Full Test Bank Nonparametric Statistics Ch.17 nan - Business Stats Contemporary Decision 10e | Test Bank by Ken Black by Ken Black. DOCX document preview.
File: Ch17, Chapter 17: Nonparametric Statistics
True/False
1. Statistical techniques based on assumptions about the population from which the sample data are selected are called parametric statistics.
Response: See section 17.1
Difficulty: Easy
Learning Objective: 17.1: Use both the small-sample and large-sample runs tests to determine whether the order of observations in a sample is random.
2. The methods of parametric statistics can be applied to nominal or ordinal data.
Response: See section 17.1
Difficulty: Medium
Learning Objective: 17.1: Use both the small-sample and large-sample runs tests to determine whether the order of observations in a sample is random.
3. Nonparametric statistical techniques are based on fewer assumptions about the population and the parameters compared to parametric statistical techniques.
Response: See section 17.1
Difficulty: Easy
Learning Objective: 17.1: Use both the small-sample and large-sample runs tests to determine whether the order of observations in a sample is random.
4. Nonparametric statistics are sometimes called distribution-dependent statistics.
Response: See section 17.1
Difficulty: Easy
Learning Objective: 17.1: Use both the small-sample and large-sample runs tests to determine whether the order of observations in a sample is random.
5. 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.
Response: See section 17.1
Difficulty: Hard
Learning Objective: 17.1: Use both the small-sample and large-sample runs tests to determine whether the order of observations in a sample is random.
6. A disadvantage of nonparametric statistics is that the probability statements obtained from most nonparametric tests are not exact probabilities.
Response: See section 17.1
Difficulty: Hard
Learning Objective: 17.1: Use both the small-sample and large-sample runs tests to determine whether the order of observations in a sample is random.
7. The one-sample runs test is a nonparametric test of randomness in the sample data.
Response: See section 17.1 Runs Test
Difficulty: Easy
Learning Objective: 17.1: Use both the small-sample and large-sample runs tests to determine whether the order of observations in a sample is random.
8. 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.
Response: See section 17.1 Runs Test
Difficulty: Medium
Learning Objective: 17.1: Use both the small-sample and large-sample runs tests to determine whether the order of observations in a sample is random.
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 (i.e., the number of observations for each of two possible characteristics is greater than 20) is approximately normal, if H0 is true.
Response: See section 17.1 Runs Test
Difficulty: Medium
Learning Objective: 17.1: Use both the small-sample and large-sample runs tests to determine whether the order of observations in a sample is random.
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.
Response: See section 17.2 Mann-Whitney U Test
Difficulty: Medium
Learning Objective: 17.2: 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.
11. 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, The Mann-Whitney U test should be used instead of the t-test for independent samples..
Response: See section 17.2 Mann-Whitney U Test
Difficulty: Medium
Learning Objective: 17.2: 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.
12. The Mann-Whitney U test is a generalization of the two-sample t-test.
Response: See section 17.2 Mann-Whitney U Test
Difficulty: Medium
Learning Objective: 17.2: 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.
13. The Mann-Whitney U test is used to test whether three or more independent samples of observations are drawn from the same or identical distributions.
Response: See section 17.2 Mann-Whitney U Test
Difficulty: Medium
Learning Objective: 17.2: 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.
14. The Mann-Whitney U test requires that the two samples under consideration have the same number of observations.
Response: See section 17.2 Mann-Whitney U Test
Difficulty: Medium
Learning Objective: 17.2: 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.
15. The nonparametric counterpart of the t test to compare the means of two independent populations is the Mann-Whitney U test.
Response: See section 17.2 Mann-Whitney U Test
Difficulty: Medium
Learning Objective: 17.2: 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.
16. 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.
Response: See section 17.3 Wilcoxon Matched-Pairs Signed Rank Test
Difficulty: Medium
Learning Objective: 17.3: Use both the small-sample and large-sample cases of the Wilcoxon matched-pairs signed rank test to compare the difference in two related samples.
17. The appropriate test for comparing the medians of two populations using ordinal-level data from two related samples is the Wilcoxon test.
Response: See section 17.3 Wilcoxon Matched-Pairs Signed Rank Test
Difficulty: Medium
Learning Objective: 17.3: Use both the small-sample and large-sample cases of the Wilcoxon matched-pairs signed rank test to compare the difference in two related samples
18. The Mann-Whitney U test is implemented differently for small samples than for large samples.
Response: See section 17.2 Mann-Whitney U Test
Difficulty: Medium
Learning Objective: 17.2: 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.
19. No assumptions on the distribution of the difference are needed for the use of the Wilcoxon matched-pairs signed rank.
Response: See section 17.3 Wilcoxon Matched-Pairs Signed Rank Test
Difficulty: Medium
Learning Objective: 17.3: Use both the small-sample and large-sample cases of the Wilcoxon matched-pairs signed rank test to compare the difference in two related samples.
20. The nonparametric alternative to linear regression is the Kruskal-Wallis test.
Response: See section 17.4 Kruskal-Wallis Test
Difficulty: Medium
Learning Objective: 17.4: Use the Kruskal-Wallis test to determine whether samples come from the same or different populations.
21. The Kruskal-Wallis test is an extension of the Mann-Whitney U test to 3 or more groups.
Response: See section 17.4 Kruskal-Wallis Test
Difficulty: Medium
Learning Objective: 17.4: Use the Kruskal-Wallis test to determine whether samples come from the same or different populations.
22. The nonparametric alternative to analysis of variance for a randomized block design is the Friedman test.
Response: See section 17.5 Friedman Test
Difficulty: Medium
Learning Objective: 17.5: use the Friedman test to determine whether different treatment levels come from the same population when a blocking variable is available.
23. The alternative hypothesis for the Friedman test is that at least one treatment is different from at least one other treatment.
Response: See section 17.5 Friedman Test
Difficulty: Medium
Learning Objective: 17.5: use the Friedman test to determine whether different treatment levels come from the same population when a blocking variable is available.
24. Prior to computing a Friedman test, the data are ranked within each block from smallest to largest.
Response: See section 17.5 Friedman Test
Difficulty: Medium
Learning Objective: 17.5: use the Friedman test to determine whether different treatment levels come from the same population when a blocking variable is available.
25. The degree of association of two variables cannot be estimated when only ordinal-level data are available.
Response: See section 17.6 Spearman’s Rank Correlation
Difficulty: Medium
Learning Objective: 17.6: Use Spearman’s rank correlation to analyze the degree of association of two variables.
26. 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.
Response: See section 17.6 Spearman’s Rank Correlation
Difficulty: Medium
Learning Objective: 17.6: Use Spearman’s rank correlation to analyze the degree of association of two variables.
27. Spearman rank correlation values, rs, range between +1 and 0.
Response: See section 17.6 Spearman’s Rank Correlation
Difficulty: Medium
Learning Objective: 17.6: Use Spearman’s rank correlation to analyze the degree of association of two variables.
