Chapter 9: Testing The Difference Between Two Means

Test Bank

Multiple Choice

1. The sampling distribution of the difference helps us determine ______.

a. the probability of obtaining a particular value of the population mean (µ)

b. the modality of a set of data

c. whether a set of data is skewed (asymmetric)

d. the probability of obtaining a particular difference between sample means

Cognitive Domain: Knowledge

Answer Location: The Sampling Distribution of the Difference

Difficulty Level: Easy

2. The ______ of the difference help us determine the probability of obtaining a particular difference between sample means.

a. standard error

b. sampling distribution

c. modality of a set of data

d. probability of obtaining a particular value of the population mean

Cognitive Domain: Knowledge

Answer Location: The Sampling Distribution of the Difference

Difficulty Level: Easy

3. The ______ of the sampling distribution of the difference is equal to ______.

a. variability; 0

b. mean; 0

c. variability; 1

d. mean; 1

Cognitive Domain: Knowledge

Answer Location: Characteristics of the Sampling Distribution of the Difference

Difficulty Level: Easy

4. The mean of the sampling distribution of the difference is equal to ______.

a. the population mean (μ)

b. 0

c. 1

d. the standard error of the difference

Cognitive Domain: Knowledge

Answer Location: Characteristics of the Sampling Distribution of the Difference

Difficulty Level: Easy

5. The ______ of the sampling distribution of the difference is equal to ______.

a. mean; σ

b. standard deviation;

c. mean; 1

d. standard deviation; 0

Cognitive Domain: Knowledge

Answer Location: Characteristics of the Sampling Distribution of the Difference

Difficulty Level: Easy

6. The variability of the sampling distribution of the difference is measured by the ______.

a. standard error of the differences

b. sample means

c. modality of a set of data

d. probability of obtaining a particular value of the population mean

Cognitive Domain: Knowledge

Answer Location: Characteristics of the Sampling Distribution of the Difference

Difficulty Level: Easy

7. ______ represent(s) the variability of differences between two sample means.

a. The probability of obtaining a particular value of the population mean (μ)

b. The modality of a set of data

c. Whether a set of data is skewed (asymmetric)

d. Standard error of the differences

Cognitive Domain: Knowledge

Answer Location: The Sampling Distribution of the Difference

Difficulty Level: Easy

8. The ______ symbol is part of the ______ hypothesis, and implies this hypothesis is ______.

a. ≠; null; directional

b. =; alternative; directional

c. ≠; alternative; two-tailed

d. < or >; null; non-directional

Cognitive Domain: Comprehension

Answer Location: State the Null and Alternative Hypotheses (H₀ and H₁)

Difficulty Level: Medium

9. A ______ symbol is part of the ______ hypothesis, and implies this hypothesis is ______.

a. ≠; null; directional

b. ≠; alternative; directional

c. < or >; null; non-directional

d. <; alternative; one-tailed

Cognitive Domain: Comprehension

Answer Location: State the Null and Alternative Hypotheses (H₀ and H₁)

Difficulty Level: Medium

10. A ______ symbol is part of the ______ hypothesis, and implies this hypothesis is ______.

a. >; alternative; one-tailed

b. ≠; null; directional

c. ≠; alternative; directional

d. < or >; null; non-directional

Cognitive Domain: Comprehension

Answer Location: State the Null and Alternative Hypotheses (H₀ and H₁)

Difficulty Level: Medium

11. A ______ symbol is part of the ______ hypothesis, and implies this hypothesis is ______.

a. >; null; one-tailed

b. ≠; null; directional

c. ≠; alternative; directional

d. < or >; alternative; non-directional

Cognitive Domain: Comprehension

Answer Location: State the Null and Alternative Hypotheses (H₀ and H₁)

Difficulty Level: Medium

12. This distribution illustrates a ______.

a. directional null hypothesis

b. non-directional alternative hypothesis

c. non-directional null hypothesis

d. directional alternative hypothesis

Cognitive Domain: Comprehension

Answer Location: State the Null and Alternative Hypotheses (H₀ and H₁)

Difficulty Level: Medium

13. This distribution illustrates a ______.

a. directional null hypothesis

b. non-directional alternative hypothesis

c. non-directional null hypothesis

d. directional alternative hypothesis

Cognitive Domain: Comprehension

Answer Location: State the Null and Alternative Hypotheses (H₀ and H₁)

Difficulty Level: Medium

14. This distribution illustrates a ______.

a. directional null hypothesis

b. directional alternative hypothesis

c. non-directional alternative hypothesis

d. non-directional null hypothesis

Cognitive Domain: Comprehension

Answer Location: State the Null and Alternative Hypotheses (H₀ and H₁)

Difficulty Level: Medium

15. A researcher hypothesizes that women are more in favor of gun control than are men. In conducting an analysis to test this hypothesis, how should the null hypothesis be stated?

a. H₀: μD = 0

b. H₀: Women > Men

c. H₀: Women = Men

d. H₀: μ₁ = μ₂

Cognitive Domain: Application

Answer Location: State the Null and Alternative Hypotheses (H₀ and H₁)

Difficulty Level: Hard

16. A researcher hypothesizes that Drug A is more effective than Drug B. In conducting an analysis to test this hypothesis, how should the null hypothesis be stated?

a. H₀: μ₁ = μ₂

b. H₀: μ_{Drug A} > μ_{Drug B}

c. H₀: μ_{Drug A} = μ_{Drug B}

d. H₀: μ_{Drug A} ≠ μ_{Drug B}

Cognitive Domain: Application

Answer Location: State the Null and Alternative Hypotheses (H₀ and H₁)

Difficulty Level: Hard

17. In testing the difference between two means, which of these is implied by the null hypothesis (H₀)?

a. μ₁= μ₂ = 0

b. μ₁ – μ₂ = 0

c. μ₁ – μ₂ ≠ 0

d.

