitney U test, the Wilcoxon test is used when the data are related in some way. The Wilcoxon test is used to analyze the data by ranks of the differences of the raw data.

4. Use the Kruskal-Wallis test to determine whether samples come from the same or different populations. The Kruskal-Wallis test is a nonparametric one-way ANOVA technique. It is particularly useful when the assumptions underlying the F test of the parametric one-way ANOVA cannot be met. The Kruskal-Wallis test is usually used when the researcher wants to determine whether three or more groups or samples are from the same or equivalent populations. This test is based on the assumption that the sample items are selected randomly and that the groups are independent. The raw data are converted to ranks and the Kruskal-Wallis test is used to analyze the ranks with the equivalent of a chi-square statistic.

5. Use the Friedman test to determine whether different treatment levels come from the same population when a blocking variable is available. The Friedman test is a nonparametric alternative to the randomized block design. Friedman’s test is computed by ranking the observations within each block and then summing the ranks for each treatment level. The resulting test statistic X_r²r is approximately chi-square distributed.

6. Use Spearman’s rank correlation to analyze the degree of association of two variables. If two variables contain data that are ordinal in level of measurement, a Spearman’s rank correlation can be used to determine the amount of relationship or association between the variables. Spearman’s rank correlation coefficient is a nonparametric alternative to Pearson’s product-moment correlation coefficient. Spearman’s rank correlation coefficient is interpreted in a manner similar to the Pearson r.

TRUE-FALSE STATEMENTS

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

Difficulty: Easy

Section Reference: See introduction to Chapter 17

Bloom’s: Knowledge

AACSB: Reflective Thinking

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

Difficulty: Medium

Section Reference: See introduction to Chapter 17

Bloom’s: Knowledge

AACSB: Reflective Thinking

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

Difficulty: Easy

Section Reference: See introduction to Chapter 17

Bloom’s: Knowledge

AACSB: Reflective Thinking

4. Nonparametric statistics are sometimes called distribution-dependent statistics.

Difficulty: Easy

Section Reference: See introduction to Chapter 17

Bloom’s: Knowledge

AACSB: Reflective Thinking

5. An advantage of nonparametric statistics is that some nonparametric tests can be used to analyze situations in which data is available at only the nominal or the ordinal level.

Difficulty: Hard

Section Reference: See introduction to Chapter 17

Bloom’s: Knowledge

AACSB: Reflective Thinking

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

Difficulty: Hard

Section Reference: See introduction to Chapter 17

Bloom’s: Knowledge

AACSB: Reflective Thinking

7. The one-sample runs test is a nonparametric test for sequential independence.

Difficulty: Easy

Learning Objective: Use both the small-sample and large-sample runs tests to determine whether the order of observations in a sample is random.

Section Reference: 17.1 Runs Test

Bloom’s: Knowledge

AACSB: Reflective Thinking

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

Difficulty: Easy

Learning Objective: Use both the small-sample and large-sample runs tests to determine whether the order of observations in a sample is random.

Section Reference: 17.1 Runs Test

Bloom’s: Knowledge

AACSB: Reflective Thinking

9. In the one-sample runs test for randomness of the observations in a large sample (i.e., the number of observations with each of two possible characteristics is greater than 20) the sampling distribution of R, the number of runs, is approximately binomial.

Difficulty: Medium

Learning Objective: Use both the small-sample and large-sample runs tests to determine whether the order of observations in a sample is random.

Section Reference: 17.1 Runs Test

Bloom’s: Knowledge

AACSB: Reflective Thinking

10. The sampling distribution of R, the number of runs, in the one-sample runs test for randomness of the observations in a large sample (i.e., the number of observations with each of two possible characteristics is greater than 20) is approximately normal.

Difficulty: Medium

Learning Objective: Use both the small-sample and large-sample runs tests to determine whether the order of observations in a sample is random.

Section Reference: 17.1 Runs Test

Bloom’s: Knowledge

AACSB: Reflective Thinking

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

Difficulty: Medium

Learning Objective: Use both the small-sample and large-sample cases of the Mann-Whitney U test to determine if there is a difference in two independent populations.

