Statistics for Business and Economics

David R. Anderson, Dennis J. Sweeney, Thomas A. Williams

Chapter 1

Data and Statistics - all with Video Answers

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Chapter Questions

Problem 1

Discuss the differences between statistics as numerical facts and statistics as a discipline or field of study.

Rashmi Sinha

Rashmi Sinha

Numerade Educator

Problem 2

Condé Nast Traveler magazine conducts an annual survey of subscribers in order to determine the best places to stay throughout the world. Table 1.6 shows a sample of nine European hotels (Condé Nast Traveler, January 2000 ). The price of a standard double room during the hotel's high season ranges from $\$$ (lowest price) to $\$ \$ \$ \$$ (highest price). The overall score includes subscribers' evaluations of each hotel's rooms, service, restaurants, location/atmosphere, and public areas; a higher overall score corresponds to a higher level of satisfaction.
a. How many elements are in this data set?
b. How many variables are in this data set?
c. Which variables are qualitative and which variables are quantitative?
d. What type of measurement scale is used for each of the variables?

Sandra Kudolo

Numerade Educator

Problem 3

Refer to Table 1.6
a. What is the average number of rooms for the nine hotels?
b. Compute the average overall score.
c. What is the percentage of hotels located in England?
d. What is the percentage of hotels with a room rate of $\$ \$ ?$

Sandra Kudolo

Numerade Educator

Problem 4

All-in-one sound systems, called minisystems, typically include an AM/FM tuner, a dualcassette tape deck, and a CD changer in a book-sized box with two separate speakers. The data in Table 1.7 show the retail price, sound quality, $\mathrm{CD}$ capacity, $\mathrm{FM}$ tuning sensitivity and selectivity, and the number of tape decks for a sample of 10 minisystems (Consumer Reports Buying Guide 2002 ).
a. How many elements does this data set contain?
b. What is the population?
c. Compute the average price for the sample.
d. Using the results in part (c), estimate the average price for the population.

Sandra Kudolo

Numerade Educator

Problem 5

Consider the data set for the sample of 10 minisystems in Table 1.7
a. How many variables are in the data set?
b. Which of the variables are quantitative and which are qualitative?
c. What is the average CD capacity for the sample?
d. What percentage of the minisystems provides an FM tuning rating of very good or excellent?
e. What percentage of the minisystems includes two tape decks?

Sandra Kudolo

Numerade Educator

Problem 6

Columbia House provides CDs to its mail-order club members. A Columbia House Music Survey asked new club members to complete an 11 -question survey. Some of the questions asked were:
a. How many CDs have you bought in the last 12 months?
b. Are you currently a member of a national mail-order book club? (Yes or No)
c. What is your age?
d. Including yourself, how many people (adults and children) are in your household?
e. What kind of music are you interested in buying? Fifteen categories were listed, including hard rock, soft rock, adult contemporary, heavy metal, rap, and country. Comment on whether each question provides qualitative or quantitative data.

Sandra Kudolo

Numerade Educator

Problem 7

The Ritz-Carlton Hotel used a customer opinion questionnaire to obtain performance data about its dining and entertainment services (The Ritz-Carrolton Hotel, Naples, Florida, February 2006 ). Customers were asked to rate six factors: Welcome, Service, Food, Menu Appeal, Atmosphere, and Overall Experience. Data were recorded for each factor with 1 for Fair, 2 for Average, 3 for Good, and 4 for Excellent.
a. The customer responses provided data for six variables. Are the variables qualitative or quantitative?
b. What measurement scale is used?

Sandra Kudolo

Numerade Educator

Problem 8

The Gallup organization conducted a telephone survey with a randomly selected national sample of 1005 adults, 18 years and older. The survey asked the respondents, "How would you describe your own physical health at this time?" (www.gallup.com, February 7,2002 ). Response categories were Excellent, Good, Only Fair, Poor, and No Opinion.
a. What was the sample size for this survey?
b. Are the data qualitative or quantitative?
c. Would it make more sense to use averages or percentages as a summary of the data for this question?
d. Of the respondents, $29 \%$ said their personal health was excellent. How many individuals provided this response?

Sandra Kudolo

Numerade Educator

Problem 9

The Commerce Department reported receiving the following applications for the Malcolm Baldrige National Quality Award: 23 from large manufacturing firms, 18 from large service firms, and 30 from small businesses.
a. Is type of business a qualitative or quantitative variable?
b. What percentage of the applications came from small businesses?

Sandra Kudolo

Numerade Educator

Problem 10

The Wall Street Journal subscriber survey (October 13,2003 ) asked 46 questions about subscriber characteristics and interests. State whether each of the following questions provided qualitative or quantitative data and indicate the measurement scale appropriate for each.
a. What is your age?
b. Are you male or female?
c. When did you first start reading the $W S J ?$ High school, college, early career, midcareer, late career, or retirement?
d. How long have you been in your present job or position?
e. What type of vehicle are you considering for your next purchase? Nine response categories include sedan, sports car, SUV, minivan, and so on.

