Chapter 15: Cousins or Just Good Friends? Testing Relationships Using the
Correlation Coefficient
Test Bank
MULTIPLE CHOICE
1. The correlation coefficient is a measure of _______.
a. Mean differences
b. Causation
c. Prediction
d. Association
ANS: D
PTS: 1
DIF: Easy
REF: Introduction to Testing the Significance of the Correlation Coefficient
OBJ: How to interpret the correlation coefficient
COG: Knowledge
2. While you can use the
correlation coefficient as its own test statistic, what is the other
appropriate test statistic often used to examine the significance of a correlation?
a. F-test
b. Cohen’s d
c. t-test
d.
ANS: C
PTS: 1
DIF: Medium
REF: Computing the Test Statistic
OBJ: How to test the significance of the correlation coefficient
COG: Knowledge
3. This chapter illustrates that you can also incorporate _______ into the correlation coefficient.
a. Statistical
significance
b. Substantial significance
c. Descriptive statistics
d. Generalizability
ANS:
REF:
OBJ:
COG:
A
PTS: 1
DIF: Easy
Introduction to Testing the Significance of the Correlation Coefficient
How to test the significance of the correlation coefficient
Knowledge
4. Correlation coefficients examine
a. Differences between two groups
b. Differences between two or more groups
c. The relationship between variables
d. How
variables can be arranged into higher-order factors
ANS: C
PTS: 1
DIF: Easy
REF: Introduction to Testing the Significance of the Correlation Coefficient
OBJ: How to interpret the correlation coefficient
COG: Knowledge
5. Correlation coefficients can test _______ variable(s) at a time.
a. Only one
b. Only two
c. One or more
d. Two or more
ANS: B
PTS: 1
DIF: Medium
OBJ: How to interpret the correlation coefficient
REF: Computing the
Test Statistic
COG: Knowledge
6. The appropriate test statistic to use is the _______.
a. t-test for the correlation coefficient
b. p-test for the correlation coefficient
c. r-test for the correlation coefficient
d. t-test for statistical significance
ANS: A
PTS: 1
DIF: Medium
REF: Computing the Test Statistic
OBJ: How to test the significance of the correlation coefficient
COG: Knowledge
7. Correlations can be _______.
a. Directional or
nondirectional
b. Only directional
c. Only nondirectional
d. Neither directional nor nondirectional
ANS: A
PTS: 1
DIF: Medium
OBJ: How to interpret the correlation coefficient
REF: Computing the Test Statistic
COG: Knowledge
8. Significant correlations are not able to indicate _______.
a. The probability level
b. The size of the effect
c. Causality
d. The strength of the effect
ANS: C
PTS: 1
REF: Causes and Associations (Again!)
COG:
Knowledge
DIF: Medium
OBJ: How to interpret the correlation coefficient
9. What is another term for a positive correlation?
a. Indirect
b. Nondirectional
c. Direct
d. Unidirectional
ANS: C
PTS: 1
DIF: Medium
OBJ: How to interpret the correlation coefficient
REF: Computing the Test Statistic
COG: Knowledge
10. What is another term for a negative correlation?
a. Indirect
b. Nondirectional
c. Direct
d. Unidirectional
ANS:
A
PTS: 1
DIF: Medium
OBJ: How to interpret the correlation coefficient
REF: Computing the Test Statistic
COG: Knowledge
11. What is the most important characteristic of a correlation coefficient?
a. Number of variables included
b. Absolute value
c. One tailed
d. Two tailed
ANS: B
PTS: 1
DIF: Medium
OBJ: How to interpret the correlation coefficient
REF: Computing the Test Statistic
COG: Knowledge
12. Which of the following is an
example of a null hypothesis for testing a correlation coefficient?
a. H1: xy = 0
b. H1: xy > 0
c. H0: xy = 0
d. H0: xy > 0
ANS: C
PTS: 1
DIF: Medium
OBJ: How to interpret the correlation coefficient
REF: Computing the Test Statistic
COG: Knowledge
13. If you posit that a relationship between two variables will be either positive or negative, what
type of test should you use?