Section Reference: 17.2 Mann-Whitney U Test

Bloom’s: Knowledge

AACSB: Reflective Thinking

12. 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, we should use the t test for independent samples rather than the Mann-Whitney U test.

Difficulty: Medium

Learning Objective: Use both the small-sample and large-sample cases of the Mann-Whitney U test to determine if there is a difference in two independent populations.

Section Reference: 17.2 Mann-Whitney U Test

Bloom’s: Knowledge

AACSB: Reflective Thinking

13. 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.

Difficulty: Medium

Learning Objective: Use both the small-sample and large-sample cases of the Mann-Whitney U test to determine if there is a difference in two independent populations.

Section Reference: 17.2 Mann-Whitney U Test

Bloom’s: Knowledge

AACSB: Reflective Thinking

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

Difficulty: Medium

Learning Objective: Use both the small-sample and large-sample cases of the Mann-Whitney U test to determine if there is a difference in two independent populations.

Section Reference: 17.2 Mann-Whitney U Test

Bloom’s: Knowledge

AACSB: Reflective Thinking

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

Difficulty: Medium

Learning Objective: Use both the small-sample and large-sample cases of the Wilcoxon matched-pairs signed rank test to compare the differences in two related samples.

Section Reference: 17.3 Wilcoxon Matched-Pairs Signed Rank Test

Bloom’s: Knowledge

AACSB: Reflective Thinking

16. The nonparametric counterpart of the t test to compare the means of two related samples is the Mann-Whitney U test.

Difficulty: Medium

Learning Objective: Use both the small-sample and large-sample cases of the Wilcoxon matched-pairs signed rank test to compare the differences in two related samples.

Section Reference: 17.3 Wilcoxon Matched-Pairs Signed Rank Test

Bloom’s: Knowledge

AACSB: Reflective Thinking

17. The nonparametric alternative to the one-way analysis of variance is the Kruskal-Wallis test.

Difficulty: Medium

Learning Objective: Use the Kruskal-Wallis test to determine whether samples come from the same or different populations.

Section Reference: 17.4 Kruskal-Wallis Test

Bloom’s: Knowledge

AACSB: Reflective Thinking

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

Difficulty: Medium

Learning Objective: Use the Friedman test to determine whether different treatment levels come from the same population when a blocking variable is available.

Section Reference: 17.5 Friedman Test

Bloom’s: Knowledge

AACSB: Reflective Thinking

19. Correlation coefficient cannot be used to analyze the association between two variables when only ordinal-level data are available.

Difficulty: Medium

Learning Objective: Use Spearman’s rank correlation to analyze the degree of association of two variables.

Section Reference: 17.6 Spearman’s Rank Correlation

Bloom’s: Knowledge

AACSB: Reflective Thinking

20. 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.

Difficulty: Medium

Learning Objective: Use Spearman’s rank correlation to analyze the degree of association of two variables.

Section Reference: 17.6 Spearman’s Rank Correlation

Bloom’s: Knowledge

AACSB: Reflective Thinking

MULTIPLE CHOICE QUESTIONS

21. 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

Difficulty: Easy

Section Reference: See introduction to Chapter 17

Bloom’s: Knowledge

AACSB: Reflective Thinking

22. 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

Difficulty: Easy

Section Reference: See introduction to Chapter 17

Bloom’s: Knowledge

AACSB: Reflective Thinking

23. 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

Difficulty: Easy

Section Reference: See introduction to Chapter 17

Bloom’s: Knowledge

AACSB: Reflective Thinking

24. Nonparametric statistics are sometimes called ___.

a) nominal statistics

b) interval statistics

c) distribution-dependent statistics

d) distribution-free statistics

e) qualitative statistics

Difficulty: Easy

Section Reference: See introduction to Chapter 17

Bloom’s: Knowledge

AACSB: Reflective Thinking

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

Difficulty: Medium

Learning Objective: Use both the small-sample and large-sample runs tests to determine whether the order of observations in a sample is random.

Section Reference: 17.1 Runs Test

Bloom’s: Knowledge

AACSB: Reflective Thinking

26. 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”

Difficulty: Easy

Learning Objective: Use both the small-sample and large-sample runs tests to determine whether the order of observations in a sample is random.