Multiple Choice
28. 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
Response: See section 17.1
Difficulty: Easy
Learning Objective: 17.1: Use both the small-sample and large-sample runs tests to determine whether the order of observations in a sample is random.
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
Response: See section 17.1
Difficulty: Easy
Learning Objective: 17.1: Use both the small-sample and large-sample runs tests to determine whether the order of observations in a sample is random.
30. 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
Response: See section 17.1
Difficulty: Easy
Learning Objective: 17.1: Use both the small-sample and large-sample runs tests to determine whether the order of observations in a sample is random.
31. Nonparametric statistics are sometimes called _______________.
a) nominal statistics
b) interval statistics
c) distribution-dependent statistics
d) distribution-free statistics
e) qualitative statistics
Response: See section 17.1
Difficulty: Easy
Learning Objective: 17.1: Use both the small-sample and large-sample runs tests to determine whether the order of observations in a sample is random.
32. 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
Response: See section 17.1 Runs Test
Difficulty: Medium
Learning Objective: 17.1: Use both the small-sample and large-sample runs tests to determine whether the order of observations in a sample is random.
33. 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
Response: See section 17.1 Runs Test
Difficulty: Easy
Learning Objective: 17.1: Use both the small-sample and large-sample runs tests to determine whether the order of observations in a sample is random.
34. 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) reject the hypothesis that 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
Response: See section 17.1 Runs Test
Difficulty: Hard
Learning Objective: 17.1: Use both the small-sample and large-sample runs tests to determine whether the order of observations in a sample is random.
35. 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”
Response: See section 17.1 Runs Test
Difficulty: Easy
Learning Objective: 17.1: Use both the small-sample and large-sample runs tests to determine whether the order of observations in a sample is random.
36. 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”
Response: See section 17.1 Runs Test
Difficulty: Easy
Learning Objective: 17.1: Use both the small-sample and large-sample runs tests to determine whether the order of observations in a sample is random.
37. 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
Response: See section 17.1 Runs Test
Difficulty: Easy
Learning Objective: 17.1: Use both the small-sample and large-sample runs tests to determine whether the order of observations in a sample is random.
38. 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
Response: See section 17.1 Runs Test
Difficulty: Easy
Learning Objective: 17.1: Use both the small-sample and large-sample runs tests to determine whether the order of observations in a sample is random.
39. 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
Response: See section 17.2 Mann-Whitney U Test
Difficulty: Hard
Learning Objective: 17.2: 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.
40. 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
Response: See section 17.2 Mann-Whitney U Test
Difficulty: Hard
Learning Objective: 17.2: 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.
41. 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 freshmen 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
Response: See section 17.2 Mann-Whitney U Test
Difficulty: Medium
Learning Objective: 17.2: 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.
42. 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) -4.89
e) -2.44
Response: See section 17.2 Mann-Whitney U Test
Difficulty: Medium
Learning Objective: 17.2: 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.
43. 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 U1 statistic is __________
a) 29
b) 45
c) 90
d) 36
e) 43
Response: See section 17.2 Mann-Whitney U Test
Difficulty: Medium
Learning Objective: 17.2: 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.
44. Suppose a research uses the Mann-Whitney U 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 U2 test statistic is _____________
a) 29
b) 45
c) 90
d) 43
e) 20
Response: See section 17.2 Mann-Whitney U Test
Difficulty: Medium
Learning Objective: 17.2: 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.
45. 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, the conclusion at α=0.05 would be __________
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.
Response: See section 17.2 Mann-Whitney U Test
Difficulty: Hard
Learning Objective: 17.2: 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.
46. 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
Response: See section 17.3 Wilcoxon Matched-Pairs Signed Rank Test
Difficulty: Hard
Learning Objective: 17.3: Use both the small-sample and large-sample cases of the Wilcoxon matched-pairs signed rank test to compare the difference in two related samples
47. 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
Response: See section 17.3 Wilcoxon Matched-Pairs Signed Rank Test
Difficulty: Hard
Learning Objective: 17.3: Use both the small-sample and large-sample cases of the Wilcoxon matched-pairs signed rank test to compare the difference in two related samples.
48. 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
Response: See section 17.3 Wilcoxon Matched-Pairs Signed Rank Test
Difficulty: Medium
Learning Objective: 17.3: Use both the small-sample and large-sample cases of the Wilcoxon matched-pairs signed rank test to compare the difference in two related samples.
49. 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.
Response: See section 17.3 Wilcoxon Matched-Pairs Signed Rank Test
Difficulty: Medium
Learning Objective: 17.3: Use both the small-sample and large-sample cases of the Wilcoxon matched-pairs signed rank test to compare the difference in two related samples.
50. 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
Response: See section 17.3 Wilcoxon Matched-Pairs Signed Rank Test
Difficulty: Medium
Learning Objective: 17.3: Use both the small-sample and large-sample cases of the Wilcoxon matched-pairs signed rank test to compare the difference in two related samples
51. 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
Response: See section 17.3 Wilcoxon Matched-Pairs Signed Rank Test
Difficulty: Medium
Learning Objective: 17.3: Use both the small-sample and large-sample cases of the Wilcoxon matched-pairs signed rank test to compare the difference in two related samples
52. 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
Response: See section 17.3 Wilcoxon Matched-Pairs Signed Rank Test
Difficulty: Medium
Learning Objective: 17.3: Use both the small-sample and large-sample cases of the Wilcoxon matched-pairs signed rank test to compare the difference in two related samples
53. 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
Response: See section 17.3 Wilcoxon Matched-Pairs Signed Rank Test
Difficulty: Medium
Learning Objective: 17.3: Use both the small-sample and large-sample cases of the Wilcoxon matched-pairs signed rank test to compare the difference in two related samples
54. 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
Response: See section 17.4 Kruskal-Wallis Test
Difficulty: Hard
Learning Objective: 17.4: Use the Kruskal-Wallis test to determine whether samples come from the same or different populations.
55. 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
Response: See section 17.4 Kruskal-Wallis Test
Difficulty: Medium
Learning Objective: 17.4: Use the Kruskal-Wallis test to determine whether samples come from the same or different populations.
56. 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:
Cake Mix A | 19 | 21 | 25 | 22 | 33 |
Cake Mix B | 30 | 24 | 28 | 31 | 35 |
Cake Mix C | 39 | 32 | 41 | 42 | 27 |
For this test, how many degrees of freedom should be used?
a) 3
b) 2
c) 4
d) 8
e) 1
Response: See section 17.4 Kruskal-Wallis Test
Difficulty: Easy
Learning Objective: 17.4: Use the Kruskal-Wallis test to determine whether samples come from the same or different populations.
57. 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:
Cake Mix A | 19 | 21 | 25 | 22 | 33 |
Cake Mix B | 30 | 24 | 28 | 31 | 35 |
Cake Mix C | 39 | 32 | 41 | 42 | 27 |
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
Response: See section 17.4 Kruskal-Wallis Test
Difficulty: Medium
Learning Objective: 17.4: Use the Kruskal-Wallis test to determine whether samples come from the same or different populations.