a. Two tailed
b. ANOVA
c. One tailed
d. Cohen’s
d
ANS: C
PTS: 1
DIF: Medium
REF: Computing the Test Statistic
OBJ: How to test the significance of the correlation coefficient
COG: Comprehension
14. If you do not predict that a relationship between two variables will be either positive or
negative, what type of test should you use?
a. Two tailed
b. ANOVA
c. One tailed
d. Cohen’s d
ANS: A
PTS: 1
DIF: Medium
REF: Computing the Test Statistic
OBJ: How to test the significance of the
correlation coefficient
COG: Comprehension
15. The level of risk or Type I error typically set for testing the level of significance of a
correlation coefficient is which of the following?
a. .01
b. .05
c. .95
d. .99
ANS: B
PTS: 1
DIF: Medium
REF: Computing the Test Statistic
OBJ: How to test the significance of the correlation coefficient
COG: Knowledge
16. Which of the following is the appropriate method for calculating the degrees of freedom
associated
with a correlation coefficient?
a. n - 1
b. n - 2
c. n - 3
d. n - 4
ANS: B
PTS: 1
DIF: Medium
REF: Computing the Test Statistic
OBJ: How to test the significance of the correlation coefficient
COG: Knowledge
17. In the formula for calculating degrees of freedom for a correlation coefficient, what does the n
represent?
a. Sample size
b. Number of groups
c. Number of pairs
d. Population
ANS: C
PTS: 1
DIF: Medium
REF: Computing the
Test Statistic
OBJ: How to test the significance of the correlation coefficient
COG: Knowledge
18. What is the name of the Greek letter
a. Phi
b. Rho
c. Chi
d. Alpha
?
ANS: B
PTS: 1
DIF: Medium
OBJ: How to interpret the correlation coefficient
REF: Computing the Test Statistic
COG: Knowledge
19. Which of the following Greek symbols is used to represent the population estimate for a
correlation coefficient?
a.
b.
c.
d.
ANS: C
PTS: 1
DIF: Medium
OBJ: How to interpret the correlation coefficient
REF: Computing the Test Statistic
COG: Knowledge
20. Which of the following represents the test statistic for a correlation coefficient?
a. t
b. r
c.
d. F
ANS: B
PTS: 1
DIF: Medium
OBJ: How to interpret the correlation coefficient
REF: Computing the Test Statistic
COG: Knowledge
21. Which of the following is another use of correlation
coefficients?
a. Testing mean differences
b. Testing causal relationships
c. Estimating reliability
d. Estimating power
ANS: C
PTS: 1
DIF: Medium
REF: So How Do I Interpret r(28) = .393, p < .05?
OBJ: How to interpret the correlation coefficient
COG: Knowledge
22. When computing the correlation coefficient, the _______ between variables, not the _______
between groups, is being examined.
a. Relationship; difference
b. Difference;
relationship
c. Means, reliability
d. Reliability; means
ANS: A
PTS: 1
DIF: Medium
REF: The Path to Wisdom and Knowledge
OBJ: How to interpret the correlation coefficient
COG: Knowledge
23. If the correlation between two variables is .496, how much of the variance has not been
accounted for?
a. 24.6%
b. 49.6%
c. 50.4%
d. 75.4%
ANS:
REF:
OBJ:
COG:
D
PTS: 1
DIF: Medium
Significance Versus Meaningfulness (Again,
Again!)
The important distinction between significance and meaningfulness (again!)
Application
24. If the correlation between two variables is .496, what is the coefficient of determination?
a. .246
b. .496
c. .504
d. .754
ANS:
REF:
OBJ:
COG:
A
PTS: 1
DIF: Medium
Significance Versus Meaningfulness (Again, Again!)
The important distinction between significance and meaningfulness (again!)