Cognitive Domain: Application

Answer Location: State the Null and Alternative Hypotheses (H₀ and H₁)

Difficulty Level: Hard

18. In testing the difference between two means, which of these is implied by the null hypothesis (H₀)?

a. μ₁= μ₂

b. μ₁ > μ₂

c. μ₁ < μ₂

d.

Cognitive Domain: Application

Answer Location: State the Null and Alternative Hypotheses (H₀ and H₁)

Difficulty Level: Hard

19. A researcher hypothesizes that nurses have higher average salaries than teachers. In conducting an analysis to test this hypothesis, how might the alternative hypothesis be stated?

a. H₁: μD = 0

b. H₁: μD ≠ 0

c. H₁: μNurses’s salaries ≠ μTeacher’s salaries

d. H₁: μNurses ≠ μTeachers

Cognitive Domain: Comprehension

Answer Location: State the Null and Alternative Hypotheses (H₀ and H₁)

Difficulty Level: Medium

20. A researcher hypothesizes that there is a difference in level of fear of crime for the elderly and young adults. In conducting an analysis to test this hypothesis, how might the alternative hypothesis be stated?

a. H₁: μD = 0

b. H₁: μD ≠ 0

c. H₁: μElderly ≠ μYoung Adults

d. H₁: μElderly > μYoung Adults

Cognitive Domain: Comprehension

Answer Location: State the Null and Alternative Hypotheses (H₀ and H₁)

Difficulty Level: Medium

21. A researcher hypothesizes that children from middle class families have higher education levels than children from lower class families. In conducting an analysis to test this hypothesis, how might the alternative hypothesis be stated?

a. H1: μD = 0

b. H1: μ Middle Class > μ Lower Class

c. H1: μ Middle Class ≠ μ Lower Class

d. H1: μ Middle Class < μ Lower Class

Cognitive Domain: Comprehension

Answer Location: State the Null and Alternative Hypotheses (H₀ and H₁)

Difficulty Level: Medium

22. In testing the difference between two means, what is implied by the alternative hypothesis (H₁)?

a. μ₁ = μ₂

b. μ₁ – μ₂ = 0

c. μ₁ – μ₂ ≠ 0

d.

Cognitive Domain: Knowledge

Answer Location: State the Null and Alternative Hypotheses (H₀ and H₁)

Difficulty Level: Easy

23. In testing the difference between two means, which of the following is implied by the alternative hypothesis (H₁)?

a. The two population means are equal to each other.

b. The difference between the two population means is equal to 0.

c. The difference between the two population means is not equal to 0.

d. The difference between the two sample means is equal to 0.

Cognitive Domain: Comprehension

Answer Location: State the Null and Alternative Hypotheses (H₀ and H₁)

Difficulty Level: Medium

24. A study tests the difference between 20 Democrats and 20 Republicans. In this example, the degrees of freedom is equal to ______.

a. 18

b. 19

c. 38

d. 39

Cognitive Domain: Application

Answer Location: Calculate the Degrees of Freedom (df)

Difficulty Level: Hard

25. A study tests the difference between 15 ants and 15 ladybugs. In this example, the degrees of freedom is ______.

a. 14

b. 15

c. 28

d. 30

Cognitive Domain: Application

Answer Location: Calculate the Degrees of Freedom (df)

Difficulty Level: Hard

26. A researcher comparing the means of two groups calculates the t-test for independent means and reports the following result: t(28) = 2.11, p <.05. This research study consisted of a TOTAL of ______ participants.

a. 14

b. 15

c. 28

d. 30

Cognitive Domain: Application

Answer Location: Calculate the Degrees of Freedom (df)

Difficulty Level: Hard

27. A researcher comparing the means of two groups calculates the t-test for independent means and reports the following result: t(32) = –3.54, p <.01. This research study consisted of a TOTAL of ______ participants.

a. 16

b. 30

c. 32

d. 34

Cognitive Domain: Application

Answer Location: Calculate the Degrees of Freedom (df)

Difficulty Level: Hard

28. A researcher comparing the means of two groups calculates the t-test for independent means and reports the following result: t(22) = -3.54, p <.01. This research study consisted of a TOTAL of ______ participants.

a. 20

b. 22

c. 24

d. 26

Cognitive Domain: Application

Answer Location: Calculate the Degrees of Freedom (df)

Difficulty Level: Hard

29. A researcher calculates the t-test for independent means and reports the following result: t(24) = 2.16, p < .05. This research study consisted of a TOTAL of ______ participants.

a. 26

b. 25

c. 24

d. 23

Cognitive Domain: Application

Answer Location: Calculate the Degrees of Freedom (df)

Difficulty Level: Hard

30. A researcher calculates the t-test for independent means and reports the following result: t(48) = 2.97, p < .01. This research study consisted of a TOTAL of ______ participants.

a. 25

b. 48

c. 49

d. 50

Cognitive Domain: Application

Answer Location: Calculate the Degrees of Freedom (df)

Difficulty Level: Hard

31. A researcher states the following hypotheses: H₀: μDogs = μCats and H₁: μDogs ≠ μ Cats. Assuming she collects data from 9 dogs and 9 cats, what is the appropriate critical value?

a. 1.734

b. 2.120

c. 2.110

d. 2.101

Cognitive Domain: Application

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

Difficulty Level: Hard

32. A researcher states the following hypotheses: H₀: μ Freshmen = μ Sophomores and H₁: μ Freshmen ≠ μ Sophomores. Assuming she collects data from 13 freshmen and 13 sophomores, what is the appropriate critical value?

a. 1.706

b. 1.711

c. 2.056

d. 2.064

Cognitive Domain: Application

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

Difficulty Level: Hard

33. A researcher states the following hypotheses: H₀: μCity1 = μCity2 and H₁: μCity1 > μCity2. Assuming she collects data from 30 people who live in city 1 and 30 people who live in city 2, what is the appropriate critical value?

