Chapter 15: Chi-square

Test Bank

Multiple Choice

1. One assumption of the chi-square statistic is that each observation in a set of data is ______.

a. independent of all other observations

b. dependent on all other observations

c. interrelated to other observations

d. independent of some observations and dependent on others

Cognitive Domain: Knowledge

Answer Location: Assumptions Underlying the Chi-Square Statistic

Difficulty Level: Easy

2. The assumption of independence is met when ______.

a. a researcher assigns each participant to only one group

b. a researcher assigns a participant to more than one group

c. a research collects data from a small sample

d. a research does not assign a participant to a group

Cognitive Domain: Knowledge

Answer Location: Assumptions Underlying the Chi-Square Statistic

Difficulty Level: Easy

3. In using the chi-square statistic, most if not all of the expected frequencies (fe) should be ______.

a. greater than 10

b. greater than or equal to 5

c. greater than 5

d. greater than 0

Cognitive Domain: Knowledge

Answer Location: Assumptions Underlying the Chi-Square Statistic

Difficulty Level: Easy

4. In using the chi-square statistic, none of the expected frequencies (fe) should be equal to ______.

a. 0

b. 1

c. 5

d. 10

Cognitive Domain: Knowledge

Answer Location: Assumptions Underlying the Chi-Square Statistic

Difficulty Level: Easy

5. Which statistical procedure should be conducted if any of the expected frequencies (fe) are less than 5?

a. Chi-square

b. Fisher’s exact test

c. Yates’ correction for continuity

d. ANOVA

Cognitive Domain: Knowledge

Answer Location: Assumptions Underlying the Chi-Square Statistic

Difficulty Level: Easy

6. Which statistical procedure should be conducted if any of the expected frequencies (fe) are between 5 and 10?

a. Chi-square

b. Fisher’s exact test

c. Yates’ correction for continuity

d. ANOVA

Cognitive Domain: Knowledge

Answer Location: Assumptions Underlying the Chi-Square Statistic

Difficulty Level: Easy

7. Which statistical procedure should be conducted if any of the expected frequencies (fe) are greater than 10?

a. Chi-square

b. Fisher’s exact test

c. Yates’ correction for continuity

d. ANOVA

Cognitive Domain: Knowledge

Answer Location: Assumptions Underlying the Chi-Square Statistic

Difficulty Level: Easy

8. If most of the expected frequencies (fe) are not greater than 5, the chi-square has the limited ability to resemble or approximate ______.

a. the sample

b. the population from which the sample was drawn

c. the normal curve

d. the sample from which the sub-sample was drawn

Cognitive Domain: Knowledge

Answer Location: Assumptions Underlying the Chi-Square Statistic

Difficulty Level: Easy

9. For a set of data with the number of groups = 5 and the total N = 200, the expected frequency (f_e) for each group is equal to ______.

a. 25

b. 30

c. 40

d. 50

Cognitive Domain: Comprehension

Answer Location: Calculate Expected Frequencies (f_e).

Difficulty Level: Medium

10. For a set of data with the number of groups = 3 and the total N = 500, the expected frequency (f_e) for each group is equal to ______.

a. 165

b. 166.67

c. 250

d. 300

Cognitive Domain: Comprehension

Answer Location: Calculate Expected Frequencies (f_e).

Difficulty Level: Medium

11. For a set of data with the number of groups = 4 and the total N = 400, the expected frequency (f_e) for each group is equal to ______.

a. 40

b. 75

c. 100

d. 200

Cognitive Domain: Comprehension

Answer Location: Calculate Expected Frequencies (f_e).

Difficulty Level: Medium

12. For a set of data with the number of groups = 5 and the total N = 300, the expected frequency (f_e) for each group is equal to ______.

a. 30

b. 60

c. 120

d. 240

Cognitive Domain: Comprehension

Answer Location: Calculate Expected Frequencies (f_e).

Difficulty Level: Medium

13. For a set of data with the number of groups = 3 and the total N = 300, the expected frequency (f_e) for each group is equal to ______.

a. 40

b. 75

c. 100

d. 200

Cognitive Domain: Comprehension

Answer Location: Calculate Expected Frequencies (f_e).

Difficulty Level: Medium

14. For a set of data with the number of groups = 4 and the total N = 250, the degrees of freedom are equal to ______.

a. 3

b. 4

c. 249

d. 250

Cognitive Domain: Comprehension

Answer Location: Calculate the Degrees of Freedom (df)

Difficulty Level: Medium

15. For a set of data with the number of groups = 5 and the total N = 300, the degrees of freedom are equal to ______.

a. 300

b. 299

c. 5

d. 4

Cognitive Domain: Comprehension

Answer Location: Calculate the Degrees of Freedom (df)

Difficulty Level: Medium

16. For a set of data with the number of groups = 3 and the total N = 196, the degrees of freedom are equal to ______.

a. 1

b. 2

c. 3

d. 195

Cognitive Domain: Comprehension

Answer Location: Calculate the Degrees of Freedom (df)

