Essentials of Modern Business Statistics

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

Chapter 1

Data and Statistics - all with Video Answers

Educators

Chapter Questions

Problem 1

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

Khalida Dawar

Khalida Dawar

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Problem 2

Comparing Tablet Computers. Tablet PC Comparison provides a wide variety of information about tablet computers. Their website enables consumers to easily compare different tablets using factors such as cost, type of operating system, display size, battery life, and CPU manufacturer. A sample of 10 tablet computers is shown in Table 1.6 (Tablet $\mathrm{PC}$ Comparison website).
a. How many elements are in this data set?
b. How many variables are in this data set?
c. Which variables are categorical and which variables are quantitative?
d. What type of measurement scale is used for each of the variables?

Nick Johnson

Numerade Educator

Problem 3

Refer to Table 1.6
a. What is the average cost for the tablets?
b. Compare the average cost of tablets with a Windows operating system to the average cost of tablets with an Android operating system.
c. What percentage of tablets use a CPU manufactured by TI OMAP?
d. What percentage of tablets use an Android operating system?

Terrisa R

Numerade Educator

Problem 4

Table 1.7 shows data for eight phones (Consumer Reports). The Overall Score, a measure of the overall quality for the phone, ranges from 0 to $100 .$ Voice Quality has possible ratings of poor, fair, good, very good, and excellent. Talk Time is the manufacturer's claim of how long the phone can be used when it is fully charged.
a. How many elements are in this data set?
b. For the variables Price, Overall Score, Voice Quality, and Talk Time, which variables are categorical and which variables are quantitative?
c. What scale of measurement is used for each variable?

Terrisa R

Numerade Educator

Problem 5

Refer to the data set in Table 1.7 .
a. What is the average price for the phones?
b. What is the average talk time for the phones?
c. What percentage of the phones have a voice quality of excellent?

Terrisa R

Numerade Educator

Problem 6

J.D. Power and Associates surveys new automobile owners to learn about the quality of recently purchased vehicles. The following questions were asked in the J.D. Power Initial Quality Survey.
a. Did you purchase or lease the vehicle?
b. What price did you pay?
c. What is the overall attractiveness of your vehicle's exterior? (Unacceptable, Average, Outstanding, or Truly Exceptional)
d. What is your average number of miles per gallon?
e. What is your overall rating of your new vehicle? (l- to 10 -point scale with 1 Unacceptable and 10 Truly Exceptional)
Comment on whether each question provides categorical or quantitative data.

Terrisa R

Numerade Educator

Problem 7

Airline Customer Satisfaction. Many service companies collect data via a followup survey of their customers. For example, to ascertain customer sentiment, Delta Air Lines sends an e-mail to customers immediately following a flight. Among other questions, Delta asks:
How likely are you to recommend Delta Air Lines to others?
The possible responses are:
$\begin{array}{llll}\text { Definitely } & \text { Probably } & \text { May or May } & \text { Probably Will } & \text { Definitely Will }\end{array}$ $\begin{array}{llll}\text { Will } & \text { Will } & \text { Not } & \text { Not } & \text { Not }\end{array}$
a. Are the data collected by Delta in this example quantitative or categorical?
b. What measurement scale is used?

Nick Johnson

Numerade Educator

Problem 8

The Tennessean, an online newspaper located in Nashville, Tennessee, conducts a daily poll to obtain reader opinions on a variety of current issues. In a recent poll, 762 readers responded to the following question: "If a constitutional amendment to ban a state income tax is placed on the ballot in Tennessee, would you want it to pass?" Possible responses were Yes, No, or Not Sure (The Tennessean website).
a. What was the sample size for this poll?
b. Are the data categorical 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, $67 \%$ said Yes, they would want it to pass. How many individuals provided this response?

Emily Himsel

Numerade Educator

Problem 9

Based on data from the U.S. Census Bureau, a Pew Research study showed that the percentage of employed individuals ages $25-29$ who are college educated is at an all-time high. The study showed that the percentage of employed individuals aged $25-29$ with at least a bachelor's degree in 2016 was $40 \%$. In the year $2000,$ this percentage was $32 \%,$ in 1985 it was $25 \%,$ and in 1964 it was only $16 \%$ (Pew Research website).
a. What is the population being studied in each of the four years in which Pew has data?
b. What question was posed to each respondent?
c. Do responses to the question provide categorical or quantitative data?