a. 1.672

b. 1.700

c. 1.960

d. 2.002

Cognitive Domain: Application

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

Difficulty Level: Hard

34. A researcher states the following hypotheses: H₀: μMales = μ Females and H₁: μMales ≠ μFemales. Assuming she collects data from 15 males and 15 females, what is the appropriate critical value?

a. 1.697

b. 1.701

c. 2.042

d. 2.048

Cognitive Domain: Application

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

Difficulty Level: Hard

35. A study compares the means of two groups, each having N = 10. If the standard deviations in the two groups are 4.00 and 6.00, what is the value for the standard error of the difference ?

a. 2.28

b. 1.00

c. 10.00

d. 5.20

Cognitive Domain: Analysis

Answer Location: Calculate a Statistic: t-Test for Independent Means

Difficulty Level: Hard

36. A study compares the means of two groups, each having N = 10. If the standard deviations in the two groups are 3.00 and 5.00, what is the value for the standard error of the difference ?

a. .89

b. 1.84

c. 3.40

d. 8.00

Cognitive Domain: Analysis

Answer Location: Calculate a Statistic: t-Test for Independent Means

Difficulty Level: Medium

37. A study compares the means of two groups, each having N = 11. If the standard deviations of the two groups are 5.00 and 3.00, what is the value for the standard error of the difference ?

a. .60

b. .85

c. 1.76

d. 3.09

Cognitive Domain: Analysis

Answer Location: Calculate a Statistic: t-Test for Independent Means

Difficulty Level: Medium

38. A study compares the means of two groups, each having N = 20. If the standard deviations of the two groups are 10.00 and 6.00, what is the value for the standard error of the difference ?

a. .89

b. 2.61

c. 5.43

d. 6.80

Cognitive Domain: Analysis

Answer Location: Calculate a Statistic: t-Test for Independent Means

Difficulty Level: Medium

39. A study compares the means of two groups, each having N = 15. If the standard deviations of the two groups are 1.67 and 2.98, what is the value for the standard error of the difference ?

a. .19

b. .778

c. .880

d. .882

Cognitive Domain: Analysis

Answer Location: Calculate a Statistic: t-Test for Independent Means

Difficulty Level: Medium

40. In testing the difference between two sample means , the greater the difference between the two means, the more the value of the t-statistic (t) differs from ______.

a. 0

b. μ

c. the alternative hypothesis

d. the region of rejection

Cognitive Domain: Comprehension

Answer Location: Characteristics of the Sampling Distribution of the Difference

Difficulty Level: Medium

41. In testing the difference between two sample means , a negative (–) value of the t-statistic (t) indicates ______.

a. the sample mean is greater than the hypothesized population mean

b. the score is less than the mean

c. the second group’s mean is larger than the first group’s mean

d. you’ve made an error in your calculations

Cognitive Domain: Comprehension

Answer Location: Calculate a Statistic: t-Test for Independent Means

Difficulty Level: Medium

42. A value of –2.01 for the t-statistic necessarily implies that ______.

a. the mean for the first group is less than the mean of the second group

b. the mean for the first group is greater than the mean of the second group

c. the difference between the two means is statistically significant

d. the distribution of scores for the dependent variable is negatively skewed

Cognitive Domain: Comprehension

Answer Location: Calculate a Statistic: t-Test for Independent Means

Difficulty Level: Medium

43. You ______ when your statistic falls in the region of ______ because this means ______.

a. reject the null hypothesis; rejection; p < .05

b. do not reject the null hypothesis; non-rejection; p < .01

c. reject the alternative hypothesis; non-rejection; p < .05

d. reject the null hypothesis; rejection; p > .01

Cognitive Domain: Application

Answer Location: Determine the Level of Significance

Difficulty Level: Hard

44. You ______ the null hypothesis when the value of the statistic falls in the region of ______ because this means ______.

a. do not reject; rejection; p > .05

b. reject; rejection; p < .05

c. do not reject; non-rejection; p < .05

d. reject; non-rejection; p > .05

Cognitive Domain: Application

Answer Location: Determine the Level of Significance

Difficulty Level: Hard

45. You ______ the null hypothesis when your statistic falls in the region of ______ because this means ______.

a. do not reject; rejection; p < .05

b. accept; rejection; p > .05

c. do not reject; non-rejection; p > .05

d. reject; non-rejection; p < .05

Cognitive Domain: Application

Answer Location: Determine the Level of Significance

Difficulty Level: Hard

46. When you ______, this implies the probability of the statistic is ______.

a. reject the null hypothesis; > .05

b. do not reject the null hypothesis; non-directional

c. reject the null hypothesis; low

d. do not reject the null hypothesis; < .05

Cognitive Domain: Application

Answer Location: Determine the Level of Significance

Difficulty Level: Hard

47. When you ______, this implies the probability of the statistic is ______.

a. do not reject the null hypothesis; in the region of rejection

b. do not reject the null hypothesis; < 5%

c. do not reject the null hypothesis; high

d. reject the null hypothesis; in the region of acceptance

Cognitive Domain: Application

Answer Location: Determine the Level of Significance

Difficulty Level: Hard

48. If your value of a statistic like the t-test falls in the ______ area of this distribution, you will ______ the null hypothesis because the probability of the statistic is ______.

a. shaded; reject; high

b. shaded; not reject; high

c. unshaded; reject; low

d. unshaded; not reject; high

Cognitive Domain: Application

Answer Location: Determine the Level of Significance

Difficulty Level: Hard

49. If your value of a statistic like the t-test falls in the ______ area of this distribution, you will ______ the null hypothesis ______ because the probability of the statistic is ______.

a. shaded; reject; low

b. shaded; not reject; high

c. unshaded; reject; low

d. unshaded; not reject; low

Cognitive Domain: Application

Answer Location: Determine the Level of Significance

Difficulty Level: Hard

50. In conducting the t-test for independent means, if you ______, the two means ______.

a. reject the null hypothesis; are significantly different from each other

b. accept the null hypothesis; are significantly different from each other

c. do not reject the null hypothesis; are significantly equal to each other

d. reject the null hypothesis; are significantly equal to each other

Cognitive Domain: Application

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

Difficulty Level: Hard

51. In conducting the t-test for independent means, if you ______, the two means ______ significantly different from each other.