Application
25. What does the statement rxy
0 represent?
a. Null hypothesis
b. t statistic
c. Mean difference
d. Research hypothesis
ANS: D
PTS: 1
DIF: Medium
OBJ: How to interpret the correlation coefficient
REF: Computing the Test Statistic
COG: Comprehension
26. If a research hypothesis does not predict the direction of a relationship, the test is _______.
a. One tailed
b. Two tailed
c. Direct
d. Positive
ANS: B
PTS: 1
DIF: Medium
REF: Computing the Test
Statistic
OBJ: How to test the significance of the correlation coefficient
COG: Comprehension
27. If a research hypothesis posits that there is a direct relationship between two variables, the test
is _______.
a. One tailed
b. Two tailed
c. Negative
d. Nondirectional
ANS: A
PTS: 1
DIF: Medium
REF: Computing the Test Statistic
OBJ: How to test the significance of the correlation coefficient
COG: Comprehension
28. In the equation r(65) = .45, p
< .05, what does r represent?
a. Observed statistic
b. Experimental statistic
c. Test statistic
d. Critical statistic
ANS: C
PTS: 1
DIF: Medium
REF: So How Do I Interpret r(28) = .393, p < .05?
OBJ: How to interpret the correlation coefficient
COG: Application
29. In the equation r(65) = .45, p < .05, what are the degrees of freedom?
a. .45
b. 45
c. .65
d. 65
ANS: D
PTS: 1
DIF: Medium
REF: So How Do I Interpret r(28) = .393,
p < .05?
OBJ: How to interpret the correlation coefficient
COG: Application
30. In the equation r(65) = .45, p < .05, what is the obtained value?
a. .45
b. 45
c. .65
d. 65
ANS: A
PTS: 1
DIF: Medium
REF: So How Do I Interpret r(28) = .393, p < .05?
OBJ: How to interpret the correlation coefficient
COG: Application
31. When computing a correlation coefficient, if you have 27 degrees of freedom, your sample
size must be
_______.
a. 29
b. 27
c. 25
d. 26
ANS: A
PTS: 1
DIF: Medium
OBJ: How to interpret the correlation coefficient
REF: Computing the Test Statistic
COG: Application
32. When computing a correlation coefficient, if you have 55 degrees of freedom, your sample
size must be _______.
a. 55
b. 53
c. 56
d. 57
ANS: D
PTS: 1
DIF: Medium
REF: Computing the Test Statistic
OBJ: How to test the significance of the correlation
coefficient
COG: Application
33. If a simple Pearson correlation value = .512, what percentage of variance is accounted for?
a. 26%
b. 49%
c. 51%
d. 74%
ANS:
REF:
OBJ:
COG:
A
PTS: 1
DIF: Medium
Significance Versus Meaningfulness (Again, Again!)
The important distinction between significance and meaningfulness (again!)
Application
34. If a simple Pearson correlation value = .685, what percentage of variance is accounted for?
a.
35%
b. 47%
c. 68%
d. 69%
ANS:
REF:
OBJ:
COG:
B
PTS: 1
DIF: Medium
Significance Versus Meaningfulness (Again, Again!)
The important distinction between significance and meaningfulness (again!)
Application
35. If a simple Pearson correlation value = .362, what percentage of variance is unaccounted for?
a. 25%
b. 36%
c. 56%
d. 87%
ANS:
REF:
OBJ:
COG:
D
PTS: 1
DIF: Medium
Significance Versus Meaningfulness
(Again, Again!)
The important distinction between significance and meaningfulness (again!)
Application
36. If a simple Pearson correlation value = .75, what percentage of variance is unaccounted for?
a. 25%
b. 44%
c. 56%
d. 75%
ANS:
REF:
OBJ:
COG:
B
PTS: 1
DIF: Medium
Significance Versus Meaningfulness (Again, Again!)
The important distinction between significance and meaningfulness (again!)
