Chapter 7: Testing One Sample Mean

Test Bank

Multiple Choice

1. A ______ is used to evaluate ______.

a. z-score; the mean of a sample

b. t-test; the difference between two means

c. z-score; the difference between a sample mean and a population mean

d. t-test; a score on a variable

Cognitive Domain: Knowledge

Answer Location: Characteristics of the Student t Distribution

Difficulty Level: Easy

2. Although their formulas are similar, one difference between the z-score (z) and the t-statistic (t) is that ______.

a. only the denominator of the z-score formula (not the t-statistic) is a measure of variability

b. z-scores evaluate sample means whereas t-statistics evaluate individual scores

c. only the numerator of the z-score formula (not the t-statistic) is the difference between means

d. the z-score evaluates individual scores whereas the t-statistic evaluates sample means

Cognitive Domain: Comprehension

Answer Location: Characteristics of the Student t Distribution

Difficulty Level: Medium

3. Which of the following is a similarity of the t-distribution and the standard normal distribution?

a. There is only one distribution for each.

b. Both distributions are symmetrical.

c. Both distributions are asymmetrical.

d. Both distributions are a function of the sample size.

Cognitive Domain: Comprehension

Answer Location: Characteristics of the Student t Distribution

Difficulty Level: Medium

4. Although their formulas are similar, one difference between the z-score (z) and the t-statistic (t) is that ______.

a. only z-scores (not t-statistics) are part of a theoretical distribution

b. z-scores evaluate sample means whereas t-statistics evaluate individual scores

c. the numerator of the t-statistic formula (not the z-score) is the difference between a score and a mean

d. the denominator of the t-statistic formula estimates the variability of sample means rather than individual scores

Cognitive Domain: Comprehension

Answer Location: Characteristics of the Student t Distribution

Difficulty Level: Medium

5. Although their formulas are similar, one difference between a z-score (z) and a t-statistic (t) is that a z-score evaluates ______ but a t-statistic evaluates ______.

a. sample means; individual scores for a variable

b. individual scores for a variable; sample means

c. scores; probabilities

d. normal distributions; skewed distributions

Cognitive Domain: Knowledge

Answer Location: Characteristics of the Student t Distribution

Difficulty Level: Easy

6. Although their formulas are similar, one primary difference between a z-score (z) and a t-statistic (t) is that the ______ of the formula for the t-statistic involves ______.

a. denominator; the variability of individual scores (Xs), not the variability of sample means

b. numerator; difference between a score (X) and a population mean (μ)

c. denominator; the variability of sample means , not the variability of individual scores (Xs)

d. numerator; the difference between a score (X) and a sample mean

Cognitive Domain: Comprehension

Answer Location: Characteristics of the Student t Distribution

Difficulty Level: Medium

7. Although their formulas are similar, one primary difference between a z-score (z) and a t-statistic (t) is that the ______ of the formula for the t-statistic contains or involves ______.

a. denominator; a sample mean rather than the population mean (μ)

b. numerator; a sample mean rather than an individual score (X)

c. numerator; the variability of individual scores (Xs) rather than sample means

d. denominator; the population mean (μ) rather than a sample mean

Cognitive Domain: Comprehension

Answer Location: Characteristics of the Student t Distribution

Difficulty Level: Medium

8. The ______ is the distribution of values of the sample mean for an infinite number of samples of size N that are randomly selected from the population.

a. sampling distribution

b. standard error of the mean

c. sampling distribution of the mean

d. population standard error of the mean

Cognitive Domain: Knowledge

Answer Location: The Sampling Distribution of the Mean

Difficulty Level: Easy

9. A researcher draws a random sample of 25 people from a population and calculates the mean of their IQs. If she were to repeat this process of drawing samples and calculating means an infinite number of times, the sample means could be used to create ______.

a. the sampling distribution of the mean

b. critical values

c. z-scores

d. research hypotheses

Cognitive Domain: Application

Answer Location: The Sampling Distribution of the Mean

Difficulty Level: Hard

10. I draw a random sample from the population and calculate the mean of this sample . If I were to do this an infinite number of times, I could create ______.

a. the sampling distribution of the mean

b. the null hypothesis

c. the standard normal distribution (normal curve)

d. the standard deviation

Cognitive Domain: Comprehension

Answer Location: The Sampling Distribution of the Mean

Difficulty Level: Medium

11. The sampling distribution of the mean helps ______.

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

b. describe the modality of a set of data

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

d. determine the probability of obtaining a particular value of a sample mean

Cognitive Domain: Knowledge

Answer Location: The Sampling Distribution of the Mean

Difficulty Level: Easy

12. The sampling distribution of the mean helps us ______.

a. calculate descriptive statistics

b. set alpha (α)

c. determine the probability of a sample mean

d. determine whether our variables are normally distributed

Cognitive Domain: Knowledge

Answer Location: The Sampling Distribution of the Mean

Difficulty Level: Easy

13. The sampling distribution of the mean ______.

a. is used to set alpha (α)

b. helps researchers evaluate sample means

c. is based on an infinite number of z-scores

d. is also known as the ‘normal curve’

Cognitive Domain: Knowledge

Answer Location: The Sampling Distribution of the Mean

Difficulty Level: Easy

14. The ______ of the sampling distribution of the mean is equal to ______.

a. mean; 0

b. variability; 0

c. variability; 1

d. mean; µ

Cognitive Domain: Knowledge

Answer Location: An Example From the Research: Do You Read Me?

Difficulty Level: Easy

15. The mean of the sampling distribution of the mean is equal to ______.

a.

b. 1

c. 0

d. µ

Cognitive Domain: Knowledge

Answer Location: An Example From the Research: Do You Read Me?