58. 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
Response: See section 17.4 Kruskal-Wallis Test
Difficulty: Medium
Learning Objective: 17.4: Use the Kruskal-Wallis test to determine whether samples come from the same or different populations
59. 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
Response: See section 17.4 Kruskal-Wallis Test
Difficulty: Easy
Learning Objective: 17.4: Use the Kruskal-Wallis test to determine whether samples come from the same or different populations
60. 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
Response: See section 17.4 Kruskal-Wallis Test
Difficulty: Easy
Learning Objective: 17.4: Use the Kruskal-Wallis test to determine whether samples come from the same or different populations
61. Performance records for 18 salespersons are selected to investigate whether compensation methods are a significant motivational factor.
Compensation Method | Sales | ||||||
Straight Salary | 18 | 12 | 22 | 28 | 28 | ||
Straight Commission | 27 | 34 | 34 | 27 | 20 | 16 | 24 |
Salary plus Commission | 11 | 17 | 27 | 14 | 30 | 22 | |
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
Response: See section 17.4 Kruskal-Wallis Test
Difficulty: Easy
Learning Objective: 17.4: Use the Kruskal-Wallis test to determine whether samples come from the same or different populations
62. Performance records for 18 salespersons are selected to investigate whether compensation methods are a significant motivational factor.
Compensation Method | Sales | ||||||
Straight Salary | 18 | 12 | 22 | 28 | 28 | ||
Straight Commission | 27 | 34 | 34 | 27 | 20 | 16 | 24 |
Salary plus Commission | 11 | 17 | 27 | 14 | 30 | 22 | |
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
Response: See section 17.4 Kruskal-Wallis Test
Difficulty: Medium
Learning Objective: 17.4: Use the Kruskal-Wallis test to determine whether samples come from the same or different populations.
63. Performance records for 18 salespersons are selected to investigate whether compensation methods are a significant motivational factor.
Compensation Method | Sales | ||||||
Straight Salary | 18 | 12 | 22 | 28 | 28 | ||
Straight Commission | 27 | 34 | 34 | 27 | 20 | 16 | 24 |
Salary plus Commission | 11 | 17 | 27 | 14 | 30 | 22 | |
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
Response: See section 17.4 Kruskal-Wallis Test
Difficulty: Hard
Learning Objective: 17.4: Use the Kruskal-Wallis test to determine whether samples come from the same or different populations.
64. Performance records for 18 salespersons are selected to investigate whether compensation methods are a significant motivational factor.
Compensation Method | Sales | ||||||
Straight Salary | 18 | 12 | 22 | 28 | 28 | ||
Straight Commission | 27 | 34 | 34 | 27 | 20 | 16 | 24 |
Salary plus Commission | 11 | 17 | 27 | 14 | 30 | 22 | |
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) do not reject the null hypothesis
d) do no reject the alternate hypothesis
e) do nothing
Response: See section 17.4 Kruskal-Wallis Test
Difficulty: Hard
Learning Objective: 17.4: Use the Kruskal-Wallis test to determine whether samples come from the same or different populations.
65. 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
Response: See section 17.5 Friedman Test
Difficulty: Hard
Learning Objective: 17.5: use the Friedman test to determine whether different treatment levels come from the same population when a blocking variable is available.
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?
Physician A | Physician B | Physician C | Physician D | |
week 1 | 8 | 4 | 6 | 7 |
week 2 | 7 | 3 | 4 | 6 |
week 3 | 8 | 2 | 5 | 4 |
week 4 | 8 | 6 | 7 | 9 |
week 5 | 4 | 2 | 5 | 10 |
- The physicians differ in the no-show rates.
- The no show rates differ by day of week
- The no show rate between physician is equal
- The no show rate between days of the week is equal
- The no show rates are dependent upon both day of week and physician.
Response: See section 17.5 Friedman Test
Difficulty: Hard
Learning Objective: 17.5: use the Friedman test to determine whether different treatment levels come from the same population when a blocking variable is available.
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 0.10, what is the critical value of χ2?
Physician A | Physician B | Physician C | Physician D | |
week 1 | 8 | 4 | 6 | 7 |
week 2 | 7 | 3 | 4 | 6 |
week 3 | 8 | 2 | 5 | 4 |
week 4 | 8 | 6 | 7 | 9 |
week 5 | 4 | 2 | 5 | 10 |
- 4.61
- 6.25
- 7.78
- 13.28
- 15.09
Response: See section 17.5 Friedman Test
Difficulty: Hard
Learning Objective: 17.5: use the Friedman test to determine whether different treatment levels come from the same population when a blocking variable is available.
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 0.10, what is the observed value of χ2?
Physician A | Physician B | Physician C | Physician D | |
week 1 | 8 | 4 | 6 | 7 |
week 2 | 7 | 3 | 4 | 6 |
week 3 | 8 | 2 | 5 | 4 |
week 4 | 8 | 6 | 7 | 9 |
week 5 | 4 | 2 | 5 | 10 |
- 85.68
- 75.0
- 13.68
- 10.68
- 23.45
Response: See section 17.5 Friedman Test
Difficulty: Hard
Learning Objective: 17.5: use the Friedman test to determine whether different treatment levels come from the same population when a blocking variable is available.
69. 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 0.10, what is the appropriate decision?
| ||||||||||||||||||||||||||||||
- Reject the null hypothesis and conclude at least one physician differs in the no-show
rates. - Reject the null hypothesis and conclude the no show rates differ by day of week
- Fail to reject the null hypothesis and conclude there is not enough evidence to demonstrate the no show rate between physician is equal
- 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
- Reject the null hypothesis and conclude the no show rates are dependent upon both day of week and physician.
Response: See section 17.5 Friedman Test
Difficulty: Hard
Learning Objective: 17.5: use the Friedman test to determine whether different treatment levels come from the same population when a blocking variable is available.
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 null hypothesis?
Tire A | Tire B | Tire C | Tire D | |
City 1 | 105 | 157 | 112 | 119 |
City 2 | 142 | 124 | 132 | 144 |
City 3 | 133 | 121 | 138 | 130 |
City 4 | 98 | 136 | 110 | 119 |
City 5 | 114 | 141 | 95 | 128 |
City 6 | 117 | 138 | 129 | 140 |
- The durability of the tires between the cities is equal.
- The durability of the tires is dependent on the city and type of tire.
- The durability of the tires is dependent on the type of tire.
- The durability between the types of tire is equal.
- The durability of the tires is dependent on the city.
Ans: d
Response: See section 17.5 Friedman Test
Difficulty: Hard
Learning Objective: 17.5: use the Friedman test to determine whether different treatment levels come from the same population when a blocking variable is available.
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 critical value of χ2?