Section Reference: 17.1 Runs Test

Bloom’s: Knowledge

AACSB: Reflective Thinking

27. 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”

Difficulty: Easy

Learning Objective: Use both the small-sample and large-sample runs tests to determine whether the order of observations in a sample is random.

Section Reference: 17.1 Runs Test

Bloom’s: Knowledge

AACSB: Reflective Thinking

28. Charles Kline 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

Difficulty: Easy

Learning Objective: Use both the small-sample and large-sample runs tests to determine whether the order of observations in a sample is random.

Section Reference: 17.1 Runs Test

Bloom’s: Application

AACSB: Analytic

29. Charles Kline 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

Difficulty: Easy

Learning Objective: Use both the small-sample and large-sample runs tests to determine whether the order of observations in a sample is random.

Section Reference: 17.1 Runs Test

Bloom’s: Application

AACSB: Analytic

30. 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

Difficulty: Hard

Learning Objective: Use both the small-sample and large-sample cases of the Mann-Whitney U test to determine if there is a difference in two independent populations.

Section Reference: 17.2 Mann-Whitney U Test

Bloom’s: Knowledge

AACSB: Reflective Thinking

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

Difficulty: Hard

Learning Objective: Use both the small-sample and large-sample cases of the Mann-Whitney U test to determine if there is a difference in two independent populations.

Section Reference: 17.2 Mann-Whitney U Test

Bloom’s: Knowledge

AACSB: Reflective Thinking

32. In a Mann-Whitney U test, U statistic was calculated to be 38.78 based on 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

Difficulty: Medium

Learning Objective: Use both the small-sample and large-sample cases of the Mann-Whitney U test to determine if there is a difference in two independent populations.

Section Reference: 17.2 Mann-Whitney U Test

Bloom’s: Application

AACSB: Analytic

33. In a Mann-Whitney U test, the U statistic was calculated to be 58.0 based on 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

Difficulty: Medium

Learning Objective: Use both the small-sample and large-sample cases of the Mann-Whitney U test to determine if there is a difference in two independent populations.

Section Reference: 17.2 Mann-Whitney U Test

Bloom’s: Application

AACSB: Analytic

34. 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

Difficulty: Hard

Learning Objective: Use both the small-sample and large-sample cases of the Wilcoxon matched-pairs signed rank test to compare the differences in two related samples.

Section Reference: 17.3 Wilcoxon Matched-Pairs Signed Rank Test

Bloom’s: Knowledge

AACSB: Reflective Thinking

35. Which of the following tests should 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

Difficulty: Hard

Learning Objective: Use both the small-sample and large-sample cases of the Wilcoxon matched-pairs signed rank test to compare the differences in two related samples.

Section Reference: 17.3 Wilcoxon Matched-Pairs Signed Rank Test

Bloom’s: Knowledge

AACSB: Reflective Thinking

36. 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

Difficulty: Medium

Learning Objective: Use both the small-sample and large-sample cases of the Wilcoxon matched-pairs signed rank test to compare the differences in two related samples.

Section Reference: 17.3 Wilcoxon Matched-Pairs Signed Rank Test

Bloom’s: Application

AACSB: Analytic

37. 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.

Difficulty: Medium

Learning Objective: Use both the small-sample and large-sample cases of the Wilcoxon matched-pairs signed rank test to compare the differences in two related samples.

Section Reference: 17.3 Wilcoxon Matched-Pairs Signed Rank Test

Bloom’s: Application

AACSB: Analytic

38. 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

Difficulty: Medium

Learning Objective: Use both the small-sample and large-sample cases of the Wilcoxon matched-pairs signed rank test to compare the differences in two related samples.

Section Reference: 17.3 Wilcoxon Matched-Pairs Signed Rank Test

Bloom’s: Analysis

AACSB: Reflective Thinking

39. 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

Difficulty: Medium

Learning Objective: Use both the small-sample and large-sample cases of the Wilcoxon matched-pairs signed rank test to compare the differences in two related samples.