Difficulty Level: Easy

16. The ______ of the sampling distribution of the mean is represented by ______.

a. mean; µ

b. variability; s

c. mean; 1

d. variability;

Cognitive Domain: Knowledge

Answer Location: An Example From the Research: Do You Read Me?

Difficulty Level: Easy

17. The variability of the sampling distribution of the mean may be represented by ______.

a. 0

b.

c. σ

d. s

Cognitive Domain: Knowledge

Answer Location: Calculate a Statistic: t-Test for One Mean

Difficulty Level: Easy

18. The ______ of the sampling distribution of the mean may be represented by ______.

a. mean; 0

b. variability;

c. mean;

d. variability; 0

Cognitive Domain: Knowledge

Answer Location: Calculate a Statistic: t-Test for One Mean

Difficulty Level: Easy

19. The ______ of the sampling distribution of the mean may be represented by ______.

a. symmetry; 0

b. variability; 1

c. modality; s

d. variability;

Cognitive Domain: Knowledge

Answer Location: Calculate a Statistic: t-Test for One Mean

Difficulty Level: Easy

20. Holding all else constant, as sample size increases, the sampling distribution of the mean ______.

a. becomes flatter

b. has greater variability

c. becomes skewed

d. becomes more peaked

Cognitive Domain: Comprehension

Answer Location: Characteristics of the Student t Distribution

Difficulty Level: Medium

21. The modality, symmetry, and variability of the sampling distribution of the mean are defined by a statistical principle known as ______.

a. random sampling

b. ratio scale of measurement

c. standard error of the mean

d. central limit theorem

Cognitive Domain: Knowledge

Answer Location: Characteristics of the Sampling Distribution of the Mean

Difficulty Level: Easy

22. What is the sufficient sample size to use for the central limit theorem?

a. at least 25

b. at least 26

c. at least 30

d. at least 31

Cognitive Domain: Knowledge

Answer Location: Characteristics of the Sampling Distribution of the Mean

Difficulty Level: Easy

23. The central limit theorem states that when an infinite number of random samples are drawn from a population, the sample means are approximately normally distributed with a mean equal to the ______ and a standard deviation equal to the ______ of the mean.

a. population mean; standard error

b. population mean; standard deviation

c. sample mean; standard error

d. sample mean standard deviation

Cognitive Domain: Knowledge

Answer Location: Characteristics of the Sampling Distribution of the Mean

Difficulty Level: Easy

24. Standard deviation measures the ______ for a variable, standard error represents the ______ calculated from samples.

a. variability of statistics; variability of scores

b. variability of scores; variability of statistics

c. variability of scores; error of scores

d. variability of statistics; error of scores

Cognitive Domain: Knowledge

Answer Location: Characteristics of the Sampling Distribution of the Mean

Difficulty Level: Easy

25. Which of the following is a correctly stated null hypothesis?

a. H₀: µ ≠ 3

b. H₀: = 3

c. H₀: µ = 3

d. H₀: = 3

Cognitive Domain: Comprehension

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

Difficulty Level: Medium

26. Which of the following is a correctly stated alternative hypothesis?

a. H₁: µ ≠ 3

b. H₁: µ = 3

c. H₁: = 3

d. H₁: > 3

Cognitive Domain: Comprehension

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

Difficulty Level: Medium

27. Which of the following is a correctly stated alternative hypothesis?

a. H₁: ≠ 3

b. H₁: µ = 3

c. H₁: α = .05 (two-tailed)

