Test bank herman aguinis – performance management ch22

Chapter 22—Bivariate Statistical Analysis: Differences Between Two Variables
TRUE/FALSE
1. Business researchers frequently use cross-tabulation techniques in data analysis.
ANS: T
PTS: 1
NAT: AACSB: Reflective Thinking

REF: p. 530

2. When the difference between two groups is measured, this is a form of bivariate statistics.
ANS: T
PTS: 1
NAT: AACSB: Reflective Thinking

REF: p. 530

3. A statistical test that is used often in business research tests the difference between two groups in terms
of some behavior (e.g. attitude).
ANS: T
PTS: 1
NAT: AACSB: Reflective Thinking

REF: p. 530

4. If a researcher is interested in whether males file work grievances more frequently than females, this is
an example of univariate statistics.
ANS: F
This is an example of bivariate statistics.
PTS: 1

REF: p. 530

NAT: AACSB: Reflective Thinking

5. A cross-tabulation is a simple way to describe the relationships between two groups.
ANS: T
PTS: 1
NAT: AACSB: Reflective Thinking

REF: p. 530

6. One way to test the significance of contingency tables is by means of the chi-square test.
ANS: T
PTS: 1
NAT: AACSB: Reflective Thinking

REF: p. 530

7. To use the chi-square test, both variables in a 2 x 2 contingency table must be measured on a ratio
scale.
ANS: F
A frequency count of data that nominally identify or categorically rank groups is acceptable.
PTS: 1

REF: p. 530

NAT: AACSB: Reflective Thinking

8. The chi-square test requires the researcher to compare the observed frequencies of the groups with the
expected frequencies of the groups.
ANS: T

PTS: 1
NAT: AACSB: Reflective Thinking

REF: p. 532

© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in
whole or in part.


9. The chi-square test tests the significance of the data in an R X C contingency table in which R stands
for row and C stands for column.
ANS: T
PTS: 1
NAT: AACSB: Reflective Thinking

REF: p. 532

10. The chi-square test requires that the expected frequency in each cell of the contingency table be at least
30.
ANS: F
The expected frequency in each cell should be at least 5.
PTS: 1

REF: p. 534

NAT: AACSB: Reflective Thinking

11. The independent samples t-test tests the differences between means taken from two independent
samples or groups.
ANS: T

PTS: 1
NAT: AACSB: Reflective Thinking

REF: p. 534

12. The t-test for comparing the means of two groups assumes that the data are in nominal scales.
ANS: F
It tests a dichotomous (two-level) independent variable associated with changes in a continuous
dependent variable.
PTS: 1

REF: p. 534

NAT: AACSB: Reflective Thinking

13. A pooled estimate of the standard error is a poorer estimate of the standard error than one based on the
variance from either sample.
ANS: F
A pooled estimate of the standard error is a better estimate.
PTS: 1

REF: p. 535

NAT: AACSB: Reflective Thinking

14. The degrees of freedom are calculated as d.f. = n − 1 when using the t-test for comparing two means.
ANS: F
In a test of two means, degrees of freedom are calculated as d.f. = n − k, where n = n1 + n2 and k =
number of groups.
PTS: 1

REF: p. 536

NAT: AACSB: Reflective Thinking

15. In practice, t-test results are commonly calculated by hand because they are so simple.
ANS: F
In practice, computer software is used to compute the t-test results.
PTS: 1

REF: p. 536

NAT: AACSB: Reflective Thinking

16. When no direction of a relationship is stated in the hypothesis, a one-tailed test is appropriate.
© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in
whole or in part.


ANS: F
A two-tailed test is appropriate.
PTS: 1

REF: p. 536

NAT: AACSB: Reflective Thinking

17. The first basic step in interpreting t-test results is to find the p-value associated with a particular t and
the corresponding degrees of freedom.
ANS: F

This is the third step. The first step is to examine the difference in means to find the “direction” of any
difference.
PTS: 1

REF: pp. 536-537

NAT: AACSB: Reflective Thinking

18. The t-test assumes that the two population variances are equal.
ANS: T
PTS: 1
NAT: AACSB: Reflective Thinking

REF: p. 538

19. Means that appear to be not so close to each other are usually statistically concluded that they are
different.
ANS: T
Even though mans appear to be not so close to each other, the statistical conclusion could be that they
are the same.
PTS: 1

REF: p. 538

NAT: AACSB: Reflective Thinking

20. A t-test is not appropriate and should not be used when the sample size is greater than 30.
ANS: T
Researchers often employ a t-test even with large samples. As samples get larger, the t-test and Z-test
will tend to yield the same results.