Section Reference: 17.3 Wilcoxon Matched-Pairs Signed Rank Test

Bloom’s: Analysis

AACSB: Reflective Thinking

40. Most "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

Difficulty: Medium

Learning Objective: Use both the small-sample and large-sample cases of the Wilcoxon matched-pairs signed rank test to compare the differences in two related samples.

Section Reference: 17.3 Wilcoxon Matched-Pairs Signed Rank Test

Bloom’s: Knowledge

AACSB: Reflective Thinking

41. 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

Difficulty: Medium

Learning Objective: Use both the small-sample and large-sample cases of the Wilcoxon matched-pairs signed rank test to compare the differences in two related samples.

Section Reference: 17.3 Wilcoxon Matched-Pairs Signed Rank Test

Bloom’s: Application

AACSB: Analytic

42. 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

Difficulty: Hard

Learning Objective: Use the Kruskal-Wallis test to determine whether samples come from the same or different populations.

Section Reference: 17.4 Kruskal-Wallis Test

Bloom’s: Knowledge

AACSB: Reflective Thinking

43. 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

Difficulty: Medium

Learning Objective: Use the Kruskal-Wallis test to determine whether samples come from the same or different populations.

Section Reference: 17.4 Kruskal-Wallis Test

Bloom’s: Knowledge

AACSB: Reflective Thinking

44. The Kruskal-Wallis test is to be used to determine whether there is a significant difference (alpha = 0.05) between the three groups using the following data:

For this test, how many degrees of freedom should be used?

a) 3

b) 2

c) 4

d) 8

e) 1

Difficulty: Easy

Learning Objective: Use the Kruskal-Wallis test to determine whether samples come from the same or different populations.

Section Reference: 17.4 Kruskal-Wallis Test

Bloom’s: Application

AACSB: Analytic

45. The Kruskal-Wallis test is to be used to determine whether there is a significant difference (alpha = 0.05) between the three groups using the following data:

For this situation, the critical (table) chi-square value is ___.

a) 15.507

b) 7.815

c) 9.488

d) 5.992

e) 3.991

Difficulty: Medium

Learning Objective: Use the Kruskal-Wallis test to determine whether samples come from the same or different populations.

Section Reference: 17.4 Kruskal-Wallis Test

Bloom’s: Application

AACSB: Analytic

46. 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

Difficulty: Medium

Learning Objective: Use the Kruskal-Wallis test to determine whether samples come from the same or different populations.

Section Reference: 17.4 Kruskal-Wallis Test

Bloom’s: Knowledge

AACSB: Reflective Thinking

47. 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

Difficulty: Easy

Learning Objective: Use the Kruskal-Wallis test to determine whether samples come from the same or different populations.

Section Reference: 17.4 Kruskal-Wallis Test

Bloom’s: Application

AACSB: Analytic

48. 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

Difficulty: Easy

Learning Objective: Use the Kruskal-Wallis test to determine whether samples come from the same or different populations.

Section Reference: 17.4 Kruskal-Wallis Test

Bloom’s: Application

AACSB: Analytic

49. 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 = 0.01. The null hypothesis is ___.

a) Group 1 = Group 2 = Group 3

b) Group 1 ≠ Group 2 ≠ Group 3

c) Group 1 ≥ Group 2 ≥ Group 3

d) Group 1 ≤ Group 2 ≤ Group 3

e) Group 1 ≤ Group 2 ≥ Group 3

Difficulty: Easy

Learning Objective: Use the Kruskal-Wallis test to determine whether samples come from the same or different populations.

Section Reference: 17.4 Kruskal-Wallis Test

Bloom’s: Analysis

AACSB: Analytic

50. 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 = 0.01. The critical chi-square value is ___.

a) 15.086

b) 13.277

c) 7.779

d) 9.210

e) 8.657

Difficulty: Medium

Learning Objective: Use the Kruskal-Wallis test to determine whether samples come from the same or different populations.

Section Reference: 17.4 Kruskal-Wallis Test

Bloom’s: Application

AACSB: Analytic

51. 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  = 0.01. The calculated K value is ___.

a) 15.086

b) 1.715

c) 7.779

d) 9.210

e) 8.657

Difficulty: Hard

Learning Objective: Use the Kruskal-Wallis test to determine whether samples come from the same or different populations.