d. H₁: µ ≠ 3

Cognitive Domain: Comprehension

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

Difficulty Level: Medium

28. The statement “µ ≠ 3” would be part of a ______.

a. non-directional alternative hypothesis

b. directional alternative hypothesis

c. non-directional null hypothesis

d. directional null hypothesis

Cognitive Domain: Comprehension

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

Difficulty Level: Medium

29. The statement “µ ≠ 3” would be part of a ______.

a. two-tailed, directional hypothesis

b. two-tailed, non-directional hypothesis

c. one-tailed, directional hypothesis

d. one-tailed, non-directional hypothesis

Cognitive Domain: Comprehension

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

Difficulty Level: Medium

30. The statement µ > 3 is an example of a ______.

a. directional null hypothesis

b. directional alternative hypothesis

c. non-directional null hypothesis

d. non-directional alternative hypothesis

Cognitive Domain: Comprehension

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

Difficulty Level: Medium

31. The statement µ > 3 is an example of a ______.

a. directional (one-tailed) null hypothesis

b. directional (one-tailed) alternative hypothesis

c. non-directional (two-tailed) null hypothesis

d. non-directional (two-tailed) alternative hypothesis

Cognitive Domain: Comprehension

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

Difficulty Level: Medium

32. The statement µ < 10 is an example of a ______.

a. directional (one-tailed) alternative hypothesis

b. directional (one-tailed) null hypothesis

c. non-directional (two-tailed) alternative hypothesis

d. non-directional (two-tailed) null hypothesis

Cognitive Domain: Comprehension

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

Difficulty Level: Medium

33. The ‘>’ symbol would appear in the ______ hypothesis and would imply that this hypothesis is ______.

a. null; non-directional

b. null; two-tailed

c. alternative; one-tailed

d. alternative; non-directional

Cognitive Domain: Knowledge

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

Difficulty Level: Easy

34. A ‘≠’ symbol in the ______ hypothesis implies this hypothesis is ______.

a. null; directional

b. null; two-tailed

c. alternative; one-tailed

d. alternative; non-directional

Cognitive Domain: Knowledge

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

Difficulty Level: Easy

35. A ______ symbol in the ______ hypothesis implies this hypothesis is ______.

a. >; null; one-tailed

b. ≠; null; directional

c. ≠; alternative; non-directional

d. =; alternative; one-tailed

Cognitive Domain: Comprehension

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

Difficulty Level: Medium

36. A ______ symbol in the ______ hypothesis implies this hypothesis is ______.

a. <; alternative; one-tailed

b. ≠; null; two-tailed

c. >; null; non-directional

d. ≠; alternative; directional

Cognitive Domain: Comprehension

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

Difficulty Level: Medium

37. A ______ alternative hypothesis (one that may have a ______ symbol) is also referred to as ______.

a. directional; ≠ ; two-tailed

b. non-directional; =; two-tailed

c. directional; >; one-tailed

d. non-directional; ≠; one-tailed

Cognitive Domain: Comprehension

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

Difficulty Level: Medium

38. A ______ alternative hypothesis (one that may have an ______ symbol) is also referred to as ______.

a. directional; ≠ ; one-tailed

b. non-directional; <; two-tailed

c. non-directional; >; asymmetrical

d. non-directional; ≠; two-tailed

Cognitive Domain: Comprehension

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

Difficulty Level: Medium

39. A ______ alternative hypothesis such as ______ is also referred to as ______.

a. directional; µ ≠ 164; two-tailed

b. non-directional; µ > 164; two-tailed

c. directional; µ > 164; one-tailed

d. non-directional; µ ≠ 164; one-tailed

Cognitive Domain: Comprehension

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

Difficulty Level: Medium

40. This distribution provides an illustration of a ______.

a. one-tailed null hypothesis

b. directional null hypothesis

c. directional alternative hypothesis

d. two-tailed alternative hypothesis

Cognitive Domain: Comprehension

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

Difficulty Level: Medium

41. This distribution illustrates a ______.

a. non-directional null hypothesis

b. directional null hypothesis

c. non-directional alternative hypothesis

d. directional alternative hypothesis

Cognitive Domain: Comprehension

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

Difficulty Level: Medium

42. The decision to use a directional versus non-directional alternative hypothesis most directly affects ______.

a. the critical value(s)

b. alpha ()

c. the sample size

d. the degrees of freedom

Cognitive Domain: Knowledge

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

Difficulty Level: Easy

43. Imagine that for a population of 200, the mean is 20.23 with a standard deviation of 5.12. What is the population standard error of the mean ?

a. .003

b. .03

c. .36

d. .50

Cognitive Domain: Application

Answer Location: Calculate a Statistic: z-test for One Mean

Difficulty Level: Hard

44. Imagine that for a population of 40, the mean is 10.25 with a standard deviation of 2.10. What is the population standard error of the mean ?

a. .03

b. .33

c. .34

d. .36

Cognitive Domain: Application

Answer Location: Calculate a Statistic: z-test for One Mean

Difficulty Level: Hard

45. A population has a mean of 15.21 and a standard deviation of 1.56. For a sample of N = 20, what is the population standard error of the mean ?

a. .35

b. .36

c. 1.56

d. 4.47

Cognitive Domain: Application

Answer Location: Calculate a Statistic: z-test for One Mean

Difficulty Level: Hard

46. A population has a mean of 55.25 and a standard deviation of 14.23. For a sample of N = 100, what is the population standard error of the mean ?

a. 7.03

b. 3.77

c. 1.43

d. 1.42

Cognitive Domain: Application

Answer Location: Calculate a Statistic: z-test for One Mean

Difficulty Level: Hard

47. A population has a mean of 606 and a standard deviation of 23. For a sample of N = 500, what is the population standard error of the mean ?

a. .10

b. 1.02

c. 1.03

d. 1.1

Cognitive Domain: Application

Answer Location: Calculate a Statistic: z-test for One Mean

Difficulty Level: Hard

48. Using the following information, calculate the z-statistic for the z-test for one mean.

= 15

μ = 22

= 3.50

a. 2.00

b. –2.00

c. 1.23

d. –3.13

Cognitive Domain: Application

Answer Location: Calculate a Statistic: z-test for One Mean

Difficulty Level: Hard

49. Using the following information, calculate the z-statistic for the z-test for one mean.

= 27

μ = 15

= 1.50

a. –8.00

b. 8.00

c. 4.00

d. –.10

Cognitive Domain: Application

Answer Location: Calculate a Statistic: z-test for One Mean

Difficulty Level: Hard

50. Using the following information, calculate the z-statistic for the z-test for one mean.

= 154

μ = 145

= 15.25

a. 9.00

b. –9.00

c. .59

d. –.59

Cognitive Domain: Application

Answer Location: Calculate a Statistic: z-test for One Mean

Difficulty Level: Hard

51. Using the following information, calculate the z-statistic for the z-test for one mean.

= 31.75

μ = 25.67

= 2.45

a. 2.48

b. –2.48

c. .10

d. -.10

Cognitive Domain: Application

Answer Location: Calculate a Statistic: z-test for One Mean

Difficulty Level: Hard

52. Using the following information, calculate the z-statistic for the z-test for one mean.

= 101

μ = 109

= 3.44

a. –2.32

b. 2.32

c. –2.33

d. 2.33

Cognitive Domain: Application

Answer Location: Calculate a Statistic: z-test for One Mean

Difficulty Level: Medium

53. For a z-statistic of –1.34, the decision about the null hypothesis is ______.

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

b. do not reject the null hypothesis (p < .01)

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

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

Cognitive Domain: Comprehension

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

Difficulty Level: Medium

54. If the value of a calculated z-statistic ______ the critical value, you would say ______.

a. exceeds; p > .05

b. exceeds; p < .05

c. does not exceed; p < .05

d. does not exceed; p < .01

Cognitive Domain: Comprehension

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

Difficulty Level: Medium

55. If the calculated value of a z-statistic ______ the critical value, you would say ______.

a. does not exceed; p < .01

b. does not exceed; p < .05

c. does not exceed; p > .05

d. exceeds; p > .05

Cognitive Domain: Comprehension

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

Difficulty Level: Hard

56. A researcher has calculated a z-statistic of 1.92. For a two-tailed test with alpha () = .05, which of the following is the most appropriate?