Application
37. If you were looking to examine the relationship between chocolate sales and student
happiness, you could test the relationship using the _______.
a. Mean difference
b. t statistic
c. Error difference
d. c statistic
ANS:
REF:
OBJ:
COG:
B
PTS: 1
DIF: Medium
The Path to Wisdom and Knowledge
How to test the significance of the correlation coefficient
Application
38. You would like to examine the association between temperature and frozen yogurt sales. You
hypothesize
that higher temperatures will be associated with increased frozen yogurt sales.
You have a _______.
a. One-tailed hypothesis
b. Two-tailed hypothesis
c. Nondirectional hypothesis
d. Invalid hypothesis
ANS: A
PTS: 1
DIF: Medium
REF: Computing the Test Statistic
OBJ: How to test the significance of the correlation coefficient
COG: Application
39. Which of the following indicates a significant correlation?
a. p = .21
b. p < .05
c. p < .20
d. p
< .50
ANS: B
PTS: 1
DIF: Medium
OBJ: How to interpret the correlation coefficient
REF: Computing the Test Statistic
COG: Comprehension
40. Which of the following indicates a NONsignificant correlation?
a. p < .05
b. p < .01
c. p = .02
d. p = .30
ANS: D
PTS: 1
DIF: Medium
REF: Computing the Test Statistic
OBJ: How to interpret the correlation coefficient
COG: Comprehension
41. When computing a correlation coefficient, if you have 36 degrees of freedom, your sample
size must be _______.
a. 35
b. 34
c. 38
d. 37
ANS: C
PTS: 1
DIF: Medium
OBJ: How to interpret the correlation coefficient
REF: Computing the Test Statistic
COG: Application
42. A professor hypothesizes that there will be a relationship between couples’ listening skills and
length of marriage. She has a _______.
a. One-tailed hypothesis
b. Invalid hypothesis
c. Valid
hypothesis
d. Two-tailed hypothesis
ANS: D
PTS: 1
DIF: Medium
OBJ: How to interpret the correlation coefficient
REF: Computing the Test Statistic
COG: Application
43. A professor hypothesizes that there will be a positive relationship between couples’ listening
skills and length of marriage. She has a _______.
a. One-tailed hypothesis
b. Invalid hypothesis
c. Valid hypothesis
d. Two-tailed hypothesis
ANS: A
PTS: 1
DIF: Medium
OBJ: How
to interpret the correlation coefficient
REF: Computing the Test Statistic
COG: Application
44. A _______ correlation is also known as a _______ correlation.
a. Negative; direct
b. Negative; nondirectional
c. Positive; direct
d. Positive; nondirectional
ANS: C
PTS: 1
DIF: Easy
OBJ: How to interpret the correlation coefficient
REF: Computing the Test Statistic
COG: Knowledge
TRUE/FALSE
1. Correlation coefficients examine the relationship
between variables.
ANS: T
PTS: 1
DIF: Medium
REF: The Path to Wisdom and Knowledge
OBJ: How to interpret the correlation coefficient
COG: Knowledge
2. A correlation coefficient can only test one variable at a time.
ANS: F
PTS: 1
DIF: Medium
REF: The Path to Wisdom and Knowledge
OBJ: How to interpret the correlation coefficient
COG: Knowledge
3. The appropriate test statistic to use is the t-test for the correlation
coefficient.
ANS: T
PTS: 1
DIF: Medium
REF: The Path to Wisdom and Knowledge
OBJ: How to interpret the correlation coefficient
COG: Knowledge
4. With regard to correlations, tests can be either directional or nondirectional.
ANS: T
PTS: 1
DIF: Medium
OBJ: How to interpret the correlation coefficient
REF: Computing the Test Statistic
COG: Comprehension
5. A significant correlation does not indicate causality.
ANS: T
PTS: 1
REF: Causes
and Associations (Again!)
COG: Comprehension
DIF: Medium
OBJ: How to interpret the correlation coefficient
6. A significant correlation indicates a meaningful relationship.
ANS:
REF:
OBJ:
COG:
T
PTS: 1
DIF: Medium
Significance Versus Meaningfulness (Again, Again!)
