1. We can apply non-parametric tests to problems involving interval or ratio data.  True    False 

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

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

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

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

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

7. The sign test is an appropriate nonparametric test for dependent samples.  True    False

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

9. The Wilcoxon rank-sum test compares two dependent populations.  True    False

10. The Wilcoxon rank-sum test computes a z test statistic.  True    False

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

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

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

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

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

Chapter 18: Multiple Choice Questions

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

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

18. For a given set of twelve ranked data values, the sum of the squared differences is 63.18. What is Spearman's coefficient of rank correlation for the data?  A. +.7791 B. -.7791 C. +.2209 D. -.2209

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

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

21. A study was conducted on the percent of total advertising dollars spent by ten local firms for advertising in the press and on cable television. Results were ranked with a resulting sum of squared differences equal to 128. What is the computed value of t?  A. 0.655. B. 0.804. C. 1.339. D. 0.719.

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

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

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

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

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

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

28. 20 economists were sampled and asked to predict if the national economy would improve during the next twelve months. Eleven of the economists predicted an increase, two economists predicted no change, and seven economists predicted a decrease in the economy. Conduct a hypothesis test at the 0.10 significance level to determine if the majority of economists predict an increase. The null hypothesis is:  A.  B.  C.  D.  

29. 20 economists were sampled and asked to predict if the national economy would improve during the next twelve months. Eleven of the economists predicted an increase, two economists predicted no change, and seven economists predicted a decrease in the economy. Conduct a hypothesis test at the 0.10 significance level to determine if the majority of economists predict an increase. The correct analysis would be:  A. A sign test based on the binomial distribution B. A sign test based on the standard normal distribution C. A chi-square test D. A Wilcoxon signed rank test 

30. 20 economists were sampled and asked to predict if the national economy would improve during the next twelve months. Eleven of the economists predicted an increase, two economists predicted no change, and seven economists predicted a decrease in the economy. Conduct a hypothesis test at the 0.10 significance level to determine if the majority of economists predict an increase. The test statistic is:  A. 0.707 B. 1.179 C. 1.707 D. 0.179

31. 20 economists were sampled and asked to predict if the national economy would improve during the next twelve months. Eleven of the economists predicted an increase, two economists predicted no change, and seven economists predicted a decrease in the economy. Conduct a hypothesis test at the 0.10 significance level to determine if the majority of economists predict an increase. Based on the analysis, we would conclude that:  A. The economists favor an increase in the economy B. The economists favor a decrease in the economy C. The economists favor no change in the economy D. No conclusion can be reached

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

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

34. A nonparametric test cannot be applied when the data are  A. Nominal B. Ordinal C. Interval D. Ratio 

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

36. To test the hypothesis, the Wilcoxon Signed-Rank test uses a  A. z-statistic. B. a T test statistic. C. Chi-square statistic. D. a student's t-statistic. 

37. Using the following data, the Wilcoxon Signed-Rank hypothesis test is used to test the hypothesis that there is no difference between the before and after populations. What are the sum of the ranks?     A. 4 and 6 B. 5 C. 17 D. 6 and -11

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

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

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

41. When the paired observations are equal in a Wilcoxon Signed-Rank test hypothesis,  A. observations are removed from the analysis. B. the ranks are averaged. C. a zero is assigned to the difference and retained in the analysis. D. observations are removed from the analysis and "n" is not changed.

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

43. In the Kruskal-Wallis test for the following data, what is the sum of the ranks for sample one?     A. 9 B. 163 C. 3 D. 23 

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

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

46. In the Kruskal-Wallis test for the following data, what is the sum of the ranks for sample one?     A. 61.5 B. 163 C. 6 D. 253

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

48. In the Kruskal-Wallis test for the following data, what is the sum of the ranks for sample three?     A. 57 B. 80 C. 4 D. 210

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

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

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

52. For a given set of twelve ranked data values, the sum of the squared differences is 63.18. What is the test statistic value to test the hypothesis that the rank correlation coefficient is zero?  A. -2.228 B. 2.228 C. 3.948 D. -3.948