Difficulty Level: Medium

17. For α = .05 and df = 4, the critical value for a chi-square statistic would be ______.

a. 5.989

b. 7.779

c. 7.815

d. 9.488

Cognitive Domain: Comprehension

Answer Location: Set Alpha (α), Identify the Critical Value, and State a Decision Rule

Difficulty Level: Medium

18. For α = .05 and df = 2, the critical value for a chi-square statistic would be ______.

a. 5.991

b. 7.815

c. 9.348

d. 12.838

Cognitive Domain: Comprehension

Answer Location: Set Alpha (α), Identify the Critical Value, and State a Decision Rule

Difficulty Level: Medium

19. For α = .01 and df = 4, the critical value for a chi-square statistic would be ______.

a. 9.488

b. 7.815

c. 13.277

d. 11.344

Cognitive Domain: Comprehension

Answer Location: Set Alpha (α), Identify the Critical Value, and State a Decision Rule

Difficulty Level: Medium

20. For α = .01 and df = 3, the critical value for a chi-square statistic would be ______.

a. 9.488

b. 7.815

c. 13.277

d. 11.344

Cognitive Domain: Comprehension

Answer Location: Set Alpha (α), Identify the Critical Value, and State a Decision Rule

Difficulty Level: Medium

21. For a study that included 5 groups, the critical value for α = .01 would be ______.

a. 13.277

b. 11.344

c. 11.070

d. 9.488

Cognitive Domain: Comprehension

Answer Location: Set Alpha (α), Identify the Critical Value, and State a Decision Rule

Difficulty Level: Medium

22. For a study that included 4 groups, the critical value for α = .01 would be ______.

a. 7.815

b. 9.348

c. 11.344

d. 13.277

Cognitive Domain: Comprehension

Answer Location: Set Alpha (α), Identify the Critical Value, and State a Decision Rule

Difficulty Level: Medium

23. For a study that included 3 groups, the critical value for α = .01 would be ______.

a. 3.841

b. 5.991

c. 7.815

d. 9.210

Cognitive Domain: Comprehension

Answer Location: Set Alpha (α), Identify the Critical Value, and State a Decision Rule

Difficulty Level: Medium

24. For a study that included 3 groups, the critical value for α = .05 would be ______.

a. 3.841

b. 5.991

c. 7.815

d. 9.210

Cognitive Domain: Comprehension

Answer Location: Set Alpha (α), Identify the Critical Value, and State a Decision Rule

Difficulty Level: Medium

25. Calculate the chi-square statistic for the following data (assume equal expected frequencies).

a. 125

b. 186.02

c. 204.56

d. 341.78

Cognitive Domain: Application

Answer Location: Calculate the Chi-Square Statistic (χ²)

Difficulty Level: Hard

26. Calculate the chi-square statistic for the following data (assume equal expected frequencies).

a. 14.85

b. 35.26

c. 42.89

d. 115.00

Cognitive Domain: Application

Answer Location: Calculate the Chi-Square Statistic (χ²)

Difficulty Level: Hard

27. Calculate the chi-square statistic for the following data (assume equal expected frequencies).

a. 0.64

b. 31.18

c. 8.91

d. 60.00

Cognitive Domain: Application

Answer Location: Calculate the Chi-Square Statistic (χ²)

Difficulty Level: Hard

28. Calculate the chi-square statistic for the following data (assume equal expected frequencies).

a. 2.12

b. 8.53

c. 30.12

d. 60.00

Cognitive Domain: Application

Answer Location: Calculate the Chi-Square Statistic (χ²)

Difficulty Level: Hard

29. For χ² = 48.76 with the number of groups = 5, the researcher would ______.

a. not reject the null hypothesis (p > .05)

b. not reject the null hypothesis (p < .05)

c. reject the null hypothesis (p >.05)

d. reject the null hypothesis (p <.05)

Cognitive Domain: Application

Answer Location: Make a Decision whether to Reject the Null Hypothesis

Difficulty Level: Hard

30. For χ² = 4.05 with the number of groups = 3, the researcher would ______.

a. not reject the null hypothesis (p > .05)

b. not reject the null hypothesis (p < .05)

c. reject the null hypothesis (p >.05)

d. reject the null hypothesis (p <.05)

Cognitive Domain: Application

Answer Location: Make a Decision whether to Reject the Null Hypothesis

Difficulty Level: Hard

31. For χ² = 31.72 with the number of groups = 3, the researcher would ______.

a. not reject the null hypothesis (p > .05)

b. not reject the null hypothesis (p < .05)

c. reject the null hypothesis (p >.05)

d. reject the null hypothesis (p <.05)

Cognitive Domain: Application

Answer Location: Make a Decision whether to Reject the Null Hypothesis

Difficulty Level: Hard

32. For χ² = 6.56 with the number of groups = 4, the researcher would ______.

a. reject the null hypothesis (p <.05)

b. reject the null hypothesis (p >.05)

c. not reject the null hypothesis (p < .05)

d. not reject the null hypothesis (p > .05)

Cognitive Domain: Application

Answer Location: Make a Decision whether to Reject the Null Hypothesis

Difficulty Level: Hard

33. For χ² = 8.56 with the number of groups = 6, the researcher would ______.

a. reject the null hypothesis (p <.05)

b. reject the null hypothesis (p >.05)

c. not reject the null hypothesis (p > .05)

d. not reject the null hypothesis (p < .05)