Section Reference: 17.4 Kruskal-Wallis Test

Bloom’s: Application

AACSB: Analytic

52. Performance records for 18 salespersons are selected to investigate whether compensation methods are a significant motivational factor.

A Kruskal-Wallis test performed with = 0.01 will result in a decision to ___.

a) reject the null hypothesis

b) reject the alternate hypothesis

c) not reject the null hypothesis

d) not reject the alternate hypothesis

e) do nothing

Difficulty: Easy

Learning Objective: Use the Kruskal-Wallis test to determine whether samples come from the same or different populations.

Section Reference: 17.4 Kruskal-Wallis Test

Bloom’s: Analysis

AACSB: Reflective Thinking

53. 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

Difficulty: Hard

Learning Objective: Use the Friedman test to determine whether different treatment levels come from the same population when a blocking variable is available.

Section Reference: 17.5 Friedman Test

Bloom’s: Knowledge

AACSB: Reflective Thinking

54. Which of the following is not an assumption of the Friedman test?

a) The blocks are independent.

b) The population has a normal distribution.

c) There is no interaction between blocks and treatments.

d) Observations within each block can be ranked.

Difficulty: Medium

Learning Objective: Use the Friedman test to determine whether different treatment levels come from the same population when a blocking variable is available.

Section Reference: 17.5 Friedman Test

Bloom’s: Knowledge

AACSB: Reflective Thinking

55. In the Friedman test of c treatment levels, the degrees of freedom will be ___.

a) n – 1

b) (r – 1)(c – 1)

c) c – 1

d) b – k – 1

e) c + 1

Difficulty: Medium

Learning Objective: Use the Friedman test to determine whether different treatment levels come from the same population when a blocking variable is available.

Section Reference: 17.5 Friedman Test

Bloom’s: Knowledge

AACSB: Reflective Thinking

56. In a Friedman test with 8 treatment levels and 5 blocks, df = ___.

a) 28

b) 40

c) 8

d) 7

e) 6

Difficulty: Medium

Learning Objective: Use the Friedman test to determine whether different treatment levels come from the same population when a blocking variable is available.

Section Reference: 17.5 Friedman Test

Bloom’s: Knowledge

AACSB: Reflective Thinking

57. In a Friedman test with 4 treatment levels and 5 blocks, the df = ___.

a) 2

b) 3

c) 4

d) 5

e) 6

Difficulty: Medium

Learning Objective: Use the Friedman test to determine whether different treatment levels come from the same population when a blocking variable is available.

Section Reference: 17.5 Friedman Test

Bloom’s: Knowledge

AACSB: Reflective Thinking

58. In a Friedman test with 7 treatment levels and 5 blocks, df = ___.

a) 16

b) 34

c) 4

d) 35

e) 6

Difficulty: Medium

Learning Objective: Use the Friedman test to determine whether different treatment levels come from the same population when a blocking variable is available.

Section Reference: 17.5 Friedman Test

Bloom’s: Knowledge

AACSB: Reflective Thinking

59. In a Friedman test with 6 treatment levels and 7 blocks, the df = ___.

a) 6

b) 5

c) 42

d) 41

e) 7

Difficulty: Medium

Learning Objective: Use the Friedman test to determine whether different treatment levels come from the same population when a blocking variable is available.

Section Reference: 17.5 Friedman Test

Bloom’s: Knowledge

AACSB: Reflective Thinking

60. A randomized block design has 7 blocking levels and 5 treatment levels. Given the level of data, a nonparametric alternative to a randomized block design must be used to analyze the data. The number of degrees of freedom for the appropriate test statistic in this test of the null hypothesis that the treatment populations are equal is ___.

a) 35

b) 34

c) 24

d) 6

e) 4

Difficulty: Medium

Learning Objective: Use the Friedman test to determine whether different treatment levels come from the same population when a blocking variable is available.