 53. A hypothesis test that a rank correlation coefficient is zero is conducted at the 5% level of significance. If the correlation coefficient is 0.50 for a sample of 15 observations, what is the computed value of the t statistic?  A. 0.456 B. 6.08 C. 2.2082 D. 2.2361

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

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

Chapter 17: True/False Questions

1. The shape of the chi-square distribution depends on the size of the sample. True    False 

2. The chi-square distribution is positively skewed. True    False 

3. A scatter plot is a useful graphical method to determine if a set of sample data is from a normal population.  True    False

4. To test the null hypothesis that a set of sample data is normally distributed, we compare an expected normal distribution of the data to an observed distribution of the data.  True    False 

5. AF-test is useful for testing the null hypothesis that a set of sample data is normally distributed.  True    False 

6. A t-statistic is useful for computing an expected normal distribution. True    False 

7. For a goodness-of-fit test, the following are possible null and alternate hypotheses: H0: Sales are uniformly distributed among the five locations. H1: Sales are not uniformly distributed among the five locations.  True    False 

8. For the goodness-of-fit test, the use of the chi-square statistic would be permissible in the following problem.     True    False

9. In the goodness-of-fit test, the chi-square distribution is used to determine how well an observed distribution of observations "fits" an expected distribution of observations.  True    False

 10. For a contingency table, the expected frequency for a cell is found by dividing the row total by the grand total. True    False

11. The shape of the chi-square distribution changes for each number of degrees of freedom.  True    False

Chapter 17: Multiple Choice Questions

12. For a chi-square test involving a contingency table, suppose the null hypothesis is rejected. We conclude that the two variables are  A. linear. B. curvilinear. C. not related. D. related.

13. Which of the following can be used to test the hypothesis that two nominal variables are related?  A. a contingency table. B. a chi-square table. C. an ANOVA table. D. a scatter diagram. 

14. When determining how well an observed set of frequencies fit an expected set of frequencies, what is the test statistic?  A. F-statistic. B. t-statistic. C. statistic. D. z-statistic. 

15. In a goodness-of-fit test, the null hypothesis (no difference between sets of observed and expected frequencies) is rejected when the  A. computed chi-square is less than the critical value. B. difference between the observed and expected frequencies is significantly large. C. difference between the observed and expected frequencies is small. D. difference between the observed and expected frequencies occurs by chance. 

16. The computed chi-square value is positive because the difference between the observed and expected frequencies is  A. squared. B. linear. C. uniform. D. always positive.

17. A personnel manager is concerned about absenteeism. She decides to sample the records to determine if absenteeism is distributed evenly throughout the six-day workweek. The null hypothesis to be tested is: Absenteeism is distributed evenly throughout the week. The 0.01 level is to be used. The sample results are:    What kind of frequencies are the numbers 12, 9, 11, 10, 9, and 9 called?  A. Acceptance B. Critical value C. Expected D. Observed 

18. A personnel manager is concerned about absenteeism. She decides to sample the records to determine if absenteeism is distributed evenly throughout the six-day workweek. The null hypothesis to be tested is: Absenteeism is distributed evenly throughout the week. The 0.01 level is to be used. The sample results are:    How many degrees of freedom are there?  A. 0 B. 3 C. 4 D. 5

19. A personnel manager is concerned about absenteeism. She decides to sample the records to determine if absenteeism is distributed evenly throughout the six-day workweek. The null hypothesis to be tested is: Absenteeism is distributed evenly throughout the week. The 0.01 level is to be used. The sample results are:    What is the expected frequency?  A. 9 B. 10 C. 11 D. 12 

20. A personnel manager is concerned about absenteeism. She decides to sample the records to determine if absenteeism is distributed evenly throughout the six-day workweek. The null hypothesis to be tested is: Absenteeism is distributed evenly throughout the week. The 0.01 level is to be used. The sample results are:    What is the calculated value of chi-square?  A. 1.0 B. 0.5 C. 0.8 D. 8.0