Cognitive Domain: Application

Answer Location: Make a Decision whether to Reject the Null Hypothesis

Difficulty Level: Hard

34. For χ² = 17.22 with the number of groups = 6, the researcher would ______.

a. reject the null hypothesis (p <.05)

b. reject the null hypothesis (p >.05)

c. not reject the null hypothesis (p > .05)

d. not reject the null hypothesis (p < .05)

Cognitive Domain: Application

Answer Location: Make a Decision whether to Reject the Null Hypothesis

Difficulty Level: Hard

35. For χ² = 12.22 with the number of groups = 4, the researcher would ______.

a. reject the null hypothesis (p <.05)

b. reject the null hypothesis (p >.05)

c. not reject the null hypothesis (p > .05)

d. not reject the null hypothesis (p < .05)

Cognitive Domain: Application

Answer Location: Make a Decision whether to Reject the Null Hypothesis

Difficulty Level: Hard

36. For χ² = 48.76 with the number of groups = 5, the researcher would ______.

a. not reject the null hypothesis (p > .05)

b. reject the null hypothesis (p <.01)

c. reject the null hypothesis (p >.05)

d. reject the null hypothesis (p <.05)

Cognitive Domain: Application

Answer Location: Determine the Level of Significance

Difficulty Level: Hard

37. For χ² = 17.22 with the number of groups = 6, the researcher would ______.

a. not reject the null hypothesis (p > .05)

b. reject the null hypothesis (p <.05)

c. reject the null hypothesis (p >.05)

d. reject the null hypothesis (p <.01)

Cognitive Domain: Application

Answer Location: Determine the Level of Significance

Difficulty Level: Hard

38. For χ² = 8.56 with the number of groups = 6, the researcher would ______.

a. not reject the null hypothesis (p > .05)

b. reject the null hypothesis (p <.05)

c. reject the null hypothesis (p >.05)

d. reject the null hypothesis (p <.01)

Cognitive Domain: Application

Answer Location: Determine the Level of Significance

Difficulty Level: Hard

39. For χ² = 6.56 with the number of groups = 4, the researcher would ______.

a. reject the null hypothesis (p >.05)

b. reject the null hypothesis (p <.05)

c. not reject the null hypothesis (p >.05)

d. reject the null hypothesis (p <.01)

Cognitive Domain: Application

Answer Location: Determine the Level of Significance

Difficulty Level: Hard

40. For χ² = 8.88 with the number of groups = 4, the researcher would ______.

a. not reject the null hypothesis (p > .05)

b. reject the null hypothesis (p <.05)

c. reject the null hypothesis (p >.05)

d. reject the null hypothesis (p <.01)

Cognitive Domain: Application

Answer Location: Determine the Level of Significance

Difficulty Level: Hard

41. For χ² = 31.72 with the number of groups = 3, the researcher would ______.

a. not reject the null hypothesis (p > .05)

b. reject the null hypothesis (p <.05)

c. reject the null hypothesis (p >.05)

d. reject the null hypothesis (p <.01)

Cognitive Domain: Application

Answer Location: Determine the Level of Significance

Difficulty Level: Hard

42. For χ² = 14.92 with number of groups = 5, the researcher would ______.

a. not reject the null hypothesis (p > .05)

b. reject the null hypothesis (p >.05)

c. reject the null hypothesis (p <.05)

d. reject the null hypothesis (p <.01)

Cognitive Domain: Application

Answer Location: Determine the Level of Significance

Difficulty Level: Hard

43. When reporting the results of a chi-square goodness of fit test, one would include ______.

a. the χ² statistic, the expected frequencies, and the level of significance

b. the χ² statistic, the level of significance, and the degrees of freedom

c. the expected frequencies, the χ² statistic, and the degrees of freedom

d. the level of significance, the degrees of freedom, and the expected frequencies

Cognitive Domain: Knowledge

Answer Location: Draw a Conclusion from the Analysis

Difficulty Level: Medium

44. For α = .05, which of the following is the appropriate critical value?

Use the following formula:

a. 15.086

b. 13.277

c. 11.070

d. 9.488

Cognitive Domain: Application

Answer Location: Set Alpha (α), Identify the Critical Value, and State a Decision Rule

Difficulty Level: Hard

45. Based on your calculations, which of the following best represents the decision regarding the null hypothesis?

Use the following formula:

a. Do not reject H0 (p > .05)

b. Do not reject H0 (p < .05)

c. Reject H0 (p < .05)

d. Reject H0 (p < .01)

Cognitive Domain: Application

Answer Location: Determine the Level of Significance

Difficulty Level: Hard

46. For α = .05, which of the following is an appropriate critical value?

Use the following formula:

a. 7.815

b. 9.488

c. 11.345

d. 13.277

Cognitive Domain: Application

Answer Location: Set Alpha (α), Identify the Critical Value, and State a Decision Rule

Difficulty Level: Hard

47. Based on your calculations, which of the following best represents the decision regarding the null hypothesis?

Use the following formula:

a. Do not reject H₀ (p > .05).

b. Do not reject H₀ (p < .05).

c. Reject H₀ (p < .05).

d. Reject H₀ (p < .01).