a. do not reject the null (p < .05)

b. do not reject the null (p > .05)

c. reject the null (p < .05)

d. reject the null (p > .05)

Cognitive Domain: Comprehension

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

Difficulty Level: Hard

57. For a z-statistic of 2.79, one would conclude (for a two-tailed test) the score is ______.

a. significant at the .05 level but not the .01 level

b. significant at both the .05 level and the .01 level

c. not significant

d. not significant at the .05 level but is significant at the .01 level

Cognitive Domain: Comprehension

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

Difficulty Level: Medium

58. For a z-statistic of 1.89, one would conclude (for a two-tailed test) the score is ______.

a. significant only at the .05 level

b. significant at both the .05 level and the .01 level

c. not significant

d. not significant at the .05 level but is significant at the .01 level

Cognitive Domain: Comprehension

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

Difficulty Level: Medium

59. For a z-statistic of 2.22, one would conclude (for a two-tailed test) the score is ______.

a. significant at the .05 level but not the .01 level

b. significant at both the .05 level and the .01 level

c. not significant

d. not significant at the .05 level but is significant at the .01 level

Cognitive Domain: Comprehension

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

Difficulty Level: Medium

60. For a z-statistic of –1.34, one would conclude (for a two-tailed test) the score is ______.

a. significant at the .05 level but not the .01 level

b. significant at both the .05 level and the .01 level

c. not significant

d. not significant at the .05 level but is significant at the .01 level

Cognitive Domain: Comprehension

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

Difficulty Level: Medium

61. Which of the following would be the most accurate way to report the following z-test?

a. z = 2.55 < 2.58 ; p < .01

b. z = 2.55 < 2.58 ; p > .05

c. z = 2.55 < 2.58 ; p < .05

d. z = 2.55 < 2.58 ; p > .01

Cognitive Domain: Comprehension

Answer Location: Determine the Level of Significance

Difficulty Level: Medium

62. Reporting the results of a z-test results typically includes all of the following EXCEPT ______.

a. the variable analyzed

b. the standard error of the sample mean

c. the sample and population means

d. the level of significance

Cognitive Domain: Knowledge

Answer Location: Draw a Conclusion From the Analysis

Difficulty Level: Easy

63. From data collected from a sample of 100 people, you obtain a mean of 16.27 and a standard deviation of 4.56. What is the value for the standard error of the mean ?

a. .46

b. .05

c. .16

d. 4.56

Cognitive Domain: Application

Answer Location: Calculate a Statistic: t-Test for One Mean

Difficulty Level: Hard

64. You collect data from a sample of 150 people, and calculate a mean of 6.87 and a standard deviation of 3.69. What is the value for the standard error of the mean ?

a. .30

b. 1.86

c. 6.87

d. 21.83

Cognitive Domain: Application

Answer Location: Calculate a Statistic: t-Test for One Mean

Difficulty Level: Hard

65. You collect data from a sample of 150 people and calculate a mean of 6.87 and a standard deviation of 3.69. What is the value for the standard error of the mean ?

a. .16

b. .30

c. 3.69

d. 12.24

Cognitive Domain: Application

Answer Location: Calculate a Statistic: t-Test for One Mean

Difficulty Level: Hard

66. Holding all else constant, as sample size increases, the value of the standard error of the mean ______.

a. increases

b. decreases

c. stays the same

d. explodes

Cognitive Domain: Application

Answer Location: Calculate a Statistic: t-Test for One Mean

Difficulty Level: Hard

67. A ______ can represent the variability of ______.

a. standard deviation; sample means

b. standard deviation; differences between two sample means

c. standard error; individual scores (X)

d. standard error; sample means

Cognitive Domain: Knowledge

Answer Location: Calculate a Statistic: t-Test for One Mean

Difficulty Level: Easy

68. If I wanted to measure the variability of ______ , I would calculate ______.

a. individual scores (Xs); the standard error of the mean

b. sample means ; the standard error of the mean

c. sample means ; the standard deviation (s)

d. individual scores (Xs); the sample mean

Cognitive Domain: Knowledge

Answer Location: Calculate a Statistic: t-Test for One Mean

Difficulty Level: Easy

69. If I wanted to measure the variability in a set of scores (Xs), I would calculate ______.

a. the standard error of the mean

b. the standard deviation (s)

c. z-scores

d. the t-statistic

Cognitive Domain: Knowledge

Answer Location: Calculate a Statistic: t-Test for One Mean

Difficulty Level: Easy

70. If I wanted to estimate the variability of sample means , I would calculate ______.

a. the standard error of the mean

b. the standard deviation (s)

c. z-scores

d. the population mean (μ)

Cognitive Domain: Knowledge

Answer Location: Calculate a Statistic: t-Test for One Mean

Difficulty Level: Easy

71. In testing the mean of a sample, the sample mean is transformed into a t-statistic in order to ______.

a. determine the critical values

b. prove our research hypotheses

c. determine whether the alternative hypothesis (H₁) should be one-tailed or two-tailed

d. determine the probability of obtaining the value of the sample mean

Cognitive Domain: Comprehension

Answer Location: Calculate a Statistic: t-Test for One Mean

Difficulty Level: Medium

72. In testing the mean of a sample, the sample mean is transformed into a ______ statistic in order to ______.

a. z; decide whether to set alpha at .05 or .01

b. t; determine the probability of a sample mean

c. z; determine the critical values

d. t; determine whether the distribution of sample means is normal

Cognitive Domain: Knowledge

Answer Location: Calculate a Statistic: t-Test for One Mean

Difficulty Level: Easy

73. In testing the mean of a sample, calculating a positive value of the t-statistic (t) necessarily implies ______.

a. the research hypothesis has been supported

b. you have done your calculations correctly (without making a mistake)

c. the value of the t-statistic falls in the region of rejection

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

Cognitive Domain: Comprehension

Answer Location: Calculate a Statistic: t-Test for One Mean

Difficulty Level: Medium

74. In testing the mean of a sample, calculating a negative value of the t-statistic (t) indicates ______.

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

b. the score is less than the mean

c. is greater than

d. you have made an error in your calculations

Cognitive Domain: Comprehension

Answer Location: Characteristics of the Student t Distribution

Difficulty Level: Medium

75. Which of the following can be a negative number in testing the mean of a sample?

a. t

b. df

c.