The important distinction between significance and meaningfulness (again!)
Application
7. If two variables are significantly correlated, this means that one variable causes the
other.
ANS: F
PTS: 1
REF: Causes and Associations (Again!)
COG: Comprehension
DIF: Medium
OBJ: How to interpret the correlation coefficient
8. The correlation coefficient can only be used for one-tailed tests.
ANS: F
PTS: 1
DIF: Medium
REF: Computing the Test Statistic
OBJ: How to test the significance of the correlation coefficient
COG: Application
9. Correlations can be used to examine the differences between groups.
ANS: F
PTS:
1
DIF: Medium
REF: The Path to Wisdom and Knowledge
OBJ: How to interpret the correlation coefficient
COG: Knowledge
10. A single correlation can be computed in order to determine the relationship between three
variables.
ANS:
REF:
OBJ:
COG:
F
PTS: 1
DIF: Medium
The Path to Wisdom and Knowledge
How to test the significance of the correlation coefficient
Comprehension
11. Dr. Moo would like to examine differences in milk production between goats that listen to
soft-jazz music and goats that listen to heavy-metal music. She will be able to test this using a
correlation coefficient.
ANS: F
PTS: 1
DIF: Medium
REF: The Path to Wisdom and Knowledge
OBJ: How to interpret the correlation coefficient
COG: Comprehension
12. The Greek letter rho represents the sample estimate of the correlation coefficient.
ANS: F
PTS: 1
DIF: Medium
OBJ: How to interpret the correlation
coefficient
REF: Computing the Test Statistic
COG: Comprehension
13. For your purposes, you may use the CORREL function, Correlation tool, and PEARSON
function in Excel interchangeably.
ANS: T
PTS: 1
DIF: Easy
OBJ: How to interpret the correlation coefficient
REF: Computing the Test Statistic
COG: Knowledge
SHORT ANSWER
1. Give an example of a one-tailed hypothesis that may be tested through a correlation.
ANS:
Example: Higher crime rates will be
associated with lower income levels.
PTS: 1
DIF: Medium
REF: Computing the Test Statistic
OBJ: How to test the significance of the correlation coefficient
COG: Application
2. Think about the t-test for the correlation coefficient. Write the equations for a research
hypothesis with a one-tailed test and for a research hypothesis with a two-tailed test. Write the
equation for the null hypothesis.
ANS:
One-tailed test H1: rxy > 0 or H1: rxy <
0
Two-tailed test H1: rxy 0
Null hypothesis H0: xy = 0
PTS: 1
DIF: Hard
REF: Computing the Test Statistic
OBJ: How to interpret the correlation coefficient
COG: Application
3. Write an example of a research hypothesis for a one-tailed t-test for the correlation coefficient.
ANS:
An example of a research hypothesis for a one-tailed t-test for the correlation coefficient
would be that there will be a positive correlation between number of hours studied and
one’s
grade on a test.
PTS: 1
DIF: Medium
REF: Computing the Test Statistic
OBJ: How to interpret the correlation coefficient
COG: Application
4. Write an example of a research hypothesis for a two-tailed t-test for the correlation
coefficient.
ANS:
An example of a research hypothesis for a two-tailed t-test for the correlation coefficient
would be that there will be a relationship between number of hours studied and one’s grade on
a test.
PTS:
1
DIF: Medium
REF: Computing the Test Statistic
OBJ: How to interpret the correlation coefficient
COG: Application
5. Write an example of a null hypothesis for a t-test for the correlation coefficient.
ANS:
An example of a null hypothesis for a t-test for the correlation coefficient would be that there
is no relationship between number of hours studied and one’s grade on a test.
PTS: 1
DIF: Medium
REF: Computing the Test Statistic
OBJ: How to interpret the
correlation coefficient
COG: Application
6. What are the eight steps involved when examining a research question?
ANS:
Step 1: State the null and research hypothesis.