Section Reference: 17.5 Friedman Test

Bloom’s: Application

AACSB: Analytic

61. A randomized block design has 7 blocking levels and 5 treatment levels. Given the level of data, a nonparametric alternative to a randomized block design must be used to analyze the data. For the test of the null hypothesis that the treatment populations are equal at a 1% level of significance, the critical value of the test statistic is ___.

a) 16.81

b) 15.09

c) 13.28

d) 9.49

e) 3.48

Difficulty: Medium

Learning Objective: Use the Friedman test to determine whether different treatment levels come from the same population when a blocking variable is available.

Section Reference: 17.5 Friedman Test

Bloom’s: Application

AACSB: Analytic

62. When using the Friedman test to test the following data to determine whether there is a significant difference between treatment levels, the df = ___.

a) 6

b) 5

c) 4

d) 3

e) 1

Difficulty: Medium

Learning Objective: Use the Friedman test to determine whether different treatment levels come from the same population when a blocking variable is available.

Section Reference: 17.5 Friedman Test

Bloom’s: Application

AACSB: Analytic

63. When using the Friedman test to test the following data to determine whether there is a significant difference between treatment levels with α = 0.05, the critical value of chi-square is ___.

a) 7.81

b) 5.99

c) 11.07

d) 9.49

e) 6.81

Difficulty: Medium

Learning Objective: Use the Friedman test to determine whether different treatment levels come from the same population when a blocking variable is available.

Section Reference: 17.5 Friedman Test

Bloom’s: Application

AACSB: Analytic

64. When using the Friedman test to test the following data to determine whether there is a significant difference between treatment levels with α = 0.01, the critical value of chi-square is ___.

a) 13.28

b) 11.34

c) 15.09

d) 9.21

e) 9.18

Difficulty: Medium

Learning Objective: Use the Friedman test to determine whether different treatment levels come from the same population when a blocking variable is available.

Section Reference: 17.5 Friedman Test

Bloom’s: Application

AACSB: Analytic

65. When using the Friedman test to test the following data to determine whether there is a significant difference between treatment levels, the ranks for block 1 are ___.

a) 2, 3, 4, 1

b) 3, 4, 1, 2

c) 4, 1, 2, 3

d) 4, 2, 3, 1

e) 1, 2, 3, 4

Difficulty: Medium

Learning Objective: Use the Friedman test to determine whether different treatment levels come from the same population when a blocking variable is available.

Section Reference: 17.5 Friedman Test

Bloom’s: Application

AACSB: Analytic

66. When using the Friedman test to test the following data to determine whether there is a significant difference between treatment levels, the ranks for block 2 are ___.

a) 2, 3, 4, 1

b) 1, 2, 3, 4

c) 4, 1, 2, 3

d) 4, 2, 3, 1

e) 3, 4, 1, 2

Difficulty: Medium

Learning Objective: Use the Friedman test to determine whether different treatment levels come from the same population when a blocking variable is available.

Section Reference: 17.5 Friedman Test

Bloom’s: Application

AACSB: Analytic

67. When using the Friedman test to test the following data to determine whether there is a significant difference between treatment levels with α = 0.05, the calculated value of chi-square is ___.

a) 4.51

b) 5.27

c) 2.83

d) 3.48

e) 1.48

Difficulty: Hard

Learning Objective: Use the Friedman test to determine whether different treatment levels come from the same population when a blocking variable is available.

Section Reference: 17.5 Friedman Test

Bloom’s: Application

AACSB: Analytic

68. When using the Friedman test to test the following data to determine whether there is a significant difference between treatment levels with α =0.05, the appropriate conclusion is ___.

a) reject H₀: the block populations are equal

b) do not reject H₀: the block populations are equal

c) reject H₀: the treatment populations are equal

d) do not reject H₀: the treatment populations are equal

e) that the test is inconclusive

Difficulty: Hard

Learning Objective: Use the Friedman test to determine whether different treatment levels come from the same population when a blocking variable is available.

Section Reference: 17.5 Friedman Test

Bloom’s: Application

AACSB: Reflective Thinking

69. Four types of bicycle tires are ridden in six different cities to see if the tires lasted about the same number of miles. If there are differences, then that tire could promote its durability to potential customers. Using the data in the table below and an alpha of 0.05, what is the null hypothesis?