d. α

Cognitive Domain: Knowledge

Answer Location: Characteristics of the Student t Distribution

Difficulty Level: Easy

76. Which of the following can be a negative number in testing the mean of a sample?

a. the degrees of freedom

b. the critical values

c. alpha

d. the standard error of the mean

Cognitive Domain: Comprehension

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

Difficulty Level: Easy

77. Looking at the ______ for a statistic like a t-statistic provides an indication of the sample size in a study.

a. research hypothesis

b. null hypothesis

c. degrees of freedom

d. alternative hypothesis

Cognitive Domain: Knowledge

Answer Location: Calculate the Degrees of Freedom (df)

Difficulty Level: Easy

78. Looking at the degrees of freedom tells you something about ______.

a. the size of the sample

b. the directionality of the alternative hypothesis

c. the level of significance of a statistic

d. the research hypothesis

Cognitive Domain: Knowledge

Answer Location: Calculate the Degrees of Freedom (df)

Difficulty Level: Easy

79. Looking at the degrees of freedom for a statistic like a t-statistic provides information regarding ______.

a. the size of the sample

b. the sample mean

c. whether alpha is one-tailed or two-tailed

d. the population mean (μ)

Cognitive Domain: Knowledge

Answer Location: Calculate the Degrees of Freedom (df)

Difficulty Level: Easy

80. Looking at ______ for a statistic like a t-statistic provides an indication of the directionality of the alternative hypothesis.

a. the null hypothesis

b. alpha

c. the critical values

d. the sample size

Cognitive Domain: Knowledge

Answer Location: Calculate the Degrees of Freedom (df)

Difficulty Level: Easy

81. A researcher calculates a mean from a sample of 10 people. In analyzing her data, she states the following hypotheses: H₀: μ = 30 and H₁: μ ≠ 30. If α = .05, which of the following is an appropriate critical value?

a. 1.833

b. 2.042

c. 2.228

d. 2.262

Cognitive Domain: Application

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

Difficulty Level: Hard

82. A researcher calculates a mean from a sample of 15 people. In analyzing her data, she states the following hypotheses: H₀: μ = 25 and H₁: μ ≠ 25. If α = .05, which of the following is an appropriate critical value?

a. 1.709

b. 1.753

c. 2.060

d. 2.145

Cognitive Domain: Application

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

Difficulty Level: Hard

83. A researcher calculates a mean from a sample of 24 people. In analyzing her data, she states the following hypotheses: H₀: μ = 20 and H₁: μ ≠ 20. For α = .05, what is the appropriate critical value for her statistic?

a. 1.714

b. 2.086

c. 2.069

d. 2.064

Cognitive Domain: Application

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

Difficulty Level: Hard

84. A researcher calculates a mean from a sample of 18 people. In analyzing her data, she states the following hypotheses: H₀: μ = 20 and H₁: μ ≠ 20. For α = .05, which is an appropriate critical value?

a. 1.734

b. 2.110

c. 2.101

d. 2.086

Cognitive Domain: Application

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

Difficulty Level: Hard

85. A researcher calculates a mean from a sample of 23 people. In analyzing her data, she states the following hypotheses: H₀: μ = 25 and H₁: μ ≠ 25. For α = .05, which is an appropriate critical value?

a. 1.717

b. 2.074

c. 2.069

d. 2.064

Cognitive Domain: Application

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

Difficulty Level: Hard

86. A researcher calculates a mean from a sample of 21 people. In analyzing her data, she states the following hypotheses: H₀: μ = 16 and H₁: μ ≠ 16. For α = .05, which is an appropriate critical value?

a. 1.725

b. 2.086

c. 2.093

d. 2.131

Cognitive Domain: Application

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

Difficulty Level: Hard

87. Another researcher calculates a mean from a sample of 25 people. For α = .05, if he states the hypotheses as H₀: μ = 100 and H₁: μ < 100, which of the following is an appropriate critical value?

a. 1.714

b. 1.711

c. 1.708

d. 2.060

Cognitive Domain: Application

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

Difficulty Level: Hard

88. A researcher calculates a mean from a sample of 19 people. For α = .05, if the researcher states the hypotheses as H₀: µ = 200 and H₁: µ < 200, which of the following is an appropriate critical value?

a. 0.688

b. 1.645

c. 1.734

d. 1.729

Cognitive Domain: Application

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

Difficulty Level: Hard

89. If the value of the t-statistic calculated from a set of data ______ the critical value, you would say ______.

a. exceeds; p < .05

b. exceeds; p > .05

c. does not exceed; p < .05

d. does not exceed; p < .01

Cognitive Domain: Comprehension

Answer Location: Alpha (α)

Difficulty Level: Medium

90. A researcher tests the mean of a sample of 25 people and calculates a value of 2.51 for the t-statistic. For α = .05 (two-tailed), which of the following is most appropriate?