21. A personnel manager is concerned about absenteeism. She decides to sample the records to determine if absenteeism is distributed evenly throughout the six-day workweek. The null hypothesis to be tested is: Absenteeism is distributed evenly throughout the week. The 0.01 level is to be used. The sample results are:    What is the critical value of chi-square with = 0.05?  A. 11.070 B. 12.592 C. 13.388 D. 15.033 

22. A recent study of the relationship between social activity and education showed the following results.    The appropriate test to analyze the relationship between social activity and education is:  A. Regression analysis B. Analysis of variance C. Contingency table analysis D. Goodness-of-fit

23. A recent study of the relationship between social activity and education showed the following results.    The appropriate test statistic for the analysis is a:  A. F-statistic B. T-statistic C. Chi-square statistic D. Z-statistic 

24. A recent study of the relationship between social activity and education showed the following results.    The null hypothesis for the analysis is:  A. There is no relationship between social activity and education. B. The correlation between social activity and education is zero. C. As social activity increases, education increases. D. The mean of social activity equals the mean of education.

25. A recent study of the relationship between social activity and education showed the following results.    The degrees of freedom for the analysis is:  A. 1 B. 2 C. 3 D. 4

26. A recent study of the relationship between social activity and education showed the following results.    Using 0.05 as the significance level, what is the critical value for the test statistic?  A. 9.488 B. 5.991 C. 7.815 D. 3.841

27. A recent study of the relationship between social activity and education showed the following results.    What is the value of the test statistic?  A. 100 B. 83.67 C. 50 D. 4.94

28. A recent study of the relationship between social activity and education showed the following results.    Based on the analysis, what can be concluded?  A. Social activity and education are correlated. B. Social activity and education are not related. C. Social activity and education are related. D. No conclusion is possible.

29. Recently, students in a marketing research class were interested in the driving behavior of students. Specifically, the marketing students were interested if exceeding the speed limit was related to social activity. They collected the following responses from 100 randomly selected students:    The null hypothesis for the analysis is:  A. There is no relationship between gender and driving behavior. B. The correlation between driving behavior and gender is zero. C. As driving behavior increases, gender increases. D. The mean of driving behavior equals the mean of gender.

30. Recently, students in a marketing research class were interested in the driving behavior of students. Specifically, the marketing students were interested if exceeding the speed limit was related to social activity. They collected the following responses from 100 randomly selected students:    The degrees of freedom for the analysis is:  A. 1 B. 2 C. 3 D. 4

31. Recently, students in a marketing research class were interested in the driving behavior of students. Specifically, the marketing students were interested if exceeding the speed limit was related to social activity. They collected the following responses from 100 randomly selected students:    Using 0.05 as the significance level, what is the critical value for the test statistic?  A. 9.488 B. 5.991 C. 7.815 D. 3.841

32. Recently, students in a marketing research class were interested in the driving behavior of students. Specifically, the marketing students were interested if exceeding the speed limit was related to social activity. They collected the following responses from 100 randomly selected students:    What is the value of the test statistic?  A. 83.67 B. 9.89 C. 50 D. 4.94

33. Recently, students in a marketing research class were interested in the driving behavior of students. Specifically, the marketing students were interested if exceeding the speed limit was related to social activity. They collected the following responses from 100 randomly selected students:    Based on the analysis, what can be concluded?  A. Driving behavior and gender are correlated. B. Driving behavior and gender are not related. C. Driving behavior and gender are related. D. No conclusion is possible.

34. A survey of the opinions of property owners about a street widening project was taken to determine whether the resulting opinion was related to the distance from the street. A randomly selected sample of 100 property owners was contacted and the results are shown below.    How many degrees of freedom are there?  A. 2 B. 3 C. 4 D. 5

35. A survey of the opinions of property owners about a street widening project was taken to determine whether the resulting opinion was related to the distance from the street. A randomly selected sample of 100 property owners was contacted and the results are shown below.    What is the critical value at the 5% level of significance?  A. 7.779 B. 9.488 C. 9.236 D. 11.070

