Business Administration
Department
Optional Marketing Research
Statistical Data Analysis Problems
Prof.
Geoff Lantos
BA
341- Marketing Research
After working through assigned statistical
problems in the text and in class some students still feel that further
practice would be helpful in mastering techniques of data analysis. Therefore, you might wish to work on some or
all of the following problems for each chapter after we go over end-of-chapter
and other problems in class. I will post
answers to problems similar to those done in class within 24 hours after each
class (e.g., if we do problems to calculate a confidence interval on Tuesday in
class, I will post answers to the confidence interval problems below on
Wednesday).
Review
of Statistical Theory and Sample Size Decisions
1. Customer attitudes toward
the Fernordner Fund were collected on a five point rating scale (5= very
favorable, 1= very unfavorable).
Attitude scores for members of the "crotchety old men" psychographic
segment were as follows:
1, 3, 2, 1, 1, 4, 2, 2, 2, 5, 1, 3, 1, 1, 2.
Required:
a. Prepare a frequency
distribution for this data.
b. Prepare a percentage
distribution for this data.
c. What proportion of the
sample rated Fernordner 4 or 5?
d. Calculate the mean, median,
and mode for this data. Describe the
relationship between these three measures.
Are any of them more meaningful or typical than others?
e. What is the range for this
data set? The variance? The standard deviation? Which of these three measures is most useful
and why?
f. Describe the skewness of
this distribution.
2. Sales data for Mr. Roger's
neighborhood delicatessen for last month is normally distributed with a mean of
$16.45 (average customer purchase) and a variance of $5.50. This data is based on a sample size of 45
customers.
Required:
a. What percentage of
customers bought between $16.45 and $18.00 worth of goods?
b. What percentage of
customers bought between $12.00 and $15.00 worth of goods?
c. What percentage of
customers bought between $14.00 and $17.00 worth of goods?
d. What percentage of
customers bought less than $13.00 worth of goods?
e. At a confidence level of
90%, what is the range of average transaction sizes? What is this range for a 99% confidence
level? Which range is wider and why?
f. If the sample size had been
22 instead of 45, what would have been the 90% and 95% confidence
intervals? How does the 90% interval
compare in size to the 90% interval you calculated in part e and why?
3. Research on a sample of 60
customers reveals that the proportion of members of the neighborhood who shop
at Mr. Roger's neighborhood deli dropped to only 11% last month after Big Bird
led a boycott of the store due to the fact that Mr. Rogers was carrying girlie
magazines. Calculate a 95% confidence
interval for the proportion of customers who shop at Mr. Roger's deli.
4. The most important question
on a survey conducted by Wilma's Wonderful fashions will ask women respondents
in her trading area (universe of about 50,000 women) how frequently they wear
lace intimate apparel, in order to calculate the average monthly frequency of
wearing such garb (number of days per month).
Past studies on frequency of wearing underclothes suggest she can expect
a standard deviation of 3 days a month.
She wishes to have a margin of error no greater than 1 day per
month. The data will also allow her to
calculate the proportion of women who wear such underwear (let's call a spade a
spade) at least once a month. Past research
combined with her "expert" gut judgment suggests it will be about
70%. She wants a confidence level of 95%
(as is traditional for all her research).
Required:
a. If she is most concerned
with the mean frequency of product use, what sample size will Wilma need?
b. If she is willing to relax
her confidence level to 90%, what will be the required sample size? How does this compare to the sample size
calculated in part a. and why?
c. If she is willing to relax
her tolerable margin of error to 2 days per month, what will be the required
sample size for a 95% confidence level?
How does this compare to the sample size calculated in part a. and why?
d. Going back to part a,
assume the population consists of only 300 women. What would be the needed sample size? How does it compare with that calculated in
part a. and why?
e. If Wilma were most
concerned with calculating the proportion of product users, what would be the
required sample size if her margin of error were to be three percent?
f. What would be the needed
sample size in part e if she allowed a margin of error of 5 percent? How does this compare to your answer in part
e and why?
g. If Wilma expects a response
rate of 20% to this particular question, how many questionnaires will she need
to mail out to get the desired sample size for part f?
Data
Preparation and Processing
1. To the question, "Do
you ever skip your Marketing Research class just for the heck of it?" 30
students said yes, 60 students said no, and 10 students indicated that they
don't know.
Required:
Tabulate these responses using absolute numbers and percentages where:
a. You use "don't
know" as a separate response category.
b. You eliminate "don't
know" answers from the total response base.
c. You distribute "don't
know" responses proportionately among other response categories using the
original base.