a. do not reject null (p < .05)

b. do not reject null (p > .05)

c. reject null (p < .05)

d. reject null (p > .01)

Cognitive Domain: Application

Answer Location: Alpha (α)

Difficulty Level: Hard

91. A researcher tests the mean of a sample of 28 people and calculates a value of 2.13 for the t-statistic. For α = .05 (two-tailed), which of the following decisions is MOST appropriate?

a. do not reject null (p < .05)

b. do not reject null (p > .05)

c. reject null (p < .05)

d. accept null (p < .05)

Cognitive Domain: Application

Answer Location: Alpha (α)

Difficulty Level: Hard

92. You test the mean of a sample of 19 people and calculate a value of 2.14 for the t-statistic. For α = .05 (two-tailed), which of the following decisions is MOST appropriate?

a. do not reject null (p > .01)

b. reject null (p > .05)

c. accept alternative (p > .05)

d. reject null (p < .05)

Cognitive Domain: Application

Answer Location: Alpha (α)

Difficulty Level: Hard

93. A researcher calculates a value of 3.21 for a t-statistic. For df = 20 and alpha = .05 (two-tailed), which of the following is the MOST accurate?

a. reject the null hypothesis

b. p < .05

c. p < .01

d. do not reject the null hypothesis

Cognitive Domain: Application

Answer Location: Alpha (α)

Difficulty Level: Hard

94. You calculate a value of 1.17 for the t-statistic and find falls in the region of non-rejection. As a result, the most appropriate conclusion is that you ______.

a. do not reject the alternative hypothesis

b. reject the null hypothesis

c. reject the alternative hypothesis

d. do not reject the null hypothesis

Cognitive Domain: Application

Answer Location: Alpha (α)

Difficulty Level: Hard

95. A researcher tests the mean of a sample of 22 people and calculates a value of 1.81 for the t-statistic. For α = .05 (two-tailed), which of the following decisions is MOST appropriate?

a. do not reject null (p < .05)

b. do not reject null (p > .05)

c. reject null (p < .05)

d. reject null (p > .05)

Cognitive Domain: Application

Answer Location: Alpha (α)

Difficulty Level: Hard

96. A researcher tests the mean of a sample of 24 people and calculates a value of 1.98 for the t-statistic. For α = .05 (two-tailed), which of the following decisions is MOST appropriate?

a. do not reject null (p > .01)

b. do not reject null (p > .05)

c. reject null (p < .05)

d. reject null (p > .05)

Cognitive Domain: Application

Answer Location: Alpha (α)

Difficulty Level: Hard

97. If the value of a t-statistic falls between the critical values for α = .05 and α = .01, you would describe the level of significance as ______.

a. p > .01

b. p > .05

c. p < .01

d. p < .05

Cognitive Domain: Application

Answer Location: Determine the Level of Significance

Difficulty Level: Hard

98. Imagine the value of a t-statistic is less than the critical value for α = .01 but greater than the critical value for α = .05. Which of the following 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: Application

Answer Location: Determine the Level of Significance

Difficulty Level: Hard

99. Imagine the value of a t-statistic is greater than the critical value for α = .05 but less than the critical value for α = .01. Which of the following is the level of significance for this t-statistic?

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

b. p > .01

c. p > .01 (but not < .05)

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

Cognitive Domain: Application

Answer Location: Determine the Level of Significance

Difficulty Level: Medium

100. A researcher tests the mean of a sample of 16 people and calculates a value of 2.42 for the t-statistic. For α = .05 (two-tailed), which of the following is the MOST appropriate level of significance?

a. p < .05

b. p > .05

c. p < .01

d. p > .01

Cognitive Domain: Application

Answer Location: Determine the Level of Significance

Difficulty Level: Hard

101. In reporting the result of a statistical analysis, a researcher reports that “p < .01”. This necessarily implies that ______.

a. the null hypothesis was not rejected

b. the research hypothesis was not supported

c. p < .05

d. p > .05

Cognitive Domain: Application

Answer Location: Determine the Level of Significance

Difficulty Level: Hard

102. If ______ , you would describe the result of the analysis as being ______.

a. p < .05; nonsignificant

b. p > .05; significant

c. p > .05; insignificant

d. p > .05; nonsignificant

Cognitive Domain: Comprehension

Answer Location: Determine the Level of Significance

Difficulty Level: Medium

103. If you were to ______ the null hypothesis, you would say the result is statistically ______.

a. reject; nonsignificant

b. not reject; insignificant

c. reject; significant

d. not reject; significant

Cognitive Domain: Comprehension

Answer Location: Determine the Level of Significance

Difficulty Level: Medium

104. You determine whether the probability of a statistic such as the t-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: Make a Decision Whether to Reject the Null Hypothesis

Difficulty Level: Medium

105. You determine whether the probability of a statistic such as the t-statistic is < .01 ______.

a. when you do not reject the null hypothesis

b. because p < .01 is more precise than p < .05

c. because p < .01 is more likely to occur than p < .05

d. because p < .01 is better than p < .05

Cognitive Domain: Comprehension

Answer Location: Determine the Level of Significance

Difficulty Level: Medium

106. You determine whether the probability of a statistic such as the t-statistic is < .01 ______.

a. because p < .01 is much more significant than p < .05

b. in order to prove the research hypothesis

c. because p < .05 is more likely to occur than p < .01

d. to be as precise as possible

Cognitive Domain: Comprehension

Answer Location: Determine the Level of Significance

Difficulty Level: Medium

107. Answering the question, “Is p < .01?” is part of ______.

a. making the decision to reject the null hypothesis

b. calculating the degrees of freedom

c. determining the level of significance

d. setting α

Cognitive Domain: Comprehension

Answer Location: Determine the Level of Significance

Difficulty Level: Medium

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

a. when you do not reject the null hypothesis

b. when you reject the null hypothesis

c. when you’ve already concluded that p > .05

d. when you’ve already concluded that p > .01

Cognitive Domain: Comprehension

Answer Location: Determine the Level of Significance

Difficulty Level: Medium

109. A study based on a sample of 13 participants calculates a value of 2.26 for the t-test for a single mean. For alpha (α) = .05 (two-tailed), which of the following is the correct way to present this analysis?