PTS: 1

REF: p. 538

NAT: AACSB: Reflective Thinking

21. A redundant-sample t-test is an appropriate test for comparing the scores of two interval drawn from
related populations.
ANS: F
This is referred to as a paired-sample t-test.
PTS: 1

REF: p. 538

NAT: AACSB: Reflective Thinking

22. A Z-test for differences of proportions requires a sample size greater than 100.
ANS: F
It requires a sample size greater than 30.
PTS: 1

REF: p. 540

NAT: AACSB: Reflective Thinking

23. The null hypothesis for an ANOVA test comparing the means of three groups is: µ1 = µ2 = µ3.

© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in
whole or in part.

ANS: T
PTS: 1
NAT: AACSB: Reflective Thinking

REF: p. 541

24. The total mean is the mean of a variable over all observations.
ANS: F
This is called the grand mean.
PTS: 1

REF: p. 544

NAT: AACSB: Reflective Thinking

25. The F-test partitions the total variance into within-group variance and between-group variance.
ANS: T
PTS: 1
NAT: AACSB: Reflective Thinking

REF: p. 546

MULTIPLE CHOICE
1. A researcher hypothesizes that males and females differ with respect to attitude toward sports
sponsorships. To investigate this hypothesis that these two groups’ attitudes differ, he will use a:
a. bivariate test of differences
b. univariate test of differences
c. multivariate test of differences
d. cluster analysis

ANS: A
PTS: 1
NAT: AACSB: Reflective Thinking

REF: p. 530

2. Another name for a cross-tabulation is:
a. ANOVA
b. Z-test
c. contingency table
d. between-group variance
ANS: C
PTS: 1
NAT: AACSB: Reflective Thinking

REF: p. 530

3. The formula given below represents the method for calculating the:

a.
b.
c.
d.

Z-test
F-test
χ2 test
α

ANS: C

PTS: 1
NAT: AACSB: Reflective Thinking

REF: p. 532

4. The formula for the chi-square test uses:
a. observed and expected frequencies
b. observed and expected percentages
c. the two sample means
© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in
whole or in part.


d. the two sample standard deviations
ANS: A
PTS: 1
NAT: AACSB: Reflective Thinking

REF: p. 532

5. How many degrees of freedom are there in a four-cell chi-square test?
a. (R + 1)
b. (R - 1)
c. (R - 1)(C - 1)
d. R(C - 1)
ANS: C
PTS: 1
NAT: AACSB: Reflective Thinking

REF: p. 533

6. If 25 of the 35 females in a research study agree with a statement, and 15 of the 35 males agree with
this statement, the expected value for males-agree is:
a. 15
b. 20
c. 25
d. 35
ANS: B
PTS: 1
REF: p. 533
NAT: AACSB: Reflective Thinking|AACSB: Analytic
7. In a brand awareness study, if 25 of a group of 35 males identify the brand correctly and 15 of a group
of 35 females identify this brand correctly, the chi-square value for this study is approximately:
a. 3.26
b. 4.15
c. 5.84
d. 2.92
ANS: C
PTS: 1
REF: p. 533
NAT: AACSB: Reflective Thinking| AACSB: Analytic
8. If the critical value of chi-square in the chi-square table is 3.84, and the obtained value of chi-square in
the study is 3.45, the researcher should:
a. reject the null hypothesis
b. accept the null hypothesis
c. accept the research hypothesis
d. reject both the null and the research hypotheses
ANS: B
PTS: 1
NAT: AACSB: Reflective Thinking

REF: p. 533

9. In order to use the chi-square test, the expected frequency in each of the cells of the contingency table
should be at least:
a. 2
b. 5
c. 30
d. 40
ANS: B
PTS: 1
REF: p. 535
NAT: AACSB: Reflective Thinking| AACSB: Analytic
10. In using the t-test to compare the means of two groups, the alternative hypothesis is typically stated as:
a. µ1 ≠ µ2
© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in
whole or in part.