2. Prof. Lantos distributed a
questionnaire at the end of the semester to students in his Marketing Research
class to get vital feedback. One of the
questions was: "I believe that this class was _____________." Postcode the following responses into
categories of your choosing.
1. "held too late in the
day."
2. "fundamentally
flawed."
3. "not composed of enough
hunks."
4. "boring."
5. "practical."
6. "stimulating."
7. "educational"
8. "too long each day."
9. "informative."
10. "devoid of practical
value."
11. "monotonous."
12. "a required course to put
us through pain and agony."
13. "extremely relevant."
14. "exciting."
15. "a piece of pie."
16. "hard work."
17. "a blow off."
18. "useless."
19. "pragmatic."
20. "difficult.”
21. "easy as pie."
22. "(expletive deleted).”
Required:
Postcode these responses into categories of your choosing.
3. The following questions
were part of a survey on characteristics of shoppers at Christina's Christian
Bookstore and Lottery Outlet:
1. How often do you shop at this store?
___ Every day
___ One to six days per week
___ Less than once per week but more
than once per month
___ Less than or equal to once per month
2. How many members, including yourself, live
in your household? ____
3. What kinds of books do you most frequently
buy in our store?
___ Bibles and/or Bible study tools
___ Bible prophecy
___ Christian living
___ Family/childcare/marriage issues
___ Social/political issues
___ Other
4. What is your educational level?
___ Less than ninth grade
___ Some high school
___ Some college
___ Some graduate school
___ Graduate school
5. What is your religious preference?
___ Evangelical Protestant
___ Charismatic Catholic
___ Mainline Protestant
___ Mainline Catholic
___ New Age
___ Eastern religion
___ Other
___ None
Required:
Design a codebook for this portion of the questionnaire.
Data
Tabulation, Summarization, and Interpretation
1. Twelve respondents were
asked the open-ended question, "What is your favorite flavor or flavors of
ice cream? Answers were as follows:
Mike - "tutti frutti and beet"
Spike - "peppermint patti"
Olga - "beet"
Horatio - "plain vanilla and chocolate;
I'm a boring person"
Millicent - "I don't do ice cream"
Zeke - "chocolate"
Tucker - "I don't like ice cream"
Morris - "vanilla and strawberry"
Ralph - "chocolate, vanilla, and
peppermint patti"
Alf - "strawberry"
Bernadette - "beet" (strange
sample of respondents!)
Fredette - "strawberry and beet
crunch" (very strange sample!!)
Required: Do a
one-way tabulation of this data four ways: using absolute frequencies for each
flavor, relative frequencies with number of responses as the base, relative
frequencies with number of respondents as the base, and relative frequencies
using a ghost question.
2. A survey of 15 Stonehill
students enrolled in "SO 459 - The Intergroup Dynamics of Swine" was
conducted to learn what kind of students takes such a course. The results were as follows:
Respondent # Gender Major
1 M Business RI
2 F Liberal Arts MA
3 F Liberal Arts NH
4 M Science MA
6 F Liberal Arts MA
7 M Business MA
8 F Liberal Arts NH
9 F Science MA
10 F Liberal Arts MA
11 M Business RI
13 M Liberal Arts MA
14 F Liberal arts NH
15 F Business MA
Required:
a. Cross-tabulate the
respondent's gender with whether or not they are a business major using
absolute frequencies, as well as relative frequencies. For the latter, in which direction did you
perform the cross tabulation and why?
b. Does there seem to be a
relationship between gender and major in this class? Explain.
c. Perform a three-way cross
tabulation for major and home state, holding gender constant (controlling for
gender).
d. Does gender serve as a
moderator variable for the relationship between major and home state?
3. Below are respondent
ratings on a five-point scale (five = high, 1 = low) for three socioeconomic
variables.
Respondent Educational Level Occupational Level After-Tax Income
Morticia 3 4 2
Beaver 2 1 v 5
Jeb 1 2 5
Granny 2 4 3
Required:
a. Calculate a social class
score for each respondent, where social class =
.5 (education level) + .3 (occupational level) + .2 (after tax income)
b. Rank order respondents
according to socioeconomic status.
4. Rank order preference data
for four brands of mock turtle soup is as follows:
Respondent Brand Timmy's Milly's Tilly's Pokey's
Arnie 1 3 2 4
Samantha 2 1 3 4
Cordelia 3 2 1 4
Wilfred 4 3 2 1
Georgette 2 3 1 4
Required: Rank
order these brands according to respondents' preferences.
5. Quarterly sales data for
Ollie's optical illusions is as follows:
Quarter Sales (000s)
1
$4567
2
$6798
3
$7704
4
$5720
Required:
Compute index numbers for each quarter.
What do the numbers for quarters 1 and 3 tell you?