QUESTIONS FOR REVIEW AND CRITICAL THINKING/ANSWERS
1. What tests of difference are appropriate in the following situations?
a. Average campaign contributions (in $) to a marketing campaign for healthy living for men and
women are to be compared.
b. Average contributions (in $) to a marketing campaign for healthy living for people who are 20-30
years old, 30-40 years old, and 40-6- years old are to be compared.
c. Human resource managers and chief executive officers have responded “yes,” “no,” or “not sure”
to an attitude question. The HR and CEO responses are to be compared.
d. One-half of a sample received an incentive in a mail survey while the other half did not. A
comparison of response rates is desired.
e. A researcher believes that married men will push the grocery cart when grocery shopping with
their wives. How would the hypothesis be tested?
f. A manager wishes to compare the job performance of a salesperson before ethics training with the
performance of that same salesperson after ethics training.
2. Perform a 2 test on the following data:
a. Regulation is the best way to ensure safe products.
Agree Disagree No Opinion
Managers 58 66 8
2 = 6.24, d.f. = 2. From Table A.4 in the Appendix, we see that the critical value at the 0.05 probability
b. Ownership of residence
3. Interpret the following computer cross-tab output including a 2 test. Variable COMMUTE is “How
did you get to work last week?” Variable GENDER is “Are you male or female?” Comment on any
particular problems with the analysis (Computer output in textbook.)
The chi square value of 7.751 with 4 degrees of freedom indicates that this test is not statistically
significant at the 0.05 level. The cross-tabs indicate that 7.0% of women work at home compared to
4. A store manager’s computer-generated list of all retail sales employees indicates that 70 percent are
full-time employees, 20 percent are part-time employees, and 10 percent are furloughed or laid-off
employees. A sample of 50 employees from the list indicates that there are 40 full-time employees, 6
part-time employees and 4 furloughed/laid-off employees. Conduct a statistical test to determine if
the sample is representative of the population.
Population Expected Observed
Distribution Frequency Frequency
X
2
= å 0
i
– E
i
( )
2
E
i
= 40 – 35
( )
2
35 + 6 – 10
( )
2
10 + 4 – 5
( )
2
5 = 5
( )
2
35 + – 4
( )
2
10 + 1
( )
2
5 =
25
35 +
16
10 +
1
5 =
. 71+ 1 . 6 + . 2 = 2 . 51
d.f. = K – 1 = 3 – 1 = 2
Not significant at = 0.05. The p-value is 0.285.
Yes No
5. Test the following hypothesis using the data summarized in the table below. Interpret your result:
H1: Internet retailers offer lower prices for Blu-ray players than do traditional in-store
retailers.
Retail Type Blu-ray Player Average Price Standard
Deviation
n
6. How does an independent samples t-test differ from the following?
First, an independent samples t-test should be explained. When a researcher needs to compare means for
a variable grouped into two categories based on some less than interval variable, a t-test is appropriate.
a. one-way ANOVA
When the means of more than two groups or populations are to be compared, one-way ANOVA is the
b. paired samples t-test
c. a 2 test
d. a Z-test for differences
7. Are t-tests or Z-tests used more often in business research? Why?
Oftentimes, a t-test is used even though the sample size is greater than 30. Strictly speaking, a Z-test
8. A sales force received some management-by-objectives training. Are the before/after mean scores for
salesmen’s job performance statistically significant at the 0.05 level? The results from the sample of
employees are as follows (use your computer and statistical software to solve this problem):
Skill Before After
Ed 4.84 5.43
Mark 5.24 5.51
Jason 5.37 5.42
SPPS Output:
Paired Samples Statistics
Mean N Std. Deviation Std. Error Mean
Paired Samples Test
Paired Differences
Mean Std. Deviation Std. Error Mean
95% Confidence Interval of the
Difference
t df Sig. (2-tailed)Lower Upper
The mean “after” score is higher than the mean “before,” but only at the 0.1 level of significance, not the
p < 0.05 level.
9. Conduct a Z-test to determine whether the following two samples indicate that the population
proportions are significantly different at the 0.05 level.