b. µ1 = µ2
c. µ1 - µ2 = 2
d. µ1 + µ2 = 1
ANS: A
PTS: 1
NAT: AACSB: Reflective Thinking

REF: p. 535

11. In comparing the difference of the means between two groups, the null hypothesis can also be stated
as:

a. µ1 - µ2 = 0
b. µ1 + µ2 = 0
c. µ1 x µ2 = 0
d. µ1 / µ2 = 0
ANS: A
PTS: 1
NAT: AACSB: Reflective Thinking

REF: p. 535

12. Another form of the alternative hypothesis when testing the difference between the means of the two
groups is:
a. µ1 - µ2 = 0
b. µ1 - µ2 ≠ 0
c. µ1 - µ2 = 2
d. µ1 - µ2 ≠ 2
ANS: B
PTS: 1
NAT: AACSB: Reflective Thinking

REF: p. 535

13. Supposed you used a 10-point rating scale to measure intention-to-buy (1 = definitely would not buy
and 10 = definitely would buy). If a group of 40 males had a mean of 7 and a standard deviation of
2.5, while a group of 35 females had a mean of 5 and a standard deviation of 1.4, the standard error of
the difference between the means would be approximately:
a. 0.48
b. 1.36
c. 2.45
d. not enough information to determine

ANS: A
PTS: 1
REF: p. 535
NAT: AACSB: Reflective Thinking| AACSB: Analytic
14. In using the t-test to compare the means of two groups, the degrees of freedom are:
a. n1 - n2 - 2
b. n1 + n2 - 2
c. n1 x n2 -2
d. n1 / n2 - 2
ANS: B
PTS: 1
NAT: AACSB: Reflective Thinking

REF: p. 536

15. Suppose that you used a 9-point rating scale and that you wanted to compare men who had an annual
income over $50,000 (Group 1) with men who had an annual income less than or equal to $50,000
(Group 2) on their liking of a new product. If you studied 40 men in Group 1 and they have a mean of
7 and a standard deviation of 2.5, while the 35 men in Group 2 have a mean of 5 and a standard
deviation of 1.4, what is the approximate value of t using the t-test?
a. 3.43
© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in
whole or in part.


b. 4.19
c. 2.64
d. not enough information to determine
ANS: B
PTS: 1

REF: p. 536
NAT: AACSB: Reflective Thinking| AACSB: Analytic
16. In a study comparing the means of two groups in which there are 45 males in Group 1 and 37 females
in Group 2, the degrees of freedom for this study when using the t-test for the difference between
means is:
a. 84
b. 80
c. 82
d. 160
ANS: B
PTS: 1
REF: p. 536
NAT: AACSB: Reflective Thinking| AACSB: Analytic
17. In practice, what is the first step in interpreting the t-test when comparing two means?
a. compute the t-test value
b. find the p-value associated with the t and the corresponding degrees of freedom
c. examine the difference in means to find the “direction” of any difference
d. examine if there is a difference at the 50 percent confidence interval before examining the
95 percent confidence interval
ANS: C
PTS: 1
NAT: AACSB: Reflective Thinking

REF: p. 536

18. Which test is appropriate for comparing the scores of two interval variables drawn from related
populations?
a. ANOVA
b. relative t-test
c. relative χ2 test

d. pair-samples t-test
ANS: D
PTS: 1
NAT: AACSB: Reflective Thinking

REF: p. 538

19. In using the Z-test for comparing two proportions, the null hypothesis is typically stated as:
a. π1 = π2.
b. π1 ≠ π2.
c. π1 x π2 = 1
d. π1 - π2 = 1
ANS: A
PTS: 1
NAT: AACSB: Reflective Thinking

REF: p. 540

20. The alternative hypothesis when using the Z-test for the difference between the proportions for two
groups is:
a. π1 = π2
b. π1 ≠ π2.
c. π1 x π2 = 2
d. π1 / π2 = 2
ANS: B

PTS: 1

REF: p. 540

© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in
whole or in part.