Step 2: Set the level of significance associated with the null hypothesis.
Steps 3 and 4: Select the appropriate test statistic.
Step 5: Determine the critical value (using appropriate tables).
Step 6: Compare the obtained value and the critical value.
Steps 7 and 8: Make a decision (as to whether to
accept or reject the null hypothesis).
PTS: 1
DIF: Hard
REF: Computing the Test Statistic
OBJ: How to test the significance of the correlation coefficient
COG: Knowledge
7. The research hypothesis posits that the relationship between two variables will be greater than
zero (H1: rxy > 0). What would be concluded for r(29) = .467, p < .05?
ANS:
The obtained value (.467) is greater than the critical value (.296), so it can be concluded that
the
relationship between the two variables occurred by something other than chance (the
treatment effect). Furthermore, the research hypothesis, which posits a positive relationship
between the variables, is also supported.
PTS: 1
DIF: Hard
REF: Computing the Test Statistic
OBJ: How to interpret the correlation coefficient
COG: Application
8. The research hypothesis posits that there will be a relationship between the number of hours a
student studies and their result on a test (H1: rxy ?0? 0). What would be concluded for r(45) =
.213, p > .05?
ANS:
The obtained value (.213) is less than the critical value (.2875), so it cannot be concluded that
the relationship between the two variables occurred by something other than chance.
Furthermore, the research hypothesis, which posits a relationship between the variables, is
also not supported.
PTS: 1
DIF: Hard
REF: Computing the Test Statistic
OBJ: How to interpret the
correlation coefficient
COG: Application
9. The research hypothesis posits that the more caffeine consumed by a subject, the longer a
subject will stay awake (H1: rxy > 0). What would be concluded for r(10)= .653, p < .05?
ANS:
The obtained value (.653) is greater than the critical value (.4973), so it can be concluded that
the relationship between the two variables occurred by something other than chance.
Furthermore, the research hypothesis, which posits a
positive relationship between the
variables, is also supported.
PTS: 1
DIF: Hard
REF: Computing the Test Statistic
OBJ: How to interpret the correlation coefficient
COG: Application
10. Give an example of a situation when it would be appropriate to use the t-test for the
correlation coefficient test statistic.
ANS:
A study comparing the relationship of the satisfaction level of dog owners to the degree to
which they liked cats would use the t-test for the
correlation coefficient test statistic.
PTS: 1
DIF: Hard
REF: Computing the Test Statistic
OBJ: How to interpret the correlation coefficient
COG: Application
11. Students participated in a study of the relationship between confidence and college success,
with the results, r = .78, indicating that 61% of the variance in college success was accounted
for by the students’ confidence. Upon learning this, your statistics classmate decided that if he
worked
to increase his confidence, he would certainly become more successful in college.
What would you say to him in response to his idea?
ANS:
You could remind your classmate that although the correlation was strong, and much of the
variance was accounted for by confidence, confidence still does not cause college success.
PTS: 1
DIF: Hard
REF: Causes and Associations (Again!)
OBJ: How to interpret the correlation coefficient
COG: Analysis
12. Dr. Moo hypothesizes that
there will be an association between grass consumption and milk
production among goats. What kind of hypothesis is this (one tailed or two tailed), and why?
ANS:
This is a two-tailed hypothesis because Dr. Moo has not predicted a direction for the
hypothesized relationship.
PTS: 1
DIF: Hard
REF: Computing the Test Statistic
OBJ: How to interpret the correlation coefficient
COG: Analysis
13. The research hypothesis posits that the treatment association between
two variables will be
greater than zero (H1: rxy > 0). What would be concluded for r(29) = .267, p > .05?
ANS:
The obtained value (.267) is less than the critical value (.296), so it can be concluded that the
relationship between the two variables may have occurred due to chance.
PTS: 1
DIF: Hard
REF: Computing the Test Statistic
OBJ: How to interpret the correlation coefficient
COG: Application