a. do not reject the null hypothesis; are not

b. do not reject the null hypothesis; are

c. reject the null hypothesis; are not

d. reject the alternative hypothesis; are

Cognitive Domain: Application

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

Difficulty Level: Hard

52. In conducting the t-test for independent means, if you ______, the two means ______.

a. do not reject the null hypothesis; do not significantly differ from each other

b. do not accept the null hypothesis; are significantly equal to each other

c. reject the null hypothesis; do not significantly differ from each other

d. reject the alternative hypothesis; are significantly different from each other

Cognitive Domain: Application

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

Difficulty Level: Hard

53. You determine whether the probability of a statistic is less than .01 (p < .01) ______.

a. when you do not reject the null hypothesis

b. when you reject the null hypothesis

c. whenever you analyze a set of data

d. when you accept the null hypothesis

Cognitive Domain: Comprehension

Answer Location: Determine the Level of Significance

Difficulty Level: Medium

54. When do you determine whether the probability of a statistic such as the t-test is less than .01?

a. when you have rejected the null hypothesis

b. when you have not rejected the null hypothesis

c. when you have already concluded that p > .01

d. when you have already concluded that p > .05

Cognitive Domain: Comprehension

Answer Location: Determine the Level of Significance

Difficulty Level: Medium

55. Your value of a statistic such as the t-test is greater than the critical value for α = .05 but less than the critical value for α = .01; consequently, you ______ the null hypothesis and state the level of significance as ______.

a. reject; p > .05

b. do not reject; p > .01

c. reject; p < .01

d. reject; p < .05

Cognitive Domain: Application

Answer Location: Determine the Level of Significance

Difficulty Level: Hard

56. Imagine the value of a statistic is greater than the critical value for α = .05 but less than the critical value for α = .01. In this situation you would ______ and state the level of significance as ______.

a. reject the null hypothesis; p > .05

b. not reject the null hypothesis; p > .05

c. reject the null hypothesis; p > .01

d. reject the null hypothesis; p < .05

Cognitive Domain: Application

Answer Location: Determine the Level of Significance

Difficulty Level: Hard

57. Imagine the value of a statistic is greater than the critical value for α = .05 but less than the critical value for α = .01. Which is the MOST appropriate way to report the level of significance?

a. p < .01

b. p > .01

c. p < .05

d. p > .05

Cognitive Domain: Knowledge

Answer Location: Determine the Level of Significance

Difficulty Level: Easy

58. Imagine the value of a t-test is greater than the α = .05 critical value but less than the α = .01 critical value. Which of the following statements is true?

a. p > .05

b. p < .01

c. You have rejected the null hypothesis.

d. The means of the two groups are significantly equal to each other.

Cognitive Domain: Comprehension

Answer Location: Determine the Level of Significance

Difficulty Level: Medium

59. In reporting a statistical analysis, a researcher writes “p < .01”. By definition this implies that ______.

a. the null hypothesis was not rejected

b. p < .05

c. the statistic was in the region of non-rejection

d. the research hypothesis was proven to be true

Cognitive Domain: Comprehension

Answer Location: Determine the Level of Significance

Difficulty Level: Medium

60. In reporting a statistical analysis, a researcher writes “p > .05”. By definition this implies that ______.

a. the null hypothesis was proven to be true

b. p < .01

c. the statistic was in the region of non-rejection

d. the differences between the means of the groups was insignificant

Cognitive Domain: Comprehension

Answer Location: Determine the Level of Significance

Difficulty Level: Medium

61. In reporting a statistical analysis, a researcher writes “p > .05”. By definition this implies that ______.

a. the null hypothesis was rejected

b. p < .01

c. the statistic was in the region of rejection

d. the means of the groups are not different from each other

Cognitive Domain: Comprehension

Answer Location: Determine the Level of Significance

Difficulty Level: Medium

62. A study compares 5 Democrats and 5 Republicans and obtains a value of 2.27 for the t-statistic. For α = .05 (two-tailed), which of the following is the correct way to present this analysis?

a. t(10) = 2.27, p > .05

b. t(8) = 2.27, p < .05

c. t(9) = 2.27, p < .05

d. t(8) = 2.27, p > .05

Cognitive Domain: Application

Answer Location: Draw a Conclusion From the Analysis

Difficulty Level: Hard

63. A study compares 6 full-time students and 6 part-time students and obtains a value of 2.31 for the t-statistic. For α = .05 (two-tailed), which of the following is the correct way to present this analysis?

a. t(5) = 2.31, p > .05

b. t(6) = 2.31, p < .05

c. t(10) = 2.31, p < .05

d. t(12) = 2.31, p < .01

Cognitive Domain: Application

Answer Location: Draw a Conclusion From the Analysis

Difficulty Level: Hard

64. In writing the results of the t-test in standard APA format, the letters “n.s.” imply ______.

a. p < .05

b. p < .01

c. p > .05

d. the null hypothesis was rejected

Cognitive Domain: Comprehension

Answer Location: Draw a Conclusion From the Analysis

Difficulty Level: Medium

65. In reporting the results of a statistical analysis in standard APA format, the letters “n.s.” mean ______.

a. “nonsignificant”

b. “not sure”

c. “non-statistical”

d. “not standard”

Cognitive Domain: Knowledge

Answer Location: Draw a Conclusion From the Analysis

Difficulty Level: Easy

66. According to the textbook, what is the difference between the terms “nonsignificant” and “insignificant”?

a. “Insignificant” is not a statistical concept.

b. You use the term “insignificant” when you make the decision to reject the null hypothesis.

c. “Insignificant” implies p < .05; “nonsignificant” implies p < .01.

d. There is no difference between the two concepts—they mean the same thing.