NAT: AACSB: Reflective Thinking
21. In using the Z-test for comparing two proportions, if the pooled estimate of the proportion of successes
is 0.36, then the pooled estimate of proportion of failures is:
a. 1
b. 0.36
c. 0.64
d. 0.13
ANS: C
PTS: 1
REF: p. 540
NAT: AACSB: Reflective Thinking| AACSB: Analytic
22. Suppose that you wanted to determine if the males in your sales force differed from the females in
your sales force in the proportion of sales that they made to mass merchandiser chains. Your data
show that the 80 males had 40% of their sales to these chains, while the 60 females had 25% of their
sales to these chains. For these data, the standard error of the difference in proportions is
approximately:
a. 0.08
b. 0.15
c. 0.02
d. 1.67
ANS: A
PTS: 1
REF: p. 541
NAT: AACSB: Reflective Thinking| AACSB: Analytic
23. In an ANOVA test of the differences between the means of three groups, the null hypothesis is:
a. µ1 = µ2 = µ3

b. µ1 ≠ µ2 ≠ µ3
c. µ1 - µ2 - µ3 = 0
d. µ1 + µ2 + µ3 = 1
ANS: A
PTS: 1
NAT: AACSB: Reflective Thinking

REF: p. 541

24. Which test should be used when comparing the means of three groups to see if they are significantly
different from one another?
a. One-group t-test
b. ANOVA test
c. Two-group t-test
d. Chi-square test
ANS: B
PTS: 1
NAT: AACSB: Reflective Thinking

REF: p. 541

25. The mean of a variable over all observations is called the:
a. master mean
b. average mean
c. grand mean
d. ANOVA mean
ANS: C
PTS: 1
NAT: AACSB: Reflective Thinking

REF: p. 544

26. Which of the following is the sum of differences between the group mean and the grand mean summed
over all groups for a given set of observations?
© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in
whole or in part.


a.
b.
c.
d.

between-groups variance
total error variance
F-statistic
χ2 value

ANS: A
PTS: 1
NAT: AACSB: Reflective Thinking

REF: p. 544

27. The sum of the differences between observed values and the group mean for a given set of
observations is known as the:
a. within-group error
b. between-groups variance
c. F-ratio
d. γ statistic

ANS: A
PTS: 1
NAT: AACSB: Reflective Thinking

REF: p. 545

28. The key statistical test for an ANOVA model is the:
a. χ2 test
b. t-test
c. F-test
d. Z-test
ANS: C
PTS: 1
NAT: AACSB: Reflective Thinking

REF: p. 545

29. The F-distribution is a function of:
a. SSB - SSE
b. SSE - SSB
c. SSB/SSE
d. SSE/SSB
ANS: C
PTS: 1
NAT: AACSB: Reflective Thinking

REF: p. 546

30. Practically speaking, what is the first thing a researcher should do when interpreting ANOVA results?
a. examine the actual means for each group

b. determine the between-groups variance
c. examine the total variance
d. check whether or not the overall model F is significant
ANS: D
PTS: 1
NAT: AACSB: Reflective Thinking

REF: p. 546

COMPLETION
1. A test of a hypothesis to determine if two groups differ with respect to the scores on one variable is
called a(n) ____________________.
ANS: test of differences
PTS: 1

REF: p. 530

NAT: AACSB: Reflective Thinking

© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in
whole or in part.


2. When two variables are studied simultaneously in a research study, this is called
____________________ statistical analysis.
ANS: bivariate
PTS: 1

REF: p. 530

NAT: AACSB: Reflective Thinking

3. The ____________________ test studies the significance of a joint frequency distribution.
ANS: chi-square
PTS: 1

REF: p. 530

NAT: AACSB: Reflective Thinking

4. The formula for determining the degrees of freedom for a chi-square test is ____________________.
ANS: (R - 1)(C - 1)
PTS: 1

REF: p. 533

NAT: AACSB: Reflective Thinking

5. When a researcher needs to compare means for a variable grouped into two categories based on some
less-than interval variable, a(n) ____________________ test is appropriate.
ANS: t
PTS: 1

REF: p. 534

NAT: AACSB: Reflective Thinking

6. In using the t-test to compare the difference between the means of two groups, the null hypothesis is
normally stated as ____________________.
ANS: µ1 = µ2

PTS: 1

REF: p. 535

NAT: AACSB: Reflective Thinking

7. In using the t-test to compare the difference between the means of two groups, the formula for
determining the degrees of freedom is ____________________.
ANS: n1 + n2 - 2
PTS: 1

REF: p. 536

NAT: AACSB: Reflective Thinking

8. One way to interpret the meaning of the results of the t-test is to focus on the ____________________
and the group means.
ANS: p-value
PTS: 1

REF: p. 538

NAT: AACSB: Reflective Thinking

9. An appropriate test for comparing the scores of two interval variables drawn from related populations
is the ____________________.
ANS: paired-samples t-test
PTS: 1

REF: p. 539

NAT: AACSB: Reflective Thinking

© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in
whole or in part.