Cognitive Domain: Application

Answer Location: Determine the Level of Significance

Difficulty Level: Hard

48. Calculate Cramér’s  for the following data:

Use the following formula:

a. .01

b. .12

c. .82

d. .90

Cognitive Domain: Application

Answer Location: Calculate a Measure of Effect Size (Cramér’s )

Difficulty Level: Hard

49. Calculate Cramér’s  for the following data:

Use the following formula:

a. .14

b. .09

c. .50

d. .56

Cognitive Domain: Application

Answer Location: Calculate a Measure of Effect Size (Cramér’s )

Difficulty Level: Hard

50. Calculate Cramér’s  for the following data:

Use the following formula:

a. .06

b. .09

c. .13

d. .21

Cognitive Domain: Application

Answer Location: Calculate a Measure of Effect Size (Cramér’s )

Difficulty Level: Hard

51. Calculate Cramér’s  for the following data:

Use the following formula:

a. .17

b. .11

c. .23

d. .02

Cognitive Domain: Application

Answer Location: Calculate a Measure of Effect Size (Cramér’s )

Difficulty Level: Hard

52. Calculate Cramér’s  for the following data:

Use the following formula:

a. .12

b. .03

c. .20

d. .06

Cognitive Domain: Application

Answer Location: Calculate a Measure of Effect Size (Cramér’s )

Difficulty Level: Hard

53. Calculate Cramér’s  for the following data:

Use the following formula:

a. .02

b. .17

c. .05

d. .12

Cognitive Domain: Application

Answer Location: Calculate a Measure of Effect Size (Cramér’s )

Difficulty Level: Hard

54. Calculate Cramér’s  for the following data:

Use the following formula:

a. .01

b. .02

c. .08

d. .14

Cognitive Domain: Application

Answer Location: Calculate a Measure of Effect Size (Cramér’s )

Difficulty Level: Hard

55. Calculate Cramér’s  for the following data:

Use the following formula:

a. .01

b. .05

c. .10

d. .14

Cognitive Domain: Application

Answer Location: Calculate a Measure of Effect Size (Cramér’s )

Difficulty Level: Hard

56. Calculate Cramér’s  for the following data:

Use the following formula:

a. .10

b. .03

c. 01

d. .21

Cognitive Domain: Application

Answer Location: Calculate a Measure of Effect Size (Cramér’s )

Difficulty Level: Hard

57. What is Cramér’s  for the following data:² = 20.22, N = 200; # groups= 4?

a. .18

b. .10

c. .07

d. .03

Cognitive Domain: Application

Answer Location: Calculate a Measure of Effect Size (Cramér’s )

Difficulty Level: Hard

58. What is the expected frequency (fe) for Type A?

a. 125.55

b. 235.03

c. 140.42

d. 94.01

Cognitive Domain: Application

Answer Location: Calculate Expected Frequencies (f_e)

Difficulty Level: Hard

59. What is the expected frequency (fe) for Type B?

a. 125.55

b. 235.03

c. 140.42

d. 94.01

Cognitive Domain: Application

Answer Location: Calculate Expected Frequencies (f_e)

Difficulty Level: Hard

60. What is the expected frequency (fe) for Type C?

a. 125.55

b. 235.03

c. 140.42

d. 94.01

Cognitive Domain: Application

Answer Location: Calculate Expected Frequencies (f_e)

Difficulty Level: Hard

61. What is the expected frequency (fe) for Type D?

a. 125.55

b. 235.03

c. 140.42

d. 94.01

Cognitive Domain: Application

Answer Location: Calculate Expected Frequencies (f_e)

Difficulty Level: Hard

62. What is the expected frequency (fe) for Type A?

a. 9

b. 45

c. 27

d. 99

Cognitive Domain: Application

Answer Location: Calculate Expected Frequencies (f_e)

Difficulty Level: Hard

63. What is the expected frequency (fe) for Type B?

a. 9

b. 45

c. 27

d. 99

Cognitive Domain: Application

Answer Location: Calculate Expected Frequencies (f_e)

Difficulty Level: Hard

64. What is the expected frequency (fe) for Type C?

a. 9

b. 45

c. 27

d. 99

Cognitive Domain: Application

Answer Location: Calculate Expected Frequencies (f_e)

Difficulty Level: Hard

65. What is the expected frequency (fe) for Type D?

a. 9

b. 45

c. 27

d. 99

Cognitive Domain: Application

Answer Location: Calculate Expected Frequencies (f_e)

Difficulty Level: Hard

66. What is the expected frequency (fe) for Type A?

a. 62.60

b. 93.90

c. 125.20

d. 31.30

Cognitive Domain: Application

Answer Location: Calculate Expected Frequencies (f_e)

Difficulty Level: Hard

67. What is the expected frequency (fe) for Type B?

a. 62.60

b. 93.90

c. 125.20

d. 31.30

Cognitive Domain: Application

Answer Location: Calculate Expected Frequencies (f_e)