Cognitive Domain: Knowledge

Answer Location: Draw a Conclusion From the Analysis

Difficulty Level: Easy

67. According to the textbook, what is the difference between the terms “nonsignificant” and “insignificant”?

a. “Nonsignificant” is less precise than “insignificant.”

b. “Nonsignificant” is a statistical concept; “insignificant” is a value judgment.

c. “Nonsignificant” refers to α = .05; “insignificant” refers to α = .01.

d. “Insignificant” is a statistical concept; “nonsignificant” is a value judgment.

Cognitive Domain: Comprehension

Answer Location: Draw a Conclusion From the Analysis

Difficulty Level: Medium

68. Which of the following would be the most informative way to report the results of a t-test?

a. The mean number of crimes for juveniles in the poverty group (M = 2.45) is significantly higher than the mean number of crimes for juveniles in the non-poverty group (M = .95), t(40) = 3.41, p < .01.

b. The mean number of crimes for juveniles in the poverty group (M = 2.45) is significantly higher than the mean number of crimes for juveniles in the non-poverty group (M = .95).

c. The mean number of crimes for juveniles in the poverty group (M = 2.45) is significantly different than the mean number of crimes for juveniles in the non-poverty group (M = .95), t(40) = 3.41, p < .01.

d. The mean number of crimes for juveniles in the poverty group is significantly higher than the mean number of crimes for juveniles in the non-poverty group, t(40) = 3.41, p < .01.

Cognitive Domain: Application

Answer Location: Draw a Conclusion From the Analysis

Difficulty Level: Hard

69. When the null hypothesis is ______, this typically means the research hypothesis is ______.

a. not rejected; supported

b. rejected; supported

c. rejected; not supported

d. rejected; proven

Cognitive Domain: Comprehension

Answer Location: Relate the Result of the Analysis to the Research hypothesis

Difficulty Level: Medium

70. When the null hypothesis is ______, this typically means the research hypothesis is ______.

a. not rejected; not supported

b. rejected; supported

c. rejected; not supported

d. rejected; proven

Cognitive Domain: Comprehension

Answer Location: Relate the Result of the Analysis to the Research Hypothesis

Difficulty Level: Medium

71. The assumption of normality is primarily concerned with ______.

a. the difference between two sample means

b. the shape of the distribution of the dependent variable

c. how samples are drawn from populations

d. the difference between a sample mean and a population mean

Cognitive Domain: Knowledge

Answer Location: Assumptions of the t-Test for Independent Means

Difficulty Level: Easy

72. In testing the difference between two sample means, you would examine the ______ of the two groups to test the assumption of homogeneity of variance.

a. standard deviations

b. t-tests

c. means

d. sample sizes

Cognitive Domain: Knowledge

Answer Location: Assumptions of the t-Test for Independent Means

Difficulty Level: Easy

73. If a researcher has developed a research design in which each participant appears in all levels or categories, this would be considered which type of research design?

a. within-subjects design

b. t-test for independent means

c. between-subjects design

d. t-test for one mean

Cognitive Domain: Knowledge

Answer Location: Inferential Statistics: Testing the Difference Between Paired Means

Difficulty Level: Easy

74. A ______ is a research design in which each participant appears in all levels or categories of the independent variable.

a. t-test for independent means

b. t-test for one mean

c. between subjects research design

d. within-subjects research design

Cognitive Domain: Knowledge

Answer Location: Inferential Statistics: Testing the Difference Between Paired Means

Difficulty Level: Easy

75. The within-subjects research design tests differences ______.

a. between different groups of participants

b. within the same participant

c. between different groups of participants and within the same participants

d. between a sample mean and a hypothesized population mean

Cognitive Domain: Comprehension

Answer Location: Inferential Statistics: Testing the Difference Between Paired Means

Difficulty Level: Medium

76. Which type of statistic would be appropriate for analyzing a within-subjects research design?

a. z-test for one mean

b. t-test for independent means

c. t-test for dependent means

d. t-test for one mean

Cognitive Domain: Comprehension

Answer Location: Research Situations Appropriate for Within-Subjects Research Designs

Difficulty Level: Medium

77. For a study analyzing the difference between test scores before and after a treatment was applied, which statistic would be most appropriate for this study?

a. z-test for one mean

b. t-test for one mean

c. t-test for independent means

d. t-test for dependent means

Cognitive Domain: Comprehension

Answer Location: Research Situations Appropriate for Within-Subjects Research Designs

Difficulty Level: Medium

78. A researcher asks 10 people to take sips out of two cups of soda (one with Coke and the other Pepsi) and rate the flavor of both sodas. In analyzing this data, how should the null hypothesis be stated?

a. H₀: µ_D = 0

b. H₀: Coke > Pepsi

c. H₀: Coke = Pepsi

d. H₀: µ₁ = µ₂

Cognitive Domain: Application

Answer Location: State the Null and Alternative Hypotheses (H₀ and H₁)

Difficulty Level: Hard

79. A researcher asks 20 people to take a sip of two different colas (first Coke and then Pepsi) and rate the flavor of both. In analyzing this data, how should the null hypothesis be stated?

a. H₀: µ_D ≠ 0

b. H₀: µ_D = 20

c. H₀: Coke = Pepsi

d. H₀: µ_D = 0

Cognitive Domain: Application

Answer Location: State the Null and Alternative Hypotheses (H₀ and H₁)

Difficulty Level: Hard

80. A researcher asks 10 people to take a bite of two different cheese pizzas (Dominos and Round Table) and rate the flavor of both pizzas. In analyzing this data, how should the null hypothesis be stated?

a. µ_D = 0

b. µ_D ≠ 0

c. Dominos = Round Table

d. µ₁ = µ₂

Cognitive Domain: Application

Answer Location: State the Null and Alternative Hypotheses (H₀ and H₁)