10. The null hypothesis when using the Z-test for the differences between the proportions of two groups is
that ____________________.
ANS: π1 = π2
PTS: 1

REF: p. 540

NAT: AACSB: Reflective Thinking

11. ____________________ is the appropriate test to use when comparing the means of three or more
groups to see if they are significantly different from one another.
ANS: ANOVA
PTS: 1

REF: p. 541

NAT: AACSB: Reflective Thinking

12. The ____________________ is the mean of a variable over all observations.
ANS: grand mean
PTS: 1

REF: p. 544

NAT: AACSB: Reflective Thinking

13. The sum of differences between the group mean and the grand mean summed over all groups for a
given set of observations is called ____________________.
ANS: between-groups variance
PTS: 1

REF: p. 544

NAT: AACSB: Reflective Thinking

14. The statistical test that is used to compare the sample variance with another sample variance is the
____________________.
ANS: F-test
PTS: 1

REF: p. 545

NAT: AACSB: Reflective Thinking

15. The F-test partitions total variance into ____________________ variance and
____________________ variance.
ANS: within-group; between-group
PTS: 1

REF: p. 546

NAT: AACSB: Reflective Thinking

ESSAY
1. Explain what an independent samples t-test is and the null hypothesis examined.
ANS:
The independent samples t-test tests the differences between means taken from two independent
samples or groups. It is a test for hypotheses stating that the mean scores for some interval- or ratioscaled variable groups based on some less-than interval classificatory variable are not the same. Thus,
the null hypothesis is µ1 = µ2, which is equivalent to µ1 - µ2 = 0
PTS: 1

REF: pp. 534-535

© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in
whole or in part.


NAT: AACSB: Reflective Thinking|AACSB: Communication
2. List the practical steps for interpreting t-test results.
ANS:
The basic steps for interpreting t-test results are:
(1) Examine the difference in means to find the “directions” on any difference.
(2) Compare or locate the computed t-test value.
(3) Find the p-value associated with this t and the corresponding degrees of freedom.
(4) The difference can also be examined using the 95 percent confidence interval.
PTS: 1
REF: pp. 536-537
NAT: AACSB: Reflective Thinking|AACSB: Communication
3. Discuss when a paired-samples t-test is appropriate and give an example of when it should be used.
ANS:
A paired-samples t-test is an appropriate test for comparing the scores of two interval variables drawn
from related populations. This is the appropriate test when the same respondent is measured twice.
For example, respondents may be asked their attitudes toward corporate sponsorship in sports and their

attitudes toward corporate sponsorship of the arts. Since the attitude scores are both provided by the
same person, the assumption that they are independent is not realistic. When a paired-samples t-test is
appropriate, the two numbers being compared are usually scored as separate variables.
PTS: 1
REF: p. 538
NAT: AACSB: Reflective Thinking|AACSB: Communication
4. Explain what a Z-test for comparing two proportions is and the appropriate null hypothesis.
ANS:
A Z-test for differences of proportions is a technique used to test the hypothesis that proportions are
significantly different for two independent samples or groups. The null hypothesis is π1 = π2, which
may be restated as π1 - π2 = 0.
PTS: 1
REF: p. 540
NAT: AACSB: Reflective Thinking|AACSB: Communication
5. What is ANOVA and when is it the appropriate statistical technique? What test is used to determine
significance?
ANS:
ANOVA stands for analysis of variance and involves the investigation of the effects of one treatment
variable on an interval-scaled dependent variable. It is a hypothesis-testing technique to determine
whether statistically significant differences in means occur between two or more groups. The F-test is
the key statistical test for an ANOVA model.
PTS: 1
REF: pp. 541-546
NAT: AACSB: Reflective Thinking|AACSB: Communication

© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in
whole or in part.