Dominador Tan

Numerade Educator

Problem 11

State whether each of the following variables is qualitative or quantitative and indicate its measurement scale.
a. Annual sales
b. Soft drink size (small, medium, large)
c. Employee classification (GS1 through GS18)
d. Earnings per share
e. Method of payment (cash, check, credit card)

James Kiss

Numerade Educator

Problem 12

The Hawaii Visitors Bureau collects data on visitors to Hawaii. The following questions were among 16 asked in a questionnaire handed out to passengers during incoming airline flights in June 2003.
$\bullet$ This trip to Hawaii is my: 1 st, 2 nd, 3 rd, 4 th, etc.
$\bullet$ The primary reason for this trip is: (10 categories including vacation, convention, honeymoon)
$\bullet$ Where I plan to stay: (11 categories including hotel, apartment, relatives, camping)
$\bullet$ Total days in Hawaii
a. What is the population being studied?
b. Is the use of a questionnaire a good way to reach the population of passengers on incoming airline flights?
c. Comment on each of the four questions in terms of whether it will provide qualitative or quantitative data.

Sandra Kudolo

Numerade Educator

Problem 13

Figure 1.8 provides a bar graph summarizing the earnings for Volkswagen for the years 1997 to 2005 (BusinessWeek, December 26,2005 ).
a. Are the data qualitative or quantitative?
b. Are the data time series or cross-sectional?
c. What is the variable of interest?
d. Comment on the trend in Volkswagen's earnings over time. The $B u$ siness Week article (December 26,2005 ) estimated earnings for 2006 at $\$ 600$ million or $\$ .6$ billion. Does Figure 1.8 indicate whether this estimate appears to be reasonable?
e. A similar article that appeared in $B u$ siness Week on July 23,2001 , only had the data from 1997 to 2000 along with higher earnings projected for $2001 .$ What was the outlook for Volkswagen's earnings in July $2001 ?$ Did an investment in Volkswagen look promising in $2001 ?$ Explain.
f. What warning does this graph suggest about projecting data such as Volkswagen's earnings into the future?

Sandra Kudolo

Numerade Educator

Problem 14

CSM Worldwide forecasts global production for all automobile manufacturers. The following CSM data show the forecast of global auto production for General Motors, Ford, DaimlerChrysler, and Toyota for the years 2004 to 2007 (USA Today, December 21,2005 ). Data are in millions of vehicles.
a. Construct a time series graph for the years 2004 to 2007 showing the number of vehicles manufactured by each automotive company. Show the time series for all four manufacturers on the same graph.
b. General Motors has been the undisputed production leader of automobiles since 1931 What does the time series graph show about who is the world's biggest car company? Discuss.
c. Construct a bar graph showing vehicles produced by automobile manufacturer using the 2007 data. Is this graph based on cross-sectional or time series data?

Dominador Tan

Numerade Educator

Problem 15

The Food and Drug Administration (FDA) reported the number of new drugs approved over an eight-year period (The Wall Street Journal, January 12,2004 ). Figure 1.9 provides a bar graph summarizing the number of new drugs approved each year.
a. Are the data qualitative or quantitative?
b. Are the data time series or cross-sectional?
c. How many new drugs were approved in $2003 ?$
d. In what year were the fewest new drugs approved? How many?
e. Comment on the trend in the number of new drugs approved by the FDA over the eight-year period.

Sandra Kudolo

Numerade Educator

Problem 16

The marketing group at your company developed a new diet soft drink that it claims will capture a large share of the young adult market.
a. What data would you want to see before deciding to invest substantial funds in introducing the new product into the marketplace?
b. How would you expect the data mentioned in part (a) to be obtained?

Sandra Kudolo

Numerade Educator

Problem 17

A manager of a large corporation recommends a $\$ 10,000$ raise be given to keep a valued subordinate from moving to another company. What internal and external sources of data might be used to decide whether such a salary increase is appropriate?

Bryan Luo

Numerade Educator

Problem 18

A survey of 430 business travelers found 155 business travelers used a travel agent to make the travel arrangements (USA Today, November 20, 2003).
a. Develop a descriptive statistic that can be used to estimate the percentage of all business travelers who use a travel agent to make travel arrangements.
b. The survey reported that the most frequent way business travelers make travel arrangements is by using an online travel site. If $44 \%$ of business travelers surveyed made their arrangements this way, how many of the 430 business travelers used an online travel site?
c. Are the data on how travel arrangements are made qualitative or quantitative?