Difficulty Level: Hard

68. What is the expected frequency (fe) for Type C?

a. 62.60

b. 93.90

c. 125.20

d. 31.30

Cognitive Domain: Application

Answer Location: Calculate Expected Frequencies (f_e)

Difficulty Level: Hard

69. What is the expected frequency (fe) for Type D?

a. 62.60

b. 93.90

c. 125.20

d. 31.30

Cognitive Domain: Application

Answer Location: Calculate Expected Frequencies (f_e)

Difficulty Level: Hard

70. Calculate the expected frequency (fe) for those who believe the police do a good job and are very afraid to walk after dark.

a. 37.62

b. 33.32

c. 53.75

d. 40.31

Cognitive Domain: Application

Answer Location: Calculate Expected Frequencies (f_e)

Difficulty Level: Hard

71. Calculate the expected frequency (fe) for those who believe the police do a good job and are somewhat afraid to walk after dark.

a. 37.62

b. 33.32

c. 53.75

d. 40.31

Cognitive Domain: Application

Answer Location: Calculate Expected Frequencies (f_e)

Difficulty Level: Hard

72. Calculate the expected frequency (fe) for those who believe the police do a good job and are slightly afraid to walk after dark.

a. 37.62

b. 33.32

c. 53.75

d. 40.31

Cognitive Domain: Application

Answer Location: Calculate Expected Frequencies (f_e)

Difficulty Level: Hard

73. Calculate the expected frequency (fe) for those who believe the police do a good job and are not at all afraid to walk after dark.

a. 37.62

b. 33.32

c. 53.75

d. 40.31

Cognitive Domain: Application

Answer Location: Calculate Expected Frequencies (f_e)

Difficulty Level: Hard

74. Calculate the expected frequency (fe) for those who believe the police do not do a good job and are very afraid to walk after dark.

a. 32.38

b. 28.68

c. 46.25

d. 34.69

Cognitive Domain: Application

Answer Location: Calculate Expected Frequencies (f_e)

Difficulty Level: Hard

75. Calculate the expected frequency (fe) for those who believe the police do not do a good job and are somewhat afraid to walk after dark.

a. 32.38

b. 28.68

c. 46.25

d. 34.69

Cognitive Domain: Application

Answer Location: Calculate Expected Frequencies (f_e)

Difficulty Level: Hard

76. Calculate the expected frequency (fe) for those who believe the police do not do a good job and are slightly afraid to walk after dark.

a. 32.38

b. 28.68

c. 46.25

d. 34.69

Cognitive Domain: Application

Answer Location: Calculate Expected Frequencies (f_e)

Difficulty Level: Hard

77. Calculate the expected frequency (fe) for those who believe the police do not do a good job and are not at all afraid to walk after dark.

a. 32.38

b. 28.68

c. 46.25

d. 34.69

Cognitive Domain: Application

Answer Location: Calculate Expected Frequencies (f_e)

Difficulty Level: Hard

78. Calculate the expected frequency (fe) for those who believe the police do a good job and are very afraid to walk after dark.

a. 27.99

b. 26.47

c. 30.54

d. 29.46

Cognitive Domain: Application

Answer Location: Calculate Expected Frequencies (f_e)

Difficulty Level: Hard

79. Calculate the expected frequency (fe) for those who believe the police do a good job and are somewhat afraid to walk after dark.

a. 27.99

b. 26.47

c. 30.54

d. 29.46

Cognitive Domain: Application

Answer Location: Calculate Expected Frequencies (f_e)

Difficulty Level: Hard

80. Calculate the expected frequency (fe) for those who believe the police do a good job and are not at all afraid to walk after dark.

a. 27.99

b. 26.47

c. 30.54

d. 29.46

Cognitive Domain: Application

Answer Location: Calculate Expected Frequencies (f_e)

Difficulty Level: Hard

81. Calculate the expected frequency (fe) for those who believe the police do not do a good job and are very afraid to walk after dark.

a. 26.47

b. 27.01

c. 25.53

d. 29.46

Cognitive Domain: Application

Answer Location: Calculate Expected Frequencies (f_e)

Difficulty Level: Hard

82. Calculate the expected frequency (fe) for those who believe the police do not do a good job and are somewhat afraid to walk after dark.

a. 30.54

b. 27.00

c. 25.53

d. 29.46

Cognitive Domain: Application

Answer Location: Calculate Expected Frequencies (f_e)

Difficulty Level: Hard

83. Calculate the expected frequency (fe) for those who believe the police do not do a good job and are not at all afraid to walk after dark.

a. 27.99

b. 27.00

c. 25.53

d. 29.46

Cognitive Domain: Application

Answer Location: Calculate Expected Frequencies (f_e)

Difficulty Level: Hard

84. For a chi-square with 4 groups for the row variable and 3 groups for the column variable, the degrees of freedom would be equal to ______.

a. 2

b. 3

c. 5

d. 6

Cognitive Domain: Comprehension

Answer Location: Calculate the Degrees of Freedom (df)

Difficulty Level: Medium

85. For a chi-square with 3 groups for the row variable and 2 groups for the column variable, the degrees of freedom would be equal to ______.

a. 2

b. 3

c. 4

d. 6

Cognitive Domain: Comprehension

Answer Location: Calculate the Degrees of Freedom (df)