1. The durability of the tires between the cities is equal.
2. The durability of the tires is dependent on the city and type of tire.
3. The durability of the tires is dependent on the type of tire.
4. The durability between the types of tire is equal.
5. The durability of the tires is dependent on the city.

Difficulty: Hard

Learning Objective: Use the Friedman test to determine whether different treatment levels come from the same population when a blocking variable is available.

Section Reference: 17.5 Friedman Test

Bloom’s: Application

AACSB: Reflective Thinking

70. Four types of bicycle tires are ridden in six different cities to see if the tires lasted about the same number of miles. If there are differences, then that tire could promote its durability to potential customers. Using the data in the table below and an alpha of 0.05, what is the critical value of χ²?

1. 7.82
2. 5.99
3. 4.61
4. 9.35
5. 3.84

Difficulty: Hard

Learning Objective: Use the Friedman test to determine whether different treatment levels come from the same population when a blocking variable is available.

Section Reference: 17.5 Friedman Test

Bloom’s: Application

AACSB: Analytic

71. Four types of bicycle tires are ridden in six different cities to see if the tires lasted about the same number of miles. If there are differences, then that tire could promote its durability to potential customers. Using the data in the table below and an alpha of 0.05, what is the observed value of χ²?

1. 77.82
2. 5.00
3. 84.67
4. 9.35
5. 4.00

Difficulty: Hard

Learning Objective: Use the Friedman test to determine whether different treatment levels come from the same population when a blocking variable is available.

Section Reference: 17.5 Friedman Test

Bloom’s: Application

AACSB: Analytic

72. Four types of bicycle tires are ridden in six different cities to see if the tires lasted about the same number of miles. If there are differences, then that tire could promote its durability to potential customers. Using the data in the table below and an alpha of 0.05, what is the appropriate decision?

1. Reject the null and conclude that all four tires have the same durability.
2. Fail to reject the null and conclude that there is at least one tire whose durability is different from another tire.
3. Reject the null and conclude that there is at least one tire whose durability is different from another tire.
4. Fail to reject the null and conclude that all four tires have the same durability.
5. Fail to reject the null and conclude that the durability of tires does not change by city.

Difficulty: Hard

Learning Objective: Use the Friedman test to determine whether different treatment levels come from the same population when a blocking variable is available.

Section Reference: 17.5 Friedman Test

Bloom’s: Analysis

AACSB: Reflective Thinking

73. 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

Difficulty: Easy

Learning Objective: Use Spearman’s rank correlation to analyze the degree of association of two variables.

Section Reference: 17.6 Spearman’s Rank Correlation

Bloom’s: Application

AACSB: Reflective Thinking

74. 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

Difficulty: Medium

Learning Objective: Use Spearman’s rank correlation to analyze the degree of association of two variables.

Section Reference: 17.6 Spearman’s Rank Correlation

Bloom’s: Knowledge

AACSB: Reflective Thinking

75. 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

Difficulty: Medium

Learning Objective: Use Spearman’s rank correlation to analyze the degree of association of two variables.

Section Reference: 17.6 Spearman’s Rank Correlation

Bloom’s: Knowledge

AACSB: Reflective Thinking

76. 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

Difficulty: Hard

Learning Objective: Use Spearman’s rank correlation to analyze the degree of association of two variables.

Section Reference: 17.6 Spearman’s Rank Correlation

Bloom’s: Application

AACSB: Analytic

77. 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

Difficulty: Hard

Learning Objective: Use Spearman’s rank correlation to analyze the degree of association of two variables.

Section Reference: 17.6 Spearman’s Rank Correlation

Bloom’s: Application

AACSB: Analytic

78. Personnel specialist Steve Jones 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) 0.25

e) 1.00

Difficulty: Hard

Learning Objective: Use Spearman’s rank correlation to analyze the degree of association of two variables.

Section Reference: 17.6 Spearman’s Rank Correlation

Bloom’s: Application

AACSB: Analytic

79. 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

Difficulty: Hard

Learning Objective: Use Spearman’s rank correlation to analyze the degree of association of two variables.

Section Reference: 17.6 Spearman’s Rank Correlation

Bloom’s: Application

AACSB: Analytic

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