Difficulty Level: Hard

81. A professor hands out a quiz 1 to the 30 students in her course, after that the students are given a study session before quiz 2. In analyzing this data, how should the null hypothesis be stated?

a. µ1 = µ2

b. µ_D ≠ 0

c. Quiz1 = Quiz2

d. µ_D = 0

Cognitive Domain: Application

Answer Location: State the Null and Alternative Hypotheses (H₀ and H₁)

Difficulty Level: Hard

82. In an introduction to statistics course, the students are given a basic exam to complete in class. Over the next few weeks, the students are given review sessions and then asked to complete the exam. The professor in the course expects the students’ grades on the exam to increase. In analyzing the data, how should the alternative hypothesis be stated?

a. µ₁ = µ₂

b. µ_D ≠ 0

c. µ₁ > µ₂

d. µ₁ < µ₂

Cognitive Domain: Application

Answer Location: State the Null and Alternative Hypotheses (H₀ and H₁)

Difficulty Level: Hard

83. For a group of 18 participants, how many degrees of freedom are there for a t-test for dependent means?

a. 36

b. 35

c. 18

d. 17

Cognitive Domain: Application

Answer Location: Make a Decision About the Null Hypothesis

Difficulty Level: Hard

84. For a group of 20 participants, how many degrees of freedom are there for a t-test for dependent means?

a. 19

b. 20

c. 39

d. 40

Cognitive Domain: Application

Answer Location: Make a Decision About the Null Hypothesis

Difficulty Level: Hard

85. For a group of 30 participants, how many degrees of freedom are there for a t-test for dependent means?

a. 28

b. 29

c. 30

d. 60

Cognitive Domain: Application

Answer Location: Make a Decision About the Null Hypothesis

Difficulty Level: Hard

86. A researcher collects data from a group of 21 people at Time 1 and Time 2. Assuming α = .05 (two-tailed), the critical value is ______.

a. 2.096

b. 2.086

c. 2.845

d. 2.528

Cognitive Domain: Application

Answer Location: Make a Decision About the Null Hypothesis

Difficulty Level: Hard

87. A researcher collects data from a group of 25 people at Time 1 and Time 2. Assuming α = .05 (two-tailed), the critical value is ______.

a. 2.064

b. 2.069

c. 2.492

d. 2.797

Cognitive Domain: Application

Answer Location: Make a Decision About the Null Hypothesis

Difficulty Level: Hard

88. A researcher states the following hypotheses: H₀: μTime 1 = μTime 2 and H₁: μTime 1 ≠ μTime 2. Assuming she collects data from 10 people, what is the appropriate critical value (α = .05; two-tailed)?

a. 1.833

b. 2.228

c. 2.262

d. 3.250

Cognitive Domain: Application

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

Difficulty Level: Hard

89. A researcher states the following hypotheses: H₀: μTime 1 = μTime 2 and H₁: μTime 1 ≠ μTime 2. Assuming she collects data from 30 people, what is the appropriate critical value (α= .05; two-tailed)?

a. 2.048

b. 2.045

c. 2.009

d. 2.000

Cognitive Domain: Application

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

Difficulty Level: Hard

90. A researcher states the following hypotheses: H₀: μTime 1 = μTime 2 and H₁: μTime 1 < μTime 2. Assuming she collects data from 15 people, what is the appropriate critical value (α = .05; one-tailed)?

a. 1.697

b. 1.761

c. 2.045

d. 2.145

Cognitive Domain: Application

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

Difficulty Level: Hard

91. In conducting the t-test for dependent means, the difference score (D) is calculated by subtracting ______.

a. the higher score from the lower score

b. the lower score from the higher score

c. the second score from the first score

d. the first score from the second score

Cognitive Domain: Knowledge

Answer Location: Make a Decision About the Null Hypothesis

Difficulty Level: Easy

92. What is the value of X_D for the following set of five difference (D) scores: 3, –8, 6, –4, –2?

a. –1.00

b. 4.60

c. –5.00

d. 23

Cognitive Domain: Analysis

Answer Location: Make a Decision About the Null Hypothesis

Difficulty Level: Medium

93. What is the value of X_D for the following set of five difference (D) scores: –6, 1, –7, –3, –13?

a. -2.80

b. -4.60

c. -5.00

d. -5.60

Cognitive Domain: Analysis

Answer Location: Make a Decision About the Null Hypothesis

Difficulty Level: Medium

94. In the t-test for dependent means, the symbol s_D stands for the ______.

a. standard error of the mean

b. standard error of the difference

c. standard deviation of the mean

d. standard deviation of difference scores

Cognitive Domain: Analysis

Answer Location: Make a Decision About the Null Hypothesis

Difficulty Level: Medium

95. For a sample of 12 participants, the t = 1.965 (α = .05; two-tailed), what would be the decision about the Null hypothesis

a. The null hypothesis could neither be rejected nor accepted.

b. The null hypothesis would not be rejected.

c. The null hypothesis would be rejected.

d. The null hypothesis would need to be retested.

Cognitive Domain: Comprehension

Answer Location: Make a Decision About the Null Hypothesis

Difficulty Level: Medium

96. For a sample of 20 participants, t = 2.500 (α= .05; two-tailed), what would be the decision about the null hypothesis?

a. The null hypothesis could be neither rejected nor accepted.

b. The null hypothesis would not be rejected.

c. The null hypothesis would be rejected.

d. The null hypothesis would need to be retested.