Difficulty Level: Medium

86. For a chi-square with 4 groups for the row variable and 2 groups for the column variable, the degrees of freedom would be equal to ______.

a. 2

b. 3

c. 4

d. 6

Cognitive Domain: Comprehension

Answer Location: Calculate the Degrees of Freedom (df)

Difficulty Level: Medium

87. For a chi-square with 5 groups for the row variable and 2 groups for the column variable, the degrees of freedom would be equal to ______.

a. 2

b. 3

c. 4

d. 6

Cognitive Domain: Application

Answer Location: Calculate the Degrees of Freedom (df)

Difficulty Level: Hard

88. For a chi-square with 5 groups for the row variable and 3 groups for the column variable, the degrees of freedom would be equal to ______.

a. 2

b. 5

c. 7

d. 8

Cognitive Domain: Application

Answer Location: Calculate the Degrees of Freedom (df)

Difficulty Level: Hard

89. For a chi-square with 2 groups for the row variable and 4 groups for the column variable, the critical value for α = .05 would be equal to ______.

a. 5.99

b. 7.81

c. 9.49

d. 11.07

Cognitive Domain: Application

Answer Location: Set Alpha (α), Identify the Critical Value, and State a Decision Rule

Difficulty Level: Hard

90. For a chi-square with 3 groups for the row variable and 3 groups for the column variable, the critical value for α = .05 would be equal to ______.

a. 5.99

b. 7.81

c. 9.49

d. 11.07

Cognitive Domain: Application

Answer Location: Set Alpha (α), Identify the Critical Value, and State a Decision Rule

Difficulty Level: Hard

91. For a chi-square with 3 groups for the row variable and 2 groups for the column variable, the critical value for α = .01 would be equal to ______.

a. 9.21

b. 11.34

c. 13.28

d. 16.81

Cognitive Domain: Application

Answer Location: Set Alpha (α), Identify the Critical Value, and State a Decision Rule

Difficulty Level: Hard

92. For a chi-square with 2 groups for the row variable and 4 groups for the column variable, the critical value for α = .01 would be equal to ______.

a. 9.21

b. 11.34

c. 13.28

d. 16.81

Cognitive Domain: Application

Answer Location: Set Alpha (α), Identify the Critical Value, and State a Decision Rule

Difficulty Level: Hard

93. For a chi-square with 3 groups for the row variable and 3 groups for the column variable, the critical value for α = .01 would be equal to ______.

a. 9.210

b. 11.34

c. 13.28

d. 16.81

Cognitive Domain: Application

Answer Location: Set Alpha (α), Identify the Critical Value, and State a Decision Rule

Difficulty Level: Hard

94. For a chi-square with 6 groups for the row variable and 2 groups for the column variable, the critical value for α = .01 would be equal to ______.

a. 9.210

b. 11.345

c. 13.277

d. 15.09

Cognitive Domain: Application

Answer Location: Set Alpha (α), Identify the Critical Value, and State a Decision Rule

Difficulty Level: Hard

95. Calculate the chi-square statistic for the data in the following table:

a. 20.34

b. 25.64

c. 30.25

d. 45.69

Cognitive Domain: Application

Answer Location: Calculate the Chi-square Statistic (χ²)

Difficulty Level: Hard

96. Calculate the chi-square statistic for the data in the following table:

a. 36.12

b. 38.41

c. 28.11

d. 48.02

Cognitive Domain: Application

Answer Location: Calculate the Chi-Square Statistic (χ²)

Difficulty Level: Hard

97. For χ² = 8.24, df = 6, and α= .05, the researcher would ______.

a. reject H₀ (p < .05)

b. reject H₀ (p > .05)

c. not reject H₀ (p < .05)

d. not reject H₀ (p > .05)

Cognitive Domain: Application

Answer Location: Make a Decision whether to Reject the Null Hypothesis

Difficulty Level: Hard

98. For χ² = 11.34, df = 4, and α = .05, the researcher would ______.

a. reject H₀ (p < .05)

b. reject H₀ (p > .05)

c. not reject H₀ (p < .05)

d. not reject H₀ (p > .05)

Cognitive Domain: Application

Answer Location: Make a Decision whether to Reject the Null Hypothesis

Difficulty Level: Hard

99. For χ² = 10.66, df = 3, and α = .05, the researcher would ______.

a. reject H₀ (p < .05)

b. reject H₀ (p > .05)

c. not reject H₀ (p < .05)

d. not reject H₀ (p > .05)

Cognitive Domain: Application

Answer Location: Make a Decision whether to Reject the Null Hypothesis

Difficulty Level: Hard

100. For χ² = 11.06, df = 5, and α = .05, the researcher would ______.

a. reject H₀ (p < .05)

b. reject H₀ (p > .05)

c. not reject H₀ (p < .05)

d. not reject H₀ (p > .05)

Cognitive Domain: Application

Answer Location: Make a Decision whether to Reject the Null Hypothesis

Difficulty Level: Hard

101. For a sample of 200, a researcher calculates χ² = 9.06 with 4 degrees of freedom. Which of the following is the correct way to present this analysis?