Tire A | Tire B | Tire C | Tire D | |
City 1 | 105 | 157 | 112 | 119 |
City 2 | 142 | 124 | 132 | 144 |
City 3 | 133 | 121 | 138 | 130 |
City 4 | 98 | 136 | 110 | 119 |
City 5 | 114 | 141 | 95 | 128 |
City 6 | 117 | 138 | 129 | 140 |
- 7.82
- 5.99
- 4.61
- 9.35
- 3.84
Ans: a
Response: See section 17.5 Friedman Test
Difficulty: Hard
Learning Objective: 17.5: use the Friedman test to determine whether different treatment levels come from the same population when a blocking variable is available.
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 observed value of χ2?
Tire A | Tire B | Tire C | Tire D | |
City 1 | 105 | 157 | 112 | 119 |
City 2 | 142 | 124 | 132 | 144 |
City 3 | 133 | 121 | 138 | 130 |
City 4 | 98 | 136 | 110 | 119 |
City 5 | 114 | 141 | 95 | 128 |
City 6 | 117 | 138 | 129 | 140 |
- 77.82
- 5.00
- 84.67
- 9.35
- 4.00
Ans: e
Response: See section 17.5 Friedman Test
Difficulty: Hard
Learning Objective: 17.5: use the Friedman test to determine whether different treatment levels come from the same population when a blocking variable is available.
73. 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?
Tire A | Tire B | Tire C | Tire D | |
City 1 | 105 | 157 | 112 | 119 |
City 2 | 142 | 124 | 132 | 144 |
City 3 | 133 | 121 | 138 | 130 |
City 4 | 98 | 136 | 110 | 119 |
City 5 | 114 | 141 | 95 | 128 |
City 6 | 117 | 138 | 129 | 140 |
- Reject the null and conclude that all four tires have the same durability.
- Fail to reject the null and conclude that there is at least one tire whose durability is different from another tire.
- Reject the null and conclude that there is at least one tire whose durability is different from another tire.
- Fail to reject the null and conclude that all four tires have the same durability.
- Fail to reject the null and conclude that the durability of tires does not change by city.
Ans: d
Response: See section 17.5 Friedman Test
Difficulty: Hard
Learning Objective: 17.5: use the Friedman test to determine whether different treatment levels come from the same population when a blocking variable is available.
74. The attention span of kindergarteners are measured in minutes. A teacher wants to see if there are differences in the attention span of kindergarteners at different times of day. Using a sample of five such children, their attention spans are measured at five different times throughout the day. Using the data in the table below and an alpha of 0.05, what is the null hypothesis?
9am | 11am | noon | 1pm | 3pm | |
Child 1 | 12 | 5 | 10 | 7 | 8 |
Child 2 | 10 | 6 | 9 | 8 | 12 |
Child 3 | 7 | 10 | 6 | 8 | 13 |
Child 4 | 11 | 8 | 5 | 4 | 10 |
Child 5 | 12 | 4 | 11 | 5 | 8 |
- The attention span between the children is equal.
- The attention span between the times of day are equal.
- The attention span differs based on time of day.
- The attention span between the times of day are equal by child.
- The attention span is dependent on the child.
Ans: b
Response: See section 17.5 Friedman Test
Difficulty: Hard
Learning Objective: 17.5: use the Friedman test to determine whether different treatment levels come from the same population when a blocking variable is available.
75. The attention span of kindergarteners are measured in minutes. A teacher wants to see if there are differences in the attention span of kindergarteners at different times of day. Using a sample of five such children, their attention spans are measured at five different times throughout the day. Using the data in the table below and an alpha of 0.05, what is the observed χ2?
9am | 11am | noon | 1pm | 3pm | |
Child 1 | 12 | 5 | 10 | 7 | 8 |
Child 2 | 10 | 6 | 9 | 8 | 12 |
Child 3 | 7 | 10 | 6 | 8 | 13 |
Child 4 | 11 | 8 | 5 | 4 | 10 |
Child 5 | 12 | 4 | 11 | 5 | 8 |
- 8.11
- 7.21
- 12.00
- 8.96
- 9.50
Ans: d
Response: See section 17.5 Friedman Test
Difficulty: Hard
Learning Objective: 17.5: use the Friedman test to determine whether different treatment levels come from the same population when a blocking variable is available.
76. The attention span of kindergarteners are measured in minutes. A teacher wants to see if there are differences in the attention span of kindergarteners at different times of day. Using a sample of five such children, their attention spans are measured at five different times throughout the day. Using the data in the table below and an alpha of 0.05, what is the appropriate conclusion?
9am | 11am | noon | 1pm | 3pm | |
Child 1 | 12 | 5 | 10 | 7 | 8 |
Child 2 | 10 | 6 | 9 | 8 | 12 |
Child 3 | 7 | 10 | 6 | 8 | 13 |
Child 4 | 11 | 8 | 5 | 4 | 10 |
Child 5 | 12 | 4 | 11 | 5 | 8 |
- Fail to reject the null and conclude that attention spans differ at different times of day.
- Reject the null and conclude that attention spans are the same between children.
- Reject the null and conclude that attention spans are impacted by time of day and child.
- Fail to reject the null and conclude that attention spans differ between children.
- Fail to reject the null and conclude that attention spans are the same at different times of day.
Ans: e
Response: See section 17.5 Friedman Test
Difficulty: Hard
Learning Objective: 17.5: use the Friedman test to determine whether different treatment levels come from the same population when a blocking variable is available.
77. 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
Response: See section 17.6 Spearman’s Rank Coefficient
Difficulty: Easy
Learning Objective: 17.6: Use Spearman’s rank correlation to analyze the degree of association of two variables.
78. 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
Response: See section 17.6 Spearman’s Rank Coefficient
Difficulty: Medium
Learning Objective: 17.6: Use Spearman’s rank correlation to analyze the degree of association of two variables.
79. 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
Response: See section 17.6 Spearman’s Rank Coefficient
Difficulty: Medium
Learning Objective: 17.6: Use Spearman’s rank correlation to analyze the degree of association of two variables.
80. What is the Spearman rank correlation coefficient for the following set of data?
x | 19 | 21 | 25 | 22 | 33 |
y | 30 | 24 | 28 | 31 | 35 |
a) -10.2
b) -2.35
c) 0.65
d) 0.50
e) 0.05
Response: See section 17.6 Spearman’s Rank Coefficient
Difficulty: Hard
Learning Objective: 17.6: Use Spearman’s rank correlation to analyze the degree of association of two variables.
81. What is the Spearman rank correlation coefficient for the following set of data?
x | 21 | 22 | 35 | 32 | 33 |
y | 18 | 24 | 28 | 22 | 35 |
a) -0.20
b) 1.00
c) 0.20
d) 0.80
e) -1.20
Response: See section 17.6 Spearman’s Rank Coefficient
Difficulty: Hard
Learning Objective: 17.6: Use Spearman’s rank correlation to analyze the degree of association of two variables.
82. 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.