Cognitive Domain: Comprehension

Answer Location: Make a Decision About the Null Hypothesis

Difficulty Level: Medium

97. In conducting the t-test for dependent means, if you ______ , the means ______ significantly different from each other.

a. accept the null hypothesis; are

b. reject the null hypothesis; are

c. do not reject the null hypothesis; are not

d. accept the alternative hypothesis; are not

Cognitive Domain: Comprehension

Answer Location: Make a Decision About the Null Hypothesis

Difficulty Level: Medium

98. In conducting the t-test for dependent means, if you ______, the participants two different scores ______.

a. reject the null hypothesis; are significantly different from each other

b. accept the null hypothesis; are significantly different from each other

c. do not reject the null hypothesis; are significantly equal to each other

d. reject the null hypothesis; are significantly equal to each other

Cognitive Domain: Comprehension

Answer Location: Make a Decision About the Null Hypothesis

Difficulty Level: Medium

99. For a t-statistic = 2.56 with 20 degrees of freedom, what would be the appropriate statement about the significance level?

a. p < .01

b. p > .05

c. p < .05

d. p > .01

Cognitive Domain: Application

Answer Location: Make a Decision About the Null Hypothesis

Difficulty Level: Hard

100. For a t-statistic = 2.99 with 20 degrees of freedom, what would be the appropriate statement about the significance level?

a. p < .01

b. p > .05

c. p < .05

d. p > .01

Cognitive Domain: Application

Answer Location: Make a Decision About the Null Hypothesis

Difficulty Level: Hard

101. For a t-statistic = 3.20 with 10 degrees of freedom, what would be the appropriate statement about the significance level?

a. p > .01

b. p < .01

c. p < .05

d. p > .05

Cognitive Domain: Application

Answer Location: Make a Decision About the Null Hypothesis

Difficulty Level: Hard

102. A researcher conducts a study measuring 10 people before and after they watch a movie and obtains a value of 2.85 for the t-statistic. For a non-directional alternative hypothesis, which of the following is the correct way to present this analysis?

a. t(10) = 2.85, p < .05

b. t(9) = 2.85, p < .05

c. t(18) = 2.85, p < .05

d. t(20) = 2.85, p < .01

Cognitive Domain: Application

Answer Location: Make a Decision About the Null Hypothesis

Difficulty Level: Hard

103. A researcher conducts a study measuring 20 children before and after they play violent video games and obtains a value of 1.98 for the t-statistic. For a non-directional alternative hypothesis, which of the following is the correct way to present this analysis?

a. t(20) = 1.98, p > .05

b. t(19) = 1.98, p > .05

c. t(18) = 1.98, p > .05

d. t(38) = 1.98, p > .01

Cognitive Domain: Application

Answer Location: Make a Decision About the Null Hypothesis

Difficulty Level: Hard

104. Which of the following null hypotheses would result in calculating the t-test for a single mean?

a. H₀: μ > 100

b. H₀: Democrat > Republican

c. H₀: Women = Men

d. H₀: μ = 50

Cognitive Domain: Application

Answer Location: Testing the Difference Between Two Means

Difficulty Level: Hard

105. A college professor was interested in comparing the average starting salaries of Engineering and English majors. Which type of statistical analysis should she use to analyze this data?

a. t-test for dependent means

b. t-test for one mean

c. t-test for independent means

d. z-test for one mean

Cognitive Domain: Application

Answer Location: State the Null and Alternative Hypotheses (H₀ and H₁)

Difficulty Level: Hard

106. A marriage counselor wishing to compare the values of married couples collects data from 10 husbands and their wives. Which type of statistical analysis should she use to analyze this data?

a. t-test for dependent means

b. t-test for one mean

c. t-test for independent means

d. z-test for one mean

Cognitive Domain: Application

Answer Location: Research Situations Appropriate for Within-Subjects Research Designs

Difficulty Level: Hard

107. In which of the following situations would you MOST likely use the t-test for dependent means?

a. comparing smokers versus non smokers

b. comparing stress levels before and after a yoga class

c. comparing first graders versus college students

d. comparing a sample mean versus a hypothesized population mean

Cognitive Domain: Application

Answer Location: Research Situations Appropriate for Within-Subjects Research Designs

Difficulty Level: Hard

108. In which of the following situations would you MOST likely use the t-test for independent means?

a. comparing brothers and their sisters

b. testing the effectiveness of a medicine designed to lower blood pressure

c. comparing BMW and Saturn car owners

d. comparing a sample mean versus a hypothesized population mean

Cognitive Domain: Application

Answer Location: Research Situations Appropriate for Within-Subjects Research Designs

Difficulty Level: Hard

109. Holding all else constant, the larger the sample size, the ______ the standard error of the difference and the ______ the value of the t-statistic (t).

a. larger; larger

b. larger; smaller

c. smaller; smaller

d. smaller; larger

Cognitive Domain: Comprehension

Answer Location: Calculate a Statistic: t-Test for Independent Means

Difficulty Level: Medium

110. Bill and Bob conduct two separate studies. By an amazing coincidence, they obtain exactly the same sample means and standard deviations. However, Bill’s sample is twice as large as Bob’s. Which of these is true?

a. Bill’s critical values will be larger than Bob’s.

b. Bill’s degrees of freedom are smaller than Bob’s.

c. Bill is more likely to reject the null hypothesis than Bob.

d. Bill’s value of α will be smaller than Bob’s.

Cognitive Domain: Application

Answer Location: Calculate a Statistic: t-Test for Independent Means

Difficulty Level: Hard

111. Mary and Joe conduct two separate studies. By an amazing coincidence, they obtain exactly the same sample means and standard deviations. However, Mary’s sample is twice as large as Joe’s. Which of these is true?

a. Mary’s alternative hypothesis will be larger than Joe’s.

b. The two studies have the same likelihood of supporting their research hypotheses.

c. Joe is more likely to reject the null hypothesis than Mary.

d. Mary’s critical values will be smaller than Joe’s.

Cognitive Domain: Application

Answer Location: Calculate a Statistic: t-Test for Independent Means

Difficulty Level: Hard

112. Holding all else constant, as sample sizes increase, the degrees of freedom ______ and the critical value(s) ______.

a. decrease; decrease

b. decrease; increase

c. increase; increase

d. increase; decrease

Cognitive Domain: Application

Answer Location: Calculate a Statistic: t-Test for Independent Means

Difficulty Level: Hard

113. What did the researcher do to cause the change in the shaded regions from Distribution A to Distribution B?

Distribution A

Distribution B

a. She increased the size of her sample.

b. She changed alpha from .05 to .10.

c. She changed from a directional to a non-directional alternative hypothesis.

d. She calculated a t-test rather than an F-ratio.