a. p < .05 (but not < .01)

b. p > .05

c. p < .01

d. p > .05 (but < .01)

Cognitive Domain: Application

Answer Location: Determine the Level of Significance

Difficulty Level: Hard

102. For a sample of 350, a researcher calculates χ² = 6.62 with 2 degrees of freedom. Which of the following is the correct way to present this analysis?

a. p < .05 (but not < .01)

b. p > .05

c. p < .01

d. p > .05 (but < .01)

Cognitive Domain: Application

Answer Location: Determine the Level of Significance

Difficulty Level: Hard

103. For a sample of 125, a researcher calculates χ² = 13.14 with 4 degrees of freedom. Which of the following is the correct way to present this analysis?

a. p < .05 (but not < .01)

b. p > .05

c. p < .01

d. p > .05 (but < .01)

Cognitive Domain: Application

Answer Location: Determine the Level of Significance

Difficulty Level: Hard

104. For a sample of 100, a researcher calculates χ² = 13.14 with 5 degrees of freedom. Which of the following is the correct way to present this analysis?

a. p < .05 (but not < .01)

b. p > .05

c. p < .01

d. p > .05 (but < .01)

Cognitive Domain: Application

Answer Location: Determine the Level of Significance

Difficulty Level: Hard

105. For a sample of 300, a researcher calculates χ² = 16.91 with 6 degrees of freedom. Which of the following is the correct way to present this analysis?

a. p < .05 (but not < .01)

b. p > .05

c. p < .01

d. p > .05 (but < .01)

Cognitive Domain: Application

Answer Location: Determine the Level of Significance

Difficulty Level: Hard

106. When reporting the results of a chi-square test of independence, one would include which of the following?

a. the measure of effect size

b. the row totals

c. the column totals

d. the expected frequencies

Cognitive Domain: Knowledge

Answer Location: Draw a Conclusion from the Analysis

Difficulty Level: Easy

107. When reporting the results of a chi-square test of independence, one would include which of the following?

a. the column totals

b. the row totals

c. the ²

d. the expected frequencies

Cognitive Domain: Knowledge

Answer Location: Draw a Conclusion from the Analysis

Difficulty Level: Easy

108. When reporting the results of a chi-square test of independence, one would include ______.

a. the column totals; the sample size; the measure of effect size

b. the ²; the column totals; the measure of effect size

c. the ²; the sample size; the measure of effect size

d. the measure of effect size; the column totals; the χ²

Cognitive Domain: Comprehension

Answer Location: Draw a Conclusion from the Analysis

Difficulty Level: Medium

109. A chi-square statistic was calculated to relate people’s feelings of safety (No, Yes) and whether they or not they felt the police did a good job (No, Yes). If the null hypothesis is not rejected, which is the most appropriate conclusion that can be made?

a. There is no relationship between people’s feelings and their satisfaction with police.

b. The groups are not all equal to each other.

c. The expected frequencies differed significantly from the observed frequencies.

d. The was a very large effect between the expected and observed frequencies.

Cognitive Domain: Comprehension

Answer Location: Draw a Conclusion from the Analysis

Difficulty Level: Medium

110. The results of the chi-square test of independence found that fear of crime depended on one’s satisfaction with police. If the null hypothesis is rejected, which is the most appropriate conclusion that can be made?

a. There is no relationship between people’s feelings and their satisfaction with police.

b. One’s fear of crime is related to whether or not they are satisfied with police.

c. The expected frequencies were equal to the observed frequencies.

d The was a very small effect between the expected and observed frequencies.

Cognitive Domain: Comprehension

Answer Location: Draw a Conclusion from the Analysis

Difficulty Level: Medium

111. The results of the chi-square test of independence found that fear of crime depended on one’s perception of whether their neighborhood was a high crime area or not. If the null hypothesis is rejected, which is the most appropriate conclusion that can be made?

a. The was a very small effect between the expected and observed frequencies.

b. There is no relationship between people’s feelings and their satisfaction with police.

c. The expected frequencies were equal to the observed frequencies.

d One’s fear of crime is related to whether or not they believe their neighborhood to be a high crime area.

Cognitive Domain: Comprehension

Answer Location: Draw a Conclusion from the Analysis

Difficulty Level: Medium

112. For the data below, a chi-square of 28.11 was calculated. What is the effect size (Cramér’s )?

Use the following formula:

a. .11

b. .28

c. .22

d. .06

Cognitive Domain: Application

Answer Location: Calculate a Measure of Effect Size (Cramér’s )

Difficulty Level: Hard

113. What is the effect size (Cramér’s ) for a 3 × 3 table for N = 150 and a chi-square value = 9.49?

Use the following formula:

a. .25

b. .06

c. .03

d. .18

Cognitive Domain: Application

Answer Location: Calculate a Measure of Effect Size (Cramér’s )

Difficulty Level: Hard

114. What is the effect size (Cramér’s ) for a 4 × 3 table for N = 200 and a chi-square value = 8.84?

Use the following formula:

a. .15

b. .20

c. .10

d. .02

Cognitive Domain: Application

Answer Location: Calculate a Measure of Effect Size (Cramér’s )