Employee | |||||
1 | 2 | 3 | 4 | 5 | |
New Supervisor | 8 | 8 | 9 | 7 | 5 |
Company Norm | 8 | 6 | 10 | 4 | 4 |
The Spearman rank correlation coefficient is ___________.
a) 0.80
b) 0.85
c) 0.90
d) 0.95
e) 1.00
Response: See section 17.6 Spearman’s Rank Coefficient
Difficulty: Hard
Learning Objective: 17.6: Use Spearman’s rank correlation to analyze the degree of association of two variables.
83. Two stock analysts rank five investment portfolios for overall performance and risk.
Portfolio | |||||
A | B | C | D | E | |
Broker 1 - Rankings | 4 | 5 | 2 | 1 | 3 |
Broker 2 - Rankings | 1 | 4 | 3 | 2 | 5 |
Using these rankings, the Spearman rank correlation coefficient is ___________.
a) 0.80
b) 0.20
c) 0.05
d) 0.95
e) 1.00
Response: See section 17.6 Spearman’s Rank Coefficient
Difficulty: Hard
Learning Objective: 17.6: Use Spearman’s rank correlation to analyze the degree of association of two variables.
84. A perfect Spearman correlation of +1 or −1 between two variables indicates
a) a perfect linear relationship between the two variables
b) a perfect nondecreasing or nonincreasing 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.
Response: See section 17.6 Spearman’s Rank Correlation
Difficulty: Medium
Learning Objective: 17.6: Use Spearman’s rank correlation to analyze the degree of association of two variables.
85. If the Spearman correlation between variable A and variable B was -0.24, then what could be said about the correlation between these two variables?
a) There is a high positive correlation between A and B
b) There is a low negative correlation between A and B
c) There is a high negative correlation between A and B
d) There is no correlation between A and B
e) There is a low positive correlation between A and B
Ans: b
Response: See section 17.6 Spearman’s Rank Correlation
Difficulty: Medium
Learning Objective: 17.6: Use Spearman’s rank correlation to analyze the degree of association of two variables.
86. If the Spearman correlation between variable A and variable B was 0.24, then what could be said about the correlation between these two variables?
a) There is a high positive correlation between A and B
b) There is a low negative correlation between A and B
c) There is a high negative correlation between A and B
d) There is no correlation between A and B
e) There is a low positive correlation between A and B
Ans: e
Response: See section 17.6 Spearman’s Rank Correlation
Difficulty: Medium
Learning Objective: 17.6: Use Spearman’s rank correlation to analyze the degree of association of two variables.
87. A table manufacturer makes tables at 12 different heights for different purposes. The CEO would like to know if customers in two different industries place the same value on each of the different heights based on a Likert scale. Ideally, the CEO would prefer that the preferences of the two industries be independent of each other. Based on this, the CEO is hoping that the Spearman correlation coefficient works out to be a _____________.
a) high positive value
b) high negative value
c) low positive value
d) value near 0
e) low negative value
Ans: e
Response: See section 17.6 Spearman’s Rank Correlation
Difficulty: Medium
Learning Objective: 17.6: Use Spearman’s rank correlation to analyze the degree of association of two variables.
88. A table manufacturer makes tables at 12 different heights for different purposes. The CEO would like to know if customers in two different industries place the same value on each of the different heights based on a Likert scale. Ideally, the CEO would prefer that the preferences of the two industries be distinctly different from each other. Based on this, the CEO is hoping that the Spearman correlation coefficient works out to be a _____________.
a) high positive value
b) high negative value
c) low positive value
d) value near 0
e) low negative value
Ans: b
Response: See section 17.6 Spearman’s Rank Correlation
Difficulty: Medium
Learning Objective: 17.6: Use Spearman’s rank correlation to analyze the degree of association of two variables.
89. A quality control supervisor wishes to determine whether the following measurements are random:
68.2 | 65 | 66.5 | 65 | 67.5 | 68 | 66 | 64.5 |
65.3 | 64.2 | 67.6 | 66.5 | 66.8 | 68.9 | 67 | 65 |
65 | 67 | 68 | 71 | 68.5 | 63.6 | 64.7 | |
71.5 | 70.7 | 66 | 68.5 | 70.5 | 69.5 | 70.1 |
For this purpose, the supervisor computes the median of previous observations, and finds it is 67.9. Then she compares each measurement to that 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) 14; 16
b) 17; 13
c) 16; 14
d) 18; 12
e) 12; 18
Response: See section 17.1
Difficulty: Easy
AACSB: Reflective thinking
Bloom’s level: Application
Learning Objective: 17.1: Use both the small-sample and large-sample runs tests to determine whether the order of observations in a sample is random.
90. A quality control supervisor wishes to determine whether the following measurements are random:
68.2 | 65 | 66.5 | 65 | 67.5 | 68 | 66 | 64.5 |
65.3 | 64.2 | 67.6 | 66.5 | 66.8 | 68.9 | 67 | 65 |
65 | 67 | 68 | 71 | 68.5 | 63.6 | 64.7 | |
71.5 | 70.7 | 66 | 68.5 | 70.5 | 69.5 | 70.1 |
For this purpose, the supervisor uses a previous median 67.9 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
Response: See section 17.1
Difficulty: Medium
AACSB: Reflective thinking
Bloom’s level: Application
Learning Objective: 17.1: Use both the small-sample and large-sample runs tests to determine whether the order of observations in a sample is random.
91. A quality control supervisor wishes to determine whether the following measurements are random:
68.2 | 65 | 66.5 | 65 | 67.5 | 68 | 66 | 64.5 |
65.3 | 64.2 | 67.6 | 66.5 | 66.8 | 68.9 | 67 | 65 |
65 | 67 | 68 | 71 | 68.5 | 63.6 | 64.7 | |
71.5 | 70.7 | 66 | 68.5 | 70.5 | 69.5 | 70.1 |
For this purpose, the supervisor uses a previous median of 67.9 and compares each measurement to the median to perform a runs test. She determines the number of runs and finds that the critical values of the Rscore are ______ and ________.
a) 10;18
b) 12;19
c) 11;20
d) 9;21
e) 10;22
Response: See section 17.1
Difficulty: Medium
AACSB: Reflective thinking
Bloom’s level: Application
Learning Objective: 17.1: Use both the small-sample and large-sample runs tests to determine whether the order of observations in a sample is random.
92. A quality control supervisor wishes to determine whether the following measurements are random:
68.2 | 65 | 66.5 | 65 | 67.5 | 68 | 66 | 64.5 |
65.3 | 64.2 | 67.6 | 66.5 | 66.8 | 68.9 | 67 | 65 |
65 | 67 | 68 | 71 | 68.5 | 63.6 | 64.7 | |
71.5 | 70.7 | 66 | 68.5 | 70.5 | 69.5 | 70.1 |
For this purpose, the supervisor uses a previous median of 67.9 and compares each measurement to that median to perform a runs test. She uses a significance level of 0.05. This is a ______ test.
a) right-tailed
b) forward-tailed
c) two-tailed
d) inside-tailed
e) left-tailed
Response: See section 17.1
Difficulty: Medium
AACSB: Reflective thinking
Bloom’s level: Application
Learning Objective: 17.1: Use both the small-sample and large-sample runs tests to determine whether the order of observations in a sample is random.