36. A survey of the opinions of property owners about a street widening project was taken to determine whether the resulting opinion was related to the distance from the street. A randomly selected sample of 100 property owners was contacted and the results are shown below.    What is the critical value at the 10% level of significance?  A. 7.779 B. 9.236 C. 9.488 D. 11.070

37. A survey of the opinions of property owners about a street widening project was taken to determine whether the resulting opinion was related to the distance from the street. A randomly selected sample of 100 property owners was contacted and the results are shown below.    What is the expected frequency for people who are undecided about the project and have property front-footage between 45 and 120 feet?  A. 2.2 B. 3.9 C. 5.0 D. 7.7 

38. A survey of the opinions of property owners about a street widening project was taken to determine whether the resulting opinion was related to the distance from the street. A randomly selected sample of 100 property owners was contacted and the results are shown below.    What is the expected frequency for people who are in favor of the project and have less than 45 feet of property foot-frontage?  A. 10 B. 12 C. 35 D. 50

39. A survey of the opinions of property owners about a street widening project was taken to determine whether the resulting opinion was related to the distance from the street. A randomly selected sample of 100 property owners was contacted and the results are shown below.    What is the expected frequency for people against the project and who have over 120 feet of property foot-frontage?  A. 1.1 B. 3.9 C. 5.0 D. 5.5 

40. To test for a normal distribution of a frequency distribution with 5 classes, we need to find  A. the t-statistic. B. the expected frequency for each class. C. the class marks. D. the class relative frequencies. 

41. To test for a normal distribution of a frequency distribution with 5 classes, we need to  A. compute aF-statistic. B. calculate a t-statistic. C. convert the class marks to standard normal z-statistics. D. convert the class limits to standard normal z-statistics. 

42. To test for a normal distribution of a frequency distribution with 5 classes, we compute probabilities for each class based on a  A. standard normal distribution. B. chi-square distribution. C. student's t distribution. D. F distribution.

43. A grouped frequency distribution has a mean of 100 and a standard deviation of 20. The class limits for one class are 50 up to 60. What are the standard normal z-statistics for the class limits?  A. -20 and 20. B. -2.5 and -2.0 C. 2.0 and 2.5 D. -50 and -40

44. A grouped frequency distribution has a mean of 100 and a standard deviation of 20. The class limits for one class are 50 up to 60. Based on the normal distribution, what is the probability that an observation would be in this class?  A. 0.4938 B. 0.4772 C. 0.0166 D. -0.0166 

45. A grouped frequency distribution has a mean of 200 and a standard deviation of 20. The class limits for one class are 220 up to 240. What are the standard normal z-statistics for the class limits?  A. -20 and 20. B. -2.0 and -1.0 C. 200 and 220 D. 1.0 and 2.0 

46. A grouped frequency distribution has a mean of 200 and a standard deviation of 20. The class limits for one class are 220 up to 240. Based on the normal distribution, what is the probability that an observation would be in this class?  A. 0.1359 B. 0.3413 C. 0.4772 D. 0.8185

47. To determine if a set of ungrouped, raw data is normally distributed, what test statistic would we use?  A. z-statistic B. F-statistic C. Anderson-Darling D. Chi-square 

48. To determine if a set of ungrouped, raw data is normally distributed, the cumulative relative frequency distribution of the raw data is compared to a  A. grouped relative frequency distribution. B. cumulative normal distribution. C. Anderson-Darling statistic. D. chi-square statistic.

49. To determine if a set of ungrouped, raw data is normally distributed, the null hypothesis is  A. the data are normally distributed. B. the data are not normally distributed. C. the Anderson-Darling test is greater than 0.0. D. the Anderson-Darling test equal to 0.0. 

50. To determine if a set of ungrouped, raw data is normally distributed, we can use  A. Graphical methods. B. A chi-square test. C. ANOVA. D. Regression. 

51. Using a graphical method to determine if a set of ungrouped, raw data is normally distributed, the data would be normally distributed if  A. the plot of the data was curvilinear. B. the data was randomly distributed. C. the plot of the data was linear. D. the plot of the data was significantly different from zero.