Difficulty Level: Hard

115. What is the effect size (Cramér’s ) for a 2 × 3 table for N = 200 and a chi-square value = 11.64?

Use the following formula:

a. .03

b. .06

c. .17

d. .24

Cognitive Domain: Application

Answer Location: Calculate a Measure of Effect Size (Cramér’s )

Difficulty Level: Hard

116. ______ such as ______ do not involve the estimation of population parameters.

a. Parametric statistical tests; t-tests

b. Nonparametric statistical tests; chi-square statistics

c. Nonparametric statistical tests; t-tests

d. Parametric statistical tests; chi-square statistics

Cognitive Domain: Knowledge

Answer Location: Parametric vs. Nonparametric Statistical Tests

Difficulty Level: Easy

117. Which of the following is an assumption about nonparametric tests?

a. Data from a sample is being used to estimate the population parameter.

b. Data collected on these variables from samples of the population are normally distributed.

c. They assume that the distribution of scores for a variable is normally distributed in the larger population.

d. They do not require variables to be normally distributed.

Cognitive Domain: Knowledge

Answer Location: Parametric vs. Nonparametric Statistical Tests

Difficulty Level: Easy

118. Nonparametric statistical tests are used in research situations in which the dependent variable is measured at which levels of measurement?

a. ratio

b. interval

c. nominal

d. incremental

Cognitive Domain: Knowledge

Answer Location: Reasons for Using Nonparametric Statistical Tests

Difficulty Level: Easy

119. When a continuous variable is normally distributed, a nonparametric test has ______ statistical power than its parametric counterpart.

a. more

b. less

c. the same

d. comparable

Cognitive Domain: Comprehension

Answer Location: Reasons for Using Nonparametric Statistical Tests

Difficulty Level: Medium

120. When data are normally distributed, using a nonparametric test (rather than its parametric counterpart) is more likely to lead to ______.

a. type II error

b. type I error

c. correctly concluding that an effect exists

d. correctly concluding that an effect does not exist

Cognitive Domain: Comprehension

Answer Location: Reasons for Using Nonparametric Statistical Tests

Difficulty Level: Medium

True/False

1. When the data are normally distributed, using nonparametric tests may be an overly conservative strategy that makes it difficult to detect effects.

Cognitive Domain: Comprehension

Answer Location: Reasons for Using Nonparametric Statistical Tests

Difficulty Level: Medium

2. Cramer’s is a statistic that provides an estimate of effect size.

Cognitive Domain: Comprehension

Answer Location: Calculate a Measure of Effect Size (Cramer’s )

Difficulty Level: Medium

3. The chi-square statistic tests the differences between observed and expected

frequencies.

Cognitive Domain: Comprehension

Answer Location: Calculate the Chi-Square Statistic (²)

Difficulty Level: Medium

4. When data consists of two categorical variables, the chi-square goodness-of-fit test is conducted.

Cognitive Domain: Comprehension

Answer Location: Inferential Statistic: Chi-Square Test of Independence

Difficulty Level: Medium

5. Nonparametric statistical tests involve the estimation of population parameters.

Cognitive Domain: Comprehension

Answer Location: Parametric vs. Nonparametric Statistical Tests

Difficulty Level: Medium

Short Answer

1. Use the following table to calculate the expected frequencies.

Cognitive Domain: Application

Answer Location: Calculate Expected Frequencies (f_e).

Difficulty Level: Hard

2. Use the following table to calculate the expected frequencies.

Cognitive Domain: Application

Answer Location: Calculate Expected Frequencies (f_e).

Difficulty Level: Hard

3. Use the following table to calculate the expected frequencies.

Cognitive Domain: Application

Answer Location: Calculate expected frequencies (f_e).

Difficulty Level: Hard

4. Calculate the chi-square statistic for the following data (assume equal expected frequencies):

Cognitive Domain: Application

Answer Location: Calculate the Chi-Square Statistic (χ²)

Difficulty Level: Hard

5. Calculate the chi-square statistic for the following data (assume equal expected frequencies):

Cognitive Domain: Application

Answer Location: Calculate the Chi-Square Statistic (χ2)

Difficulty Level: Hard

6. Calculate the chi-square statistic for the following data (assume equal expected frequencies):

Cognitive Domain: Application

Answer Location: Calculate the Chi-Square Statistic (χ²)

Difficulty Level: Hard

7. Calculate the chi-square statistic for the following data (assume equal expected frequencies):

Cognitive Domain: Application

Answer Location: Calculate the Chi-Square Statistic (χ²)

Difficulty Level: Hard

8. Calculate the chi-square statistic for the following data (assume equal expected frequencies):

Cognitive Domain: Application

Answer Location: Calculate the Chi-Square Statistic (χ²)

Difficulty Level: Hard

9. Calculate the chi-square statistic for the following data (assume equal expected frequencies):

Cognitive Domain: Application

Answer Location: Calculate the Chi-Square Statistic (χ²)

Difficulty Level: Hard

10. Calculate the chi-square statistic for the following data (assume equal expected frequencies):

Cognitive Domain: Application

Answer Location: Calculate the Chi-Square Statistic (χ²)

Difficulty Level: Hard