93. A quality control supervisor wishes to determine whether the following measurements are random:
68.2 | 65 | 66.5 | 65 | 67.5 | 68 | 66 | 64.5 |
65.3 | 64.2 | 67.6 | 66.5 | 66.8 | 68.9 | 67 | 65 |
65 | 67 | 68 | 71 | 68.5 | 63.6 | 64.7 | |
71.5 | 70.7 | 66 | 68.5 | 70.5 | 69.5 | 70.1 |
For this purpose, the supervisor uses a previous median of 67.9 and compares each measurement to the median to perform a runs test. She uses a significance level of 0.05. The appropriate decision is ______.
a) reject the null hypothesis and conclude that the observations are random
b) reject the null hypothesis and conclude that the observations are not random
c) do not reject the null hypothesis and conclude that the observations are random
d) do not reject the null hypothesis and conclude that the observations are not random
e) do nothing
Response: See section 17.1
Difficulty: Medium
AACSB: Reflective thinking
Bloom’s level: Application
Learning Objective: 17.1: Use both the small-sample and large-sample runs tests to determine whether the order of observations in a sample is random.
94. A researcher wants to determine whether the means of two independent populations are the same. She has two independent random samples, one from each population, shown in the following table:
Sample I | Sample II | |||||||
11.5 | 15.7 | 22.8 | 22.5 | 12.6 | 13.8 | 17.5 | 10.7 | 13.5 |
12.4 | 25.3 | 16.1 | 25.1 | 14.8 | 11.8 | 14.7 | 10.8 | 12.7 |
She uses the Mann-Whitney U test and a significance level of 0.05. The sum of ranks for sample I is ______.
a) 99
b) 101
c) 102
d) 104
e) 106
Response: See section 17.2 Mann-Whitney U Test
Difficulty: Medium
AACSB: Reflective thinking
Bloom’s level: Application
Learning Objective: 17.2: 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.
95. A researcher wants to determine whether the means of two independent populations are the same. She has two independent random samples, one from each population, shown in the following table:
Sample I | Sample II | |||||||
11.5 | 15.7 | 22.8 | 22.5 | 12.6 | 13.8 | 17.5 | 10.7 | 13.5 |
12.4 | 25.3 | 16.1 | 25.1 | 14.8 | 11.8 | 14.7 | 10.8 | 12.7 |
She uses the Mann-Whitney U test and a significance level of 0.05. The sum of ranks for sample II is ______.
a) 72
b) 73
c) 75
d) 77
e) 78
Response: See section 17.2 Mann-Whitney U Test
Difficulty: Medium
AACSB: Reflective thinking
Bloom’s level: Application
Learning Objective: 17.2: 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.
96. A researcher wants to determine whether the means of two independent populations are the same. She has two independent random samples, one from each population, shown in the following table:
Sample I | Sample II | |||||||
11.5 | 15.7 | 22.8 | 22.5 | 12.6 | 13.8 | 17.5 | 10.7 | 13.5 |
12.4 | 25.3 | 16.1 | 25.1 | 14.8 | 11.8 | 14.7 | 10.8 | 12.7 |
She uses the Mann-Whitney U test and a significance level of 0.05. The test statistic is ______.
a) 16
b) 17
c) 18
d) 63
e) 64
Response: See section 17.2 Mann-Whitney U Test
Difficulty: Medium
AACSB: Reflective thinking
Bloom’s level: Application
Learning Objective: 17.2: 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.
97. A researcher wants to determine whether the means of two independent populations are the same. She has two independent random samples, one from each population, shown in the following table:
Sample I | Sample II | |||||||
11.5 | 15.7 | 22.8 | 22.5 | 12.6 | 13.8 | 17.5 | 10.7 | 13.5 |
12.4 | 25.3 | 16.1 | 25.1 | 14.8 | 11.8 | 14.7 | 10.8 | 12.7 |
She uses the Mann-Whitney U test and a significance level of 0.05. Then μU is ______.
a) 4.5
b) 9
c) 31.5
d) 40
e) 63
Response: See section 17.2 Mann-Whitney U Test
Difficulty: Easy
AACSB: Reflective thinking
Bloom’s level: Application
Learning Objective: 17.2: 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.
98. A researcher wants to determine whether the means of two independent populations are the same. She has two independent random samples, one from each population, shown in the following table:
Sample I | Sample II | |||||||
11.5 | 15.7 | 22.8 | 22.5 | 12.6 | 13.8 | 17.5 | 10.7 | 13.5 |
12.4 | 25.3 | 16.1 | 25.1 | 14.8 | 11.8 | 14.7 | 10.8 | 12.7 |
She uses the Mann-Whitney U test and a significance level of 0.05. Then σU is ______.
a) 10.055
b) 11.025
c) 11.255
d) 12.025
e) 12.255
Response: See section 17.2 Mann-Whitney U Test
Difficulty: Medium
AACSB: Reflective thinking
Bloom’s level: Application
Learning Objective: 17.2: 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.
99. A researcher wants to determine whether the means of two independent populations are the same. She has two independent random samples, one from each population, shown in the following table:
Sample I | Sample II | |||||||
11.5 | 15.7 | 22.8 | 22.5 | 12.6 | 13.8 | 17.5 | 10.7 | 13.5 |
12.4 | 25.3 | 16.1 | 25.1 | 14.8 | 11.8 | 14.7 | 10.8 | 12.7 |
She uses the Mann-Whitney U test and a significance level of 0.05. This is a ______ test, and the critical ______.
a) one-tailed; value is 1.96
b) two-tailed; values are ±1.96
c) one-tailed; value is 1.645
d) two-tailed; values are ±1.645
e) one-tailed; value is −1.96
Response: See section 17.2 Mann-Whitney U Test
Difficulty: Medium
AACSB: Reflective thinking
Bloom’s level: Application
Learning Objective: 17.2: 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.
100. A researcher wants to determine whether the means of two independent populations are the same. She has two independent random samples, one from each population, shown in the following table:
Sample I | Sample II | |||||||
11.5 | 15.7 | 22.8 | 22.5 | 12.6 | 13.8 | 17.5 | 10.7 | 13.5 |
12.4 | 25.3 | 16.1 | 25.1 | 14.8 | 11.8 | 14.7 | 10.8 | 12.7 |
She uses the Mann-Whitney U test and a significance level of 0.05. The appropriate
decision is ______.
a) reject the null hypothesis that the two populations have different means
b) fail to reject the null hypothesis that the two populations have different means
c) reject the null hypothesis that the two populations have equal means
d) fail to reject the null hypothesis that the two populations have equal means
e) do nothing
Response: See section 17.2 Mann-Whitney U Test
Difficulty: Hard
AACSB: Analytic
Bloom’s level: Application
Learning Objective: 17.2: 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.
