Download IMBA 214 – Spring 2016 Take-Home Exam 1 Instructions: Take

IMBA 214 – Spring 2016
Take-Home Exam 1
Instructions:
1. Take-home exam 1 and corresponding combined data file are posted in the
“Exams” section on SacCT.
2. Please put all your answers, tables, charts, etc. in one Excel file. You may make a
separate worksheet for each question, or just answer the questions on one
worksheet, in order.
3. Name the Excel file with your solutions “Exam 1_Last name”.
4. Upload the Excel file on in the “Take-home exam 1” dropbox on SacCT before the
due date.
Chapter 1: Data and statistics
1. J. D. Power and Associates conducts vehicle quality surveys to provide automobile
manufacturers with consumer satisfaction information about their products (Vehicle Quality
Survey, January 2010). Using a sample of vehicle owners from recent vehicle purchase
records, the survey asks the owners a variety of questions about their new vehicles, such as
those shown below. For each question, state whether the data collected are categorical or
quantitative and indicate the measurement scale being used.
a. What price did you pay for the vehicle?
b. How did you pay for the vehicle? (Cash, Lease, or Finance)
c. How likely would you be to recommend this vehicle to a friend? (Definitely Not, Probably
Not, Probably Will, and Definitely Will)
d. What is the current mileage?
e. What is your overall rating of your new vehicle? A 10-point scale, ranging from 1 for
unacceptable to 10 for truly exceptional, was used.
2 The worksheet Shadow02 shows a data set containing information for 25 of the shadow
stocks tracked by the American Association of Individual Investors. Shadow stocks are
common stocks of smaller companies that are not closely followed by Wall Street analysts.
a. How many variables are in the data set?
b. Which of the variables are categorical and which are quantitative?
c. For the Exchange variable, show the frequency and the percent frequency for AMEX,
NYSE, and OTC. Construct a bar chart for the Exchange variable.
d. Show the frequency distribution for the Gross Profit Margin using the five intervals: 0–
14.9, 15–29.9, 30–44.9, 45–59.9, and 60–74.9. Construct a histogram.
e. What is the average price/earnings ratio?
Chapter 2: Descriptive statistics: Tabular and graphical presentations
3. In alphabetical order, the six most common last names in the United States are Brown,
Davis, Johnson, Jones, Smith, and Williams (U.S. Census Bureau website, November 1,
2010). A sample of 50 individuals with one of these last names is provided in the worksheet
Names.
Summarize the data by constructing the following:
a. Relative and percent frequency distributions
b. A bar chart
c. A pie chart
d. Based on these data, what are the three most common last names?
4. Fortune provides a list of America's largest corporations based on annual revenue. Shown
on the worksheet LargeCorp are the 50 largest corporations, with annual revenue expressed
in billions of dollars (CNN Moneywebsite, January 15, 2010).
Summarize the data by constructing the following:
a. A frequency distribution (classes 0–49, 50–99, 100–149, and so on).
b. A relative frequency distribution.
c. What do these distributions tell you about the annual revenue of the largest corporations
in America?
d. Show a histogram. Comment on the shape of the distribution.
e. What is the largest corporation in America and what is its annual revenue?
5. The worksheet Crosstab contains data for 30 observations involving two qualitative
variables, x and y. The categories for x are A, B, and C; the categories for y are 1 and 2.
a. Develop a crosstabulation for the data, with x as the row variable and y as the column
variable.
b. Compute the row percentages.
c. Compute the column percentages.
d. What is the relationship, if any, between x and y?
Chapter 3: Descriptive statistics: Numerical measures
6. The results of a national survey showed that on average, adults sleep 6.9 hours per night.
Suppose that the standard deviation is 1.2 hours.
a. Use Chebyshev's theorem to calculate the percentage of individuals who sleep between 4.5
and 9.3 hours.
b. Use Chebyshev's theorem to calculate the percentage of individuals who sleep between 3.9
and 9.9 hours.
c. Assume that the number of hours of sleep follows a bell-shaped distribution. Use the
empirical rule to calculate the percentage of individuals who sleep between 4.5 and 9.3 hours
per day. How does this result compare to the value that you obtained using Chebyshev's
theorem in part (a)?