Sandra Kudolo

Numerade Educator

Problem 19

A $B u$ siness Week North American subscriber study collected data from a sample of 2861 subscribers. Fifty-nine percent of the respondents indicated an annual income of $\$ 75,000$ or more, and $50 \%$ reported having an American Express credit card.
a. What is the population of interest in this study?
b. Is annual income a qualitative or quantitative variable?
c. Is ownership of an American Express card a qualitative or quantitative variable?
d. Does this study involve cross-sectional or time series data?
e. Describe any statistical inferences $B u$ siness Week might make on the basis of the survey.

Dominador Tan

Numerade Educator

Problem 20

A survey of 131 investment managers in Barron's Big Money poll revealed the following (Barron's, October 28,2002 ):
$\bullet$ $43 \%$ of managers classified themselves as bullish or very bullish on the stock market.
$\bullet$ The average expected return over the next 12 months for equities was $11.2 \%$
$\bullet$ $21 \%$ selected health care as the sector most likely to lead the market in the next 12 months.
$\bullet$ When asked to estimate how long it would take for technology and telecom stocks to resume sustainable growth, the managers' average response was 2.5 years.
a. Cite two descriptive statistics.
b. Make an inference about the population of all investment managers concerning the average return expected on equities over the next 12 months.
c. Make an inference about the length of time it will take for technology and telecom stocks to resume sustainable growth.

Dominador Tan

Numerade Educator

Problem 21

A seven-year medical research study reported that women whose mothers took the drug DES during pregnancy were twice as likely to develop tissue abnormalities that might lead to cancer as were women whose mothers did not take the drug.
a. This study involved the comparison of two populations. What were the populations?
b. Do you suppose the data were obtained in a survey or an experiment?
c. For the population of women whose mothers took the drug DES during pregnancy, a sample of 3980 women showed 63 developed tissue abnormalities that might lead to cancer. Provide a descriptive statistic that could be used to estimate the number of women out of 1000 in this population who have tissue abnormalities.
d. For the population of women whose mothers did not take the drug DES during pregnancy, what is the estimate of the number of women out of 1000 who would be expected to have tissue abnormalities?
e. Medical studies often use a relatively large sample (in this case, 3980 ). Why?

Bryan Luo

Numerade Educator

Problem 22

In the fall of $2003,$ Arnold Schwarzenegger challenged Governor Gray Davis for the governorship of California. A Policy Institute of California survey of registered voters reported Arnold Schwarzenegger in the lead with an estimated $54 \%$ of the vote (Newsweek, September 8,2003 ).
a. What was the population for this survey?
b. What was the sample for this survey?
c. Why was a sample used in this situation? Explain.

Dominador Tan

Numerade Educator

Problem 23

Nielsen Media Research conducts weekly surveys of television viewing throughout the United States, publishing both rating and market share data. The Nielsen rating is the percentage of households with televisions watching a program, while the Nielsen share is the percentage of households watching a program among those households with televisions in use. For example, Nielsen Media Research results for the 2003 Baseball World Series between the New York Yankees and the Florida Marlins showed a rating of $12.8 \%$ and a share of $22 \%$ (Associated Press, October 27,2003 ). Thus, $12.8 \%$ of households with televisions were watching the World Series and $22 \%$ of households with televisions in use were watching the World Series. Based on the rating and share data for major television programs, Nielsen publishes a weekly ranking of television programs as well as a weekly ranking of the four major networks: ABC, CBS, NBC, and Fox.
a. What is Nielsen Media Research attempting to measure?
b. What is the population?
c. Why would a sample be used in this situation?
d. What kinds of decisions or actions are based on the Nielsen rankings?

Dominador Tan

Numerade Educator

Problem 24

A sample of midterm grades for five students showed the following results: 72,65,82,90 76. Which of the following statements are correct, and which should be challenged as being too generalized?
a. The average midterm grade for the sample of five students is 77
b. The average midterm grade for all students who took the exam is 77 .
c. An estimate of the average midterm grade for all students who took the exam is 77 .
d. More than half of the students who take this exam will score between 70 and 85
e. If five other students are included in the sample, their grades will be between 65 and 90 .

Mihir Nayar

Numerade Educator

Problem 25

Table 1.8 shows a data set containing information for 25 of the shadow stocks tracked by the American Association of Individual Investors (aaii.com, February 2002 ). Shadow stocks are common stocks of smaller companies that are not closely followed by Wall Street analysts. The data set is also on the CD accompanying the text in the file named Shadow02.
a. How many variables are in the data set?
b. Which of the variables are qualitative and which are quantitative?
c. For the Exchange variable, show the frequency and the percent frequency for AMEX, NYSE, and OTC. Construct a bar graph similar to Figure 1.5 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 similar to Figure 1.6
e. What is the average price/earnings ratio?

Jerelyn Nevil

Numerade Educator