101. A researcher wants to determine the efficacy of a training program directed at improving concentration, focus, and memory on college students. She selects a random sample of 16 individuals and has them take an initial assessment test before the training program. Then the individuals complete the training program, and at the end they take a final test that’s comparable to the initial test. The results are shown in the following table:
Individ. | Before | After |
1 | 79 | 81 |
2 | 74 | 73 |
3 | 81 | 82.5 |
4 | 75 | 82.5 |
5 | 72.5 | 85 |
6 | 75 | 90 |
7 | 67.5 | 83.5 |
8 | 57.5 | 72.5 |
9 | 62.5 | 87.5 |
10 | 77.5 | 80 |
11 | 61.5 | 92.5 |
12 | 57.5 | 80 |
13 | 61.5 | 71 |
14 | 72.5 | 84 |
15 | 64 | 78.5 |
16 | 71 | 97.5 |
The analyst uses a Wilcoxon matched-pairs signed rank test with a 0.05 significance level. The test statistic T− = ______.
a) 136
b) 142
c) 134
d) 135
e) 152
Response: See section 17.3 Wilcoxon Matched-Pairs Signed Rank Test
Difficulty: Medium
AACSB: Reflective thinking
Bloom’s level: Application
Learning Objective: 17.3: Use both the small-sample and large-sample cases of the Wilcoxon matched-pairs signed rank test to compare the difference in two related samples.
102. A researcher wants to determine the efficacy of a training program directed at improving concentration, focus, and memory on college students. She selects a random sample of 16 individuals and has them take an initial assessment test before the training program. Then the individuals complete the training program, and at the end they take a final test that’s comparable to the initial test. The results are shown in the following table:
Individ. | Before | After |
1 | 79 | 81 |
2 | 74 | 73 |
3 | 81 | 82.5 |
4 | 75 | 82.5 |
5 | 72.5 | 85 |
6 | 75 | 90 |
7 | 67.5 | 83.5 |
8 | 57.5 | 72.5 |
9 | 62.5 | 87.5 |
10 | 77.5 | 80 |
11 | 61.5 | 92.5 |
12 | 57.5 | 80 |
13 | 61.5 | 71 |
14 | 72.5 | 84 |
15 | 64 | 78.5 |
16 | 71 | 97.5 |
The analyst uses a Wilcoxon matched-pairs signed rank test with a 0.05 significance level. The value of μT is ______.
a) 68
b) 69
c) 70
d) 71
e) 72
Response: See section 17.3 Wilcoxon Matched-Pairs Signed Rank Test
Difficulty: Medium
AACSB: Reflective thinking
Bloom’s level: Application
Learning Objective: 17.3: Use both the small-sample and large-sample cases of the Wilcoxon matched-pairs signed rank test to compare the difference in two related samples.
103. A researcher wants to determine the efficacy of a training program directed at improving concentration, focus, and memory on college students. She selects a random sample of 16 individuals and has them take an initial assessment test before the training program. Then the individuals complete the training program, and at the end they take a final test that’s comparable to the initial test. The results are shown in the following table:
Individ. | Before | After |
1 | 79 | 81 |
2 | 74 | 73 |
3 | 81 | 82.5 |
4 | 75 | 82.5 |
5 | 72.5 | 85 |
6 | 75 | 90 |
7 | 67.5 | 83.5 |
8 | 57.5 | 72.5 |
9 | 62.5 | 87.5 |
10 | 77.5 | 80 |
11 | 61.5 | 92.5 |
12 | 57.5 | 80 |
13 | 61.5 | 71 |
14 | 72.5 | 84 |
15 | 64 | 78.5 |
16 | 71 | 97.5 |
The analyst uses a Wilcoxon matched-pairs signed rank test with a 0.05 significance level. The value of σT is ______.
a) 17.257
b) 19.339
c) 21.257
d) 23.339
e) 25.257
Response: See section 17.3 Wilcoxon Matched-Pairs Signed Rank Test
Difficulty: Medium
AACSB: Reflective thinking
Bloom’s level: Application
Learning Objective: 17.3: Use both the small-sample and large-sample cases of the Wilcoxon matched-pairs signed rank test to compare the difference in two related samples.
104. A researcher wants to determine the efficacy of a training program directed at improving concentration, focus, and memory on college students. She selects a random sample of 16 individuals and has them take an initial assessment test before the training program. Then the individuals complete the training program, and at the end they take a final test that’s comparable to the initial test. The results are shown in the following table:
Individ. | Before | After |
1 | 79 | 81 |
2 | 74 | 73 |
3 | 81 | 82.5 |
4 | 75 | 82.5 |
5 | 72.5 | 85 |
6 | 75 | 90 |
7 | 67.5 | 83.5 |
8 | 57.5 | 72.5 |
9 | 62.5 | 87.5 |
10 | 77.5 | 80 |
11 | 61.5 | 92.5 |
12 | 57.5 | 80 |
13 | 61.5 | 71 |
14 | 72.5 | 84 |
15 | 64 | 78.5 |
16 | 71 | 97.5 |
The analyst uses a Wilcoxon matched-pairs signed rank test with a 0.05 significance level. The observed z score is ______.
a) −3.4645
b) −3.2157
c) −3.0178
d) −2.9857
e) −2.7978
Response: See section 17.3 Wilcoxon Matched-Pairs Signed Rank Test
Difficulty: Hard
AACSB: Reflective thinking
Bloom’s level: Application
Learning Objective: 17.3: Use both the small-sample and large-sample cases of the Wilcoxon matched-pairs signed rank test to compare the difference in two related samples.
105. A researcher wants to determine the efficacy of a training program directed at improving concentration, focus, and memory on college students. She selects a random sample of 16 individuals and has them take an initial assessment test before the training program. Then the individuals complete the training program, and at the end they take a final test that’s comparable to the initial test. The results are shown in the following table:
Individ. | Before | After |
1 | 79 | 81 |
2 | 74 | 73 |
3 | 81 | 82.5 |
4 | 75 | 82.5 |
5 | 72.5 | 85 |
6 | 75 | 90 |
7 | 67.5 | 83.5 |
8 | 57.5 | 72.5 |
9 | 62.5 | 87.5 |
10 | 77.5 | 80 |
11 | 61.5 | 92.5 |
12 | 57.5 | 80 |
13 | 61.5 | 71 |
14 | 72.5 | 84 |
15 | 64 | 78.5 |
16 | 71 | 97.5 |
The analyst uses a Wilcoxon matched-pairs signed rank test with a 0.05 significance level. The appropriate decision is ______.
a) fail to reject the null hypothesis that the before and after scores are different
b) reject the null hypothesis that that the before and after scores are different
c) fail to reject the null hypothesis that the before and after scores are not different
d) reject the null hypothesis that the before and after scores are not different
e) do nothing
Response: See section 17.3 Wilcoxon Matched-Pairs Signed Rank Test
Difficulty: Hard
AACSB: Analytic
Bloom’s level: Application
Learning Objective: 17.3: Use both the small-sample and large-sample cases of the Wilcoxon matched-pairs signed rank test to compare the difference in two related samples.