Sample 1 Sample 2
10. In an experiment with wholesalers, a researcher manipulated perception of task difficulty and
measured level of aspiration for performing the task a second time. Group 1 was told the task was
very difficult, group 2 was told the task was somewhat difficult but attainable, and group 3 was told
the task was easy. Perform an ANOVA on the resulting data:
LEVEL OF ASPIRATION
(10-POINT SCALE)
Subject
sGroup 1 Group 2 Group 3
1 6 5 5
SPSS Output:
Descriptives
aspiration
N Mean Std. Deviation Std. Error
95% Confidence Interval for Mean
Minimum MaximumLower Bound Upper Bound
ANOVA
aspiration
Sum of Squares df Mean Square F Sig.
11. Interpret the following output (see the textbook for the output) examining group differences for
purchase intentions. The three groups refer to consumers from three states: Illinois, Louisiana, and
Texas.
RESEARCH ACTIVITIES
1. [Ethics Question/Internet Question] How ethical is it to do business in different countries around the
world? An international organization, Transparency International, keeps track of the perception of
ethical practices in different countries. Visit the Web site and search for the CPI
(http://www.transparency.org/policy_and_research/surveys_indices/cpi). Using the data found here,
test the following research questions.
a. Are Nations from Europe and North America perceived to be more ethical than
nations from Asia, Africa and South America?
b. Are there differences in the corruption indices in the past 5 years (between 2003 and
2008)?
Results of these analyses will vary depending on when students collect this data and which countries they
include in the analyses. For example, corruption perception indices (CPIs) are given for 180 countries.
2. [Internet Question] The Bureau of Labor Statistics of the United States Government maintains a
website that contains current and historic data related to the United States economy. Navigate to the
BLS website at http://www.bls.gov. In the “Latest Numbers” section, select the small dinosaur next
to the Unemployment Rate link. Select a year and its 12-month unemployment data, and then select
the most current year for comparison. What statistical tests are appropriate?
CASE 22.1 Old School versus New School Sports Fans
Data: Students are instructed to download the data from the website or to request them from the
instructor.
Objective: Illustrating the analysis of a chi-square test from an SPSS computer program is the purpose of
this case.
Summary: Three academic researchers investigated the idea that, in America in sports, there are two
segments with opposing views of what each considers as the goal of competition (i.e., winning versus
self-actualization) and the acceptable/desirable way of achieving this goal. Persons who believe in
“winning at any cost” are proponents of sports success as a product and can be labeled new school (NS)
individuals. The new school is founded on notions of the player before the team, loyalty to the highest
bidder, and high-tech production and consumption of professional sports. On the other hand, persons who
value the process of sports, and believe that “how you play the game matters,” can be labeled old school
(OS) individuals. The old school emerges from old-fashioned American notions of the team before the
player, sportsmanship and loyalty above all else, and competition simply for the “love of the game.”
New school was measured by asking agreement with ten attitude statements. Higher scores represent old
school values. For this case the scores were grouped into high, medium, and low groups. Case Exhibit
22.1-1 shows the SPSS output of a cross-tabulation to relate the gender of the respondent with the New
School/Old School grouping.
Questions
1. Interpret the computer output. What do the results presented above indicate?
Two-Way Frequency Table with Chi-square Test:
The title of the two-way frequency table is printed OLDSKOOL*GENDER. The variable OLDSKOOL is
9 count
This cell can be compared for men who are high on the scale. It indicates there is a very small percentage
The next task is to determine if in fact these differences are statistically significant. Beneath the two-way
frequency table is a frequency table where we have our raw chi-square value of 6.557 indicated with the
Managerial Implications of Chi-Square Test:
One of the more important concepts in marketing management is that of market segmentation. Our
two-way frequency table indicates that there are sex differences in terms of new school values.
2. Is the analytical approach used here appropriate?
3. Describe an alternative approach to the analysis of the original data. Which of these two analyses
would you suggest using?
New School/Old School was originally assessed using ten attitude statements that were combined, with