7. The Associated Press Team Marketing Report listed the Dallas Cowboys as the team with
the highest ticket prices in the National Football League (USA Today, October 20, 2009).
Data showing the average ticket price for a sample of 14 teams in the National Football
League are shown in the worksheet NFLTickets.
a. What is the mean ticket price?
b. The previous year, the mean ticket price was $72.20. What was the percentage increase in
the mean ticket price for the one-year period?
c. Compute the median ticket price.
d. Compute the first and third quartiles.
e. Compute the standard deviation.
f. What is the z -score for the Dallas Cowboys ticket price? Should this price be considered an
outlier? Explain.
8. Naples, Florida, hosts a half-marathon (13.1-mile race) in January each year. The event
attracts top runners from throughout the United States as well as from around the world. In
January 2009, 22 men and 31 women entered the 19–24 age class. Finish times in minutes
are shown in the file Runners (Naples Daily News, January 19, 2009). Times are shown in
order of finish.
a. George Towett of Marietta, Georgia, finished in first place for the men and Lauren Wald of
Gainesville, Florida, finished in first place for the women. Compare the first-place finish
times for men and women. If the 53 men and women runners had competed as one group, in
what place would Lauren have finished?
b. What is the median time for men and women runners? Compare men and women runners
based on their median times.
c. Provide a five-number summary for both the men and the women.
d. Are there outliers in either group?
9. At the beginning of 2009, the economic downturn resulted in the loss of jobs and an
increase in delinquent loans for housing. The national unemployment rate was 6.5% and the
percentage of delinquent loans was 6.12% (The Wall Street Journal, January 27, 2009). In
projecting where the real estate market was headed in the coming year, economists studied
the relationship between the jobless rate and the percentage of delinquent loans. The
expectation was that if the jobless rate continued to increase, there would also be an increase
in the percentage of delinquent loans. The data in the file Housing show the jobless rate and
the delinquent loan percentage for 27 major real estate markets.
a. Compute the correlation coefficient. Is there a positive correlation between the jobless rate
and the percentage of delinquent housing loans? What is your interpretation?
b. Show a scatter diagram of the relationship between jobless rate and the percentage of
delinquent housing loans.
Chapter 4: Introduction to probability
10. Simple random sampling uses a sample of size n from a population of size N to obtain
data that can be used to make inferences about the characteristics of a population. Suppose
that, from a population of 50 bank accounts, we want to take a random sample of four
accounts in order to learn about the population. How many different random samples of four
accounts are possible?
11. A company that manufactures toothpaste is studying five different package designs.
Assuming that one design is just as likely to be selected by a consumer as any other design,
what selection probability would you assign to each of the package designs? In an actual
experiment, 100 consumers were asked to pick the design they preferred. The following data
were obtained. Do the data confirm the belief that one design is just as likely to be selected as
another? Explain.
Design
Number of Times Preferred
1
5
2
15
3
30
4
40
5
10
12. The U.S. Census Bureau provides data on the number of young adults, ages 18–24, who
are living in their parents' home. Let
M = the event a male young adult is living in his parents' home
F = the event a female young adult is living in her parents' home
If we randomly select a male young adult and a female young adult, the Census Bureau data
enable us to conclude P(M) = .56 and P(F) = .42 (The World Almanac, 2006). The probability
that both are living in their parents' home is .24.
a. What is the probability at least one of the two young adults selected is living in his or her
parents' home?
b. What is the probability both young adults selected are living on their own (neither is living
in their parents' home)?
13. In a survey of MBA students, the following data were obtained on "students' first reason
for application to the school in which they matriculated."
a. Develop a joint probability table for these data.
b. Use the marginal probabilities of school quality, school cost or convenience, and other to
comment on the most important reason for choosing a school.
c. If a student goes full time, what is the probability that school quality is the first reason for
choosing a school?
d. If a student goes part time, what is the probability that school quality is the first reason
for choosing a school?
e. Let A denote the event that a student is full time and let B denote the event that the
student lists school quality as the first reason for applying. Are events A and B independent?
Justify your answer.