106. A researcher wants to study the effects of physical exercise on depression. She randomly selects a group of 24 individuals who are equally depressed. None of these individuals currently exercises. She then randomly assigns them in one of three groups: group 1 stays without exercising (sedentary group), group 2 exercises once a week, and group 3 exercises two times a week. Individuals in groups 2 and 3 meet with a personal trainer so they carry out a very similar exercise program (kinds of exercises and intensity). After two months, the researcher has all individuals take a depression-assessment test. The score of the test goes from 0 = totally miserable to 100 = complete satisfaction.
The scores are shown in the following table:
Group 1 | Group 2 | Group 3 |
25 | 24 | 35 |
15 | 16 | 22 |
20 | 19 | 31 |
17 | 24 | 32 |
23 | 25 | 31 |
21 | 25 | 29 |
19 | 21 | 33 |
18 | 18 | 35 |
The researcher uses a Kruskal-Wallis test and a significance level α = 0.05. The sum of the ranks for group 3, T3, is ______.
a) 157
b) 158
c) 159
d) 160
e) 161
Response: See section 17.4 Kruskal-Wallis Test
Difficulty: Medium
AACSB: Reflective thinking
Bloom’s level: Application
Learning Objective: 17.4: Use the Kruskal-Wallis test to determine whether samples come from the same or different populations.
107. A researcher wants to study the effects of physical exercise on depression. She randomly selects a group of 24 individuals who are equally depressed. None of these individuals currently exercises. She then randomly assigns them in one of three groups: group 1 stays without exercising (sedentary group), group 2 exercises once a week, and group 3 exercises two times a week. Individuals in groups 2 and 3 meet with a personal trainer so they carry out a very similar exercising program, both in kinds of exercises and in intensity. After two months, the researcher has all individuals take a depression-assessment test. The score of the test goes from 0 = totally miserable to 100 = complete satisfaction.
The scores are shown in the following table:
Group 1 | Group 2 | Group 3 |
25 | 24 | 35 |
15 | 16 | 22 |
20 | 19 | 31 |
17 | 24 | 32 |
23 | 25 | 31 |
21 | 25 | 29 |
19 | 21 | 33 |
18 | 18 | 35 |
The researcher uses a Kruskal-Wallis test and a significance level α = 0.05. The observed K statistic is ______.
a) 10.16625
b) 10.7525
c) 11.16625
d) 12.7525
e) 13.16625
Response: See section 17.4 Kruskal-Wallis Test
Difficulty: Hard
AACSB: Reflective thinking
Bloom’s level: Application
Learning Objective: 17.4: Use the Kruskal-Wallis test to determine whether samples come from the same or different populations.
108. A researcher wants to study the effects of physical exercise on depression. She randomly selects a group of 24 individuals who are equally depressed. None of these individuals currently exercises. She then randomly assigns them in one of three groups: group 1 stays without exercising (sedentary group), group 2 exercises once a week, and group 3 exercises two times a week. Individuals in groups 2 and 3 meet with a personal trainer so they carry out a very similar exercising program, both in kinds of exercises and in intensity. After two months, the researcher has all individuals take a depression-assessment test. The score of the test goes from 0 = totally miserable to 100 = complete satisfaction.
The scores are shown in the following table:
Group 1 | Group 2 | Group 3 |
25 | 24 | 35 |
15 | 16 | 22 |
20 | 19 | 31 |
17 | 24 | 32 |
23 | 25 | 31 |
21 | 25 | 29 |
19 | 21 | 33 |
18 | 18 | 35 |
The researcher uses a Kruskal-Wallis test and a significance level α = 0.05. The relevant number of degrees of freedom is ______.
a) 1
b) 2
c) 3
d) 23
e) 24
Response: See section 17.4 Kruskal-Wallis Test
Difficulty: Easy
AACSB: Reflective thinking
Bloom’s level: Application
Learning Objective: 17.4: Use the Kruskal-Wallis test to determine whether samples come from the same or different populations.
109. A researcher wants to study the effects of physical exercise on depression. She randomly selects a group of 24 individuals who are equally depressed. None of these individuals currently exercises. She then randomly assigns them in one of three groups: group 1 stays without exercising (sedentary group), group 2 exercises once a week, and group 3 exercises two times a week. Individuals in groups 2 and 3 meet with a personal trainer so they carry out a very similar exercising program, both in kinds of exercises and in intensity. After two months, the researcher has all individuals take a depression-assessment test. The score of the test goes from 0 = totally miserable to 100 = complete satisfaction.
The scores are shown in the following table:
Group 1 | Group 2 | Group 3 |
25 | 24 | 35 |
15 | 16 | 22 |
20 | 19 | 31 |
17 | 24 | 32 |
23 | 25 | 31 |
21 | 25 | 29 |
19 | 21 | 33 |
18 | 18 | 35 |
The researcher uses a Kruskal-Wallis test and a significance level α = 0.05. The critical chi-square value is ______.
a) 9.35
b) 7.82
c) 7.38
d) 6.82
e) 5.99
Response: See section 17.4 Kruskal-Wallis Test
Difficulty: Medium
AACSB: Reflective thinking
Bloom’s level: Application
Learning Objective: 17.4: Use the Kruskal-Wallis test to determine whether samples come from the same or different populations.
110. A researcher wants to study the effects of physical exercise on depression. She randomly selects a group of 24 individuals who are equally depressed. None of these individuals currently exercises. She then randomly assigns them in one of three groups: group 1 stays without exercising (sedentary group), group 2 exercises once a week, and group 3 exercises two times a week. Individuals in groups 2 and 3 meet with a personal trainer so they carry out a very similar exercising program, both in kinds of exercises and in intensity. After two months, the researcher has all individuals take a depression-assessment test. The score of the test goes from 0 = totally miserable to 100 = complete satisfaction.
The scores are shown in the following table:
Group 1 | Group 2 | Group 3 |
25 | 24 | 35 |
15 | 16 | 22 |
20 | 19 | 31 |
17 | 24 | 32 |
23 | 25 | 31 |
21 | 25 | 29 |
19 | 21 | 33 |
18 | 18 | 35 |
The researcher uses a Kruskal-Wallis test and a significance level α = 0.05. The appropriate decision is ______.
a) fail to reject the null hypothesis that the three groups have different levels of depression
b) reject the null hypothesis that the three groups have different levels of depression
c) fail to reject the null hypothesis that the three groups have equal levels of depression
d) reject the null hypothesis that the three groups have equal levels of depression
e) fail to reject the null hypothesis that the sample is random
Response: See section 17.4 Kruskal-Wallis Test
Difficulty: Hard
AACSB: Analytic
Bloom’s level: Application
Learning Objective: 17.4: Use the Kruskal-Wallis test to determine whether samples come from the same or different populations.
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Business Stats Contemporary Decision 10e | Test Bank by Ken Black
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