a. t(11) = 2.26, p < .05

b. t(12) = 2.26, p < .05

c. t(12) = 2.26, p < .01

d. t(13) = 2.26, p < .01

Cognitive Domain: Application

Answer Location: Summary

Difficulty Level: Hard

110. A study based on a sample of 17 participants calculates a value of 2.33 for the t-test for a single mean. For alpha (α) = .05 (two-tailed), which of the following is the correct way to present this analysis?

a. t(16) = 2.33, p < .05

b. t(16) = 2.33, p > .05

c. t(17) = 2.33, p < .05

d. t(17) = 2.33, p > .01

Cognitive Domain: Application

Answer Location: Summary

Difficulty Level: Hard

111. A study based on a sample of 14 participants calculates a value of 2.58 for the t-test for a single mean. For alpha (α) = .05 (two-tailed), which of the following is the correct way to present this analysis?

a. t(13) = 2.58, p < .05

b. t(13) = 2.58, p > .01

c. t(14) = 2.58, p < .05

d. t(14) = 2.58, p < .01

Cognitive Domain: Application

Answer Location: Summary

Difficulty Level: Hard

112. A study based on a sample of 22 participants calculates a value of 1.86 for the t-statistic. For alpha (α) = .05 (two-tailed), which of the following is the correct way to present this analysis?

a. t(20) = 1.86, p > .01

b. t(21) = 1.86, p > .05

c. t(21) = 1.86, p < .01

d. t(22) = 1.86, p < .05

Cognitive Domain: Application

Answer Location: Summary

Difficulty Level: Hard

113. A study based on a sample of 20 participants calculates a value of 1.92 for the t-test for a single mean. For alpha (α) = .05 (two-tailed), which of the following is the correct way to present this analysis?

a. t(18) = 1.92, p > .01

b. t(19) = 1.92, p < .05

c. t(19) = 1.92, p > .05

d. t(19) = 1.92, p < .01

Cognitive Domain: Application

Answer Location: Summary

Difficulty Level: Hard

114. A study based on a sample of 13 participants calculates a value of 1.89 for the t-test for a single mean. For alpha (α) = .05 (two-tailed), which of the following is the correct way to present this analysis?

a. t(12) = 1.89, p < .05

b. t(12) = 1.89, p > .05

c. t(13) = 1.89, p < .05

d. t(13) = 1.89, p > .01

Cognitive Domain: Application

Answer Location: Summary

Difficulty Level: Hard

115. A study based on a sample of 30 participants calculates a value of 2.56 for the t-test for a single mean. For alpha (α) = .05 (two-tailed), which of the following is the correct way to present this analysis?

a. t(29) = 2.56, p > .05

b. t(29) = 2.56, p > .01

c. t(29) = 2.56, p < .05

d. t(29) = 2.56, p < .01

Cognitive Domain: Application

Answer Location: Summary

Difficulty Level: Hard

NARRBEGIN: Alcohol

Use this information below to answer questions 116–120.

As alcohol-related problems are a concern on college campuses, research has been conducted regarding students’ perceptions of drinking behavior. For example, one study found students have misconceptions regarding what is considered excessive (“binge”) drinking (White et al, 2004). Imagine you believe students’ definition of binge drinking will differ from the government’s definition. More specifically, you hypothesize students will overestimate the number of drinks needed to be consumed to be defined as binge drinking. To test this hypothesis, a group of college students are asked, “How many drinks in a row must a man drink in order to define it as “binge drinking?” The responses of some of the students in this class are summarized as:

N = 16

= 7.94

s = 4.63

NARREND

116. The government has defined binge drinking as consuming at least 5 drinks in a row. Therefore, in this study, how would the null and alternative hypotheses be stated?

a. H₀: μ < 5; H₁: μ > 5

b. H₀: μ = 5; H₁: μ ≠ 5

c. H₀: μ ≠ 5; H₁: μ = 5

d. H₀: μ = 5; H₁: μ < 5

Cognitive Domain: Comprehension

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

Difficulty Level: Medium

NAR: Alcohol

117. What is the value for the standard error of the mean ?

a. .29

b. .50

c. .86

d. 1.16

Cognitive Domain: Analysis

Answer Location: Calculate a Statistic: t-Test for One Mean

Difficulty Level: Medium

NAR: Alcohol

118. For α = .05 (two-tailed), which of the following is an appropriate critical value?

a. 1.746

b. 2.042

c. 2.120

d. 2.131

Cognitive Domain: Application

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

Difficulty Level: Hard

NAR: Alcohol

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

a. Do not reject H₀ (p > .05)

b. Reject H₀ (p < .05)

c. Reject H₀ (p < .01)

d. Reject H₀ (p > .01)

Cognitive Domain: Analysis

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

Difficulty Level: Medium

NAR: Alcohol

120. Based on your analysis, which of the following represents your conclusion regarding the research hypothesis?

a. The analysis does not support the research hypothesis.

b. The analysis supports the research hypothesis.

c. The analysis disproves the research hypothesis.

d. The analysis proves the research hypothesis.

Cognitive Domain: Analysis

Answer Location: Draw a Conclusion from the Analysis

Difficulty Level: Medium

NAR: Alcohol

NARRBEGIN: Weddings

Use this information below to answer questions 121–122.