Cognitive Domain: Application

Answer Location: Calculate a Statistic: t-Test for independent means

Difficulty Level: Hard

114. The larger the ______, the ______ likely you are to reject the null hypothesis.

a. sample size; less

b. value for alpha; more

c. value of the statistic; less

d. value for alpha; less

Cognitive Domain: Comprehension

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

Difficulty Level: Medium

115. The smaller the ______, the ______ likely you are to reject the null hypothesis.

a. sample size; less

b. value for alpha; more

c. value of the statistic; less

d. value for alpha; less

Cognitive Domain: Comprehension

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

Difficulty Level: Medium

116. In making the decision to reject H₀, what happens if you set α at .10 rather than .05?

a. The region of rejection gets bigger.

b. The critical value(s) gets larger.

c. You are less likely to reject the null hypothesis.

d. The sample size gets smaller.

Cognitive Domain: Comprehension

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

Difficulty Level: Medium

117. What happens when you change α from .05 to .10?

a. The region of rejection gets smaller.

b. The critical value(s) get smaller.

c. You are less likely to reject the null hypothesis.

d. The region of non-rejection gets bigger.

Cognitive Domain: Comprehension

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

Difficulty Level: Medium

118. In making the decision to reject the null hypothesis, what would happen if you were to change α from .05 to .01?

a. You would be less likely to reject the null hypothesis.

b. Your sample would get smaller.

c. The region of rejection would get larger.

d. You would be more likely to reject the null hypothesis.

Cognitive Domain: Comprehension

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

Difficulty Level: Medium

119. What did the researcher do to cause the change in the shaded regions in the two distributions?

“Before”

“After”

a. She changed alpha from .05 to .01.

b. She changed alpha from .05 to .10.

c. She changed from a directional to a non-directional alternative hypothesis.

d. She changed from a non-directional to a directional alternative hypothesis.

Cognitive Domain: Comprehension

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

Difficulty Level: Medium

120. What did the researcher do to cause the change in the shaded regions in the two distributions?

“Before”

“After”

a. She changed alpha from .05 to .01.

b. She changed alpha from .05 to .10.

c. She changed from a directional to a non-directional alternative hypothesis.

d. She changed from a non-directional to a directional alternative hypothesis.

Cognitive Domain: Comprehension

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

Difficulty Level: Medium

121. In which of the following situations would you be most likely to set alpha at .10 rather than the traditional .05?

a. Your target population is very small.

b. You collect data from a large (rather than small) sample.

c. You don’t want to reject the null hypothesis.

d. You want to use a directional alternative hypothesis.

Cognitive Domain: Comprehension

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

Difficulty Level: Medium

122. In which of the following situations would you be most likely to use a one-tailed rather than two-tailed alternative hypothesis?

a. The hypothesized effect can only be in one direction.

b. You want to set α at .10 rather than .05.

c. Your sample is very small.

d. You don’t expect or want to reject the null hypothesis.

Cognitive Domain: Comprehension

Answer Location: Relate the Result of the Analysis to the Research Hypothesis

Difficulty Level: Medium

123. You are ______ likely to reject the null hypothesis when the alternative hypothesis is ______.

a. less; directional

b. equally; non-directional

c. more; non-directional

d. more; directional

Cognitive Domain: Comprehension

Answer Location: Relate the Result of the Analysis to the Research Hypothesis

Difficulty Level: Medium

124. You are ______ likely to reject the null hypothesis when the alternative hypothesis is ______.

a. less; non-directional

b. equally; non-directional

c. more; non-directional

d. less; directional

Cognitive Domain: Comprehension

Answer Location: Relate the Result of the Analysis to the Research Hypothesis

Difficulty Level: Medium

125. What did the researcher do to cause the change in the shaded regions in the two distributions?

a. She changed alpha from .05 to .01.

b. She changed alpha from .05 to .10.

c. She increased the size of her sample.

d. She changed from a non-directional to a directional alternative hypothesis.

Cognitive Domain: Application

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

Difficulty Level: Hard

126. Holding all else constant, the larger the standard deviations, the ______ the standard error of the difference and the ______ the value of the t-statistic (t).

a. smaller; larger

b. larger; smaller

c. larger; larger

d. smaller; smaller

Cognitive Domain: Application

Answer Location: Calculate a Statistic: t-Test for Independent Means

Difficulty Level: Hard

127. Holding all else constant, the smaller the standard deviations, the ______ the standard error of the difference and the ______ the value of the t-statistic (t).

a. larger; larger

b. larger; smaller

c. smaller; larger

d. smaller; smaller

Cognitive Domain: Application

Answer Location: Calculate a Statistic: t-Test for Independent Means

Difficulty Level: Hard

True/False

1. When reporting the results of a t-statistic, the researcher should include the means of both groups.

Cognitive Domain: Knowledge

Answer Location: Draw a Conclusion From the Analysis

Difficulty Level: Easy

2. When reporting the results of a t-statistic, the researcher should include information about the inferential statistics such as the calculated t, degrees of freedom, value of the statistic and the significance level.

Cognitive Domain: Knowledge

Answer Location: Draw a Conclusion From the Analysis

Difficulty Level: Easy

3. The mean of the sampling distribution of the difference is equal to one.

Cognitive Domain: Knowledge

Answer Location: Characteristics of the Sampling Distribution of the Difference

Difficulty Level: Easy

4. The t statistic can only be a positive number.

Cognitive Domain: Comprehension

Answer Location: Calculate a Statistic: The t-Test for Independent Means

Difficulty Level: Medium

5. One assumption related to the t-test for independent means is that of normality.

Cognitive Domain: Comprehension

Answer Location: Assumptions of the t-Test for Independent Means

Difficulty Level: Medium