A researcher looked at young people’s Knowledge of the cost of weddings, where it’s been found that many students’ estimates of the cost of a wedding was less than the actual average. As a result of this finding, imagine you hypothesize that young people will underestimate the average cost of a wedding gown. To test this hypothesis, a group of college students are asked, “According to the Brides.com (http://www.brides.com) 2009 American Wedding Survey, what is the average cost of a wedding gown?” The responses of some of the students in this class are summarized as:

N = 28

= 2432.14

s = 1643.18

NARREND

121. According to Brides.com, the average cost of a wedding gown was $1075. Therefore, in this study, how would the null and alternative hypotheses be stated?

a. H₀: μ > 1075; H₁: μ < 1075

b. H₀: μ ≠ 1075; H₁: μ = 1075

c. H₀: μ = 1075; H₁: μ ≠ 1075

d. H₀: μ = 2432.14; H₁: μ ≠ 2432.14

Cognitive Domain: Comprehension

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

Difficulty Level: Medium

NAR: Weddings

122. For α = .05 (two-tailed), which of the following is an appropriate critical value?

a. 1.703

b. 1.706

c. 2.052

d. 2.056

Cognitive Domain: Application

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

Difficulty Level: Hard

NAR: Weddings

123. A researcher conducted an analysis that supported the research hypothesis that SJSU students spend less on textbooks than the average California college student. As a result of this finding, imagine you hypothesize that SJSU freshmen owe less on their credit cards than the average college freshman. To test this hypothesis, a group of college students are asked, “If you have your own credit card(s), how much do you currently owe on them?” The responses of some of the students in this class are summarized as:

N = 25

= 834.53

s = 169.40

According to a recent study, the average college freshman owes $900 on their credit cards (Arano, 2006). Therefore, in this analysis, how could the null and alternative hypotheses be stated?

a. H₀: μ > 900; H₁: μ < 900

b. H₀: μ ≠ 900; H₁: μ = 900

c. H₀: μ = 900; H₁: μ ≠ 900

d. H₀: μ = 834.53; H₁: μ ≠ 834.53

Cognitive Domain: Comprehension

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

Difficulty Level: Medium

124. A researcher conducted an analysis that supported the research hypothesis that SJSU students spend less on textbooks than the average California college student. As a result of this finding, you hypothesize that SJSU freshmen owe less on their credit cards than the average college freshman. To test this hypothesis, a group of college students are asked, “If you have your own credit card(s), how much do you currently owe on them?” The responses of some of the students in this class are summarized as: N = 25

= 834.53

s = 169.40

According to a recent study, the average college freshman owes $900 on their credit cards (Arano, 2006). Given the information above, what is the value for the t-statistic (t)?

a. –.39

b. 4.93

c. –1.92

d. 26.56

Cognitive Domain: Analysis

Answer Location: Calculate a Statistic: t-Test for One Mean

Difficulty Level: Medium

125. A researcher conducted an analysis that supported the research hypothesis that SJSU students spend less on textbooks than the average California college student. As a result of this finding, imagine you hypothesize that SJSU freshmen owe less on their credit cards than the average college freshman. To test this hypothesis, a group of college students are asked, “If you have your own credit card(s), how much do you currently owe on them?” The responses of some of the students in this class are summarized as:

N = 25

= 834.53

s = 169.40

For α = .05 (two-tailed), which of the following is an appropriate critical value?

a. 1.711

b. 1.708

c. 2.060

d. 2.064

Cognitive Domain: Application

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

Difficulty Level: Hard

126. A researcher conducted an analysis that supported the research hypothesis that SJSU students spend less on textbooks than the average California college student. As a result of this finding, imagine you hypothesize that SJSU freshmen owe less on their credit cards than the average college freshman. To test this hypothesis, a group of college students are asked, “If you have your own credit card(s), how much do you currently owe on them?” The responses of some of the students in this class are summarized as:

N = 25

= 834.53

s = 169.40

According to a recent study, the average college freshman owes $900 on their credit cards (Arano, 2006).

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

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: Analysis

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

Difficulty Level: Hard

True/False

1. A z-statistic of 1.35 is significant at the .05 alpha level for a two-tailed test.

Cognitive Domain: Knowledge

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

Difficulty Level: Easy

2. A z-statistic of 2.70 is significant at both the .05 and .01 alpha levels for a two-tailed test.

Cognitive Domain: Knowledge

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

Difficulty Level: Easy

3. A statistic with less than a .01 probability is not simply statistically “significant”, but should be referred to as “highly significant”.

Cognitive Domain: Knowledge

Answer Location: Determine the Level of Significance

Difficulty Level: Easy

4. When reporting the results of a z-test, you should state whether or not the null hypothesis was rejected.

Cognitive Domain: Knowledge

Answer Location: Draw a Conclusion From the Analysis

Difficulty Level: Easy

5. If a calculated z-statistic is equal to 2.61, you would report that the sample mean is significantly different from the population mean at the .01 level of significance.

Cognitive Domain: Knowledge

Answer Location: Determine the Level of Significance

Difficulty Level: Easy

6. When drawing conclusions about the sample mean compared to the population mean, a researcher should indicate whether the sample mean is greater than or less than the population mean.

Cognitive Domain: Knowledge

Answer Location: Draw a Conclusion From the Analysis

Difficulty Level: Easy

7. When reporting the results of a statistical analysis, it would be appropriate to report that the research hypothesis has been proven to be correct.

Cognitive Domain: Knowledge

Answer Location: Draw a Conclusion From the Analysis

Difficulty Level: Easy

8. When reporting the results of a statistical analysis, it would be more appropriate to report that the research hypothesis has been “supported” rather than “proven.”

Cognitive Domain: Knowledge

Answer Location: Draw a Conclusion From the Analysis

Difficulty Level: Easy