Emily Himsel

Numerade Educator

Problem 10

The Bureau of Transportation Statistics Omnibus Household Survey is conducted annually and serves as an information source for the U.S. Department of Transportation. In one part of the survey the person being interviewed was asked to respond to the following statement: "Drivers of motor vehicles should be allowed to talk on a hand-held cell phone while driving." Possible responses were strongly agree, somewhat agree, somewhat disagree, and strongly disagree. Forty-four respondents said that they strongly agree with this statement, 130 said that they somewhat agree, 165 said they somewhat disagree, and 741 said they strongly disagree with this statement.
a. Do the responses for this statement provide categorical or quantitative data?
b. Would it make more sense to use averages or percentages as a summary of the responses for this statement?
c. What percentage of respondents strongly agree with allowing drivers of motor vehicles to talk on a hand-held cell phone while driving?
d. Do the results indicate general support for or against allowing drivers of motor vehicles to talk on a hand-held cell phone while driving?

Emily Himsel

Numerade Educator

Problem 11

A Gallup Poll utilizing a random sample of 1,503 adults ages 18 or older was conducted in April 2018 . The survey indicated a majority of Americans $(53 \%)$ say driverless cars will be common in the next 10 years (Gallup, https://news.gallup.com/poll/234152/americans-expect-driverless-cars-common-next
-decade.aspx). The question asked was:
Thinking about fully automated, "driverless cars," cars that use technology to drive and do not need a human driver, based on what you have heard or read, how soon do you think driverless cars will be commonly used in the [United States]?

Figure 1.10 shows a summary of results of the survey in a histogram indicating the percentage of the total responses in different time intervals.
a. Are the responses to the survey question quantitative or categorical?
b. How many of the respondents said that they expect driverless cars to be common in the next 10 years?
c. How many respondents answered in the range $16-20$ years?

Jorge Villanueva

Jorge Villanueva

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.
$\cdot$ This trip to Hawaii is $\mathrm{my}: 1 \mathrm{st}, 2 \mathrm{nd}, 3 \mathrm{rd}, 4 \mathrm{th},$ etc.
$\cdot$ The primary reason for this trip is: (10 categories, including vacation, convention, honeymoon)
Where I plan to stay: ( 11 categories, including hotel, apartment, relatives, camping)
$\cdot$ 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 categorical or quantitative data.

Jorge Villanueva

Jorge Villanueva

Numerade Educator

Problem 13

Facebook Advertising Revenue. Figure 1.11 provides a bar chart showing the annual advertising revenue for Facebook from 2010 to 2017 (Facebook Annual Reports).
a. What is the variable of interest?
b. Are the data categorical or quantitative?
c. Are the data time series or cross-sectional?
d. Comment on the trend in Facebook's annual advertising revenue over time.

Nick Johnson

Numerade Educator

Problem 14

The following data show the number of rental cars in service for three rental car companies: Hertz, Avis, and Dollar, over a four-year period.
$$
\begin{array}{lcccc}
& & {2}{c} {\text { Cars in Service (1000s) }} & \\
\text { Company } & \text { Year 1 } & \text { Year 2 } & \text { Year 3 } & \text { Year 4 } \\
\text { Hertz } & 327 & 311 & 286 & 290 \\
\text { Dollar } & 167 & 140 & 106 & 108 \\
\text { Avis } & 204 & 220 & 300 & 270
\end{array}
$$
a. Construct a time series graph for the years 1 to 4 showing the number of rental cars in service for each company. Show the time series for all three companies on the same graph.
b. Comment on who appears to be the market share leader and how the market shares are changing over time.
c. Construct a bar chart showing rental cars in service for Year $4 .$ Is this chart based on cross-sectional or time series data?

Jorge Villanueva

Jorge Villanueva

Numerade Educator

Problem 15

The U.S. Census Bureau tracks sales per month for various products and services through its Monthly Retail Trade Survey. Figure 1.12 shows monthly jewelry sales in millions of dollars for 2016 .
a. Are the data quantitative or categorical?
b. Are the data cross-sectional or time series?
c. Which four months have the highest sales?
d. Why do you think the answers to part c might be the highest four months?

Jorge Villanueva

Jorge Villanueva

Numerade Educator

Problem 16

Athletic Shoe Sales. Skechers U.S.A., Inc., is a performance footwear company headquartered in Manhattan Beach, California. The sales revenue for Skechers over a four-year period are as follows:
a. Are these cross-sectional or time-series data?
b. Construct a bar graph similar to Figure 1.12 .
c. What can you say about how Skechers' sales are changing over these four years?

Jorge Villanueva

Jorge Villanueva

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 random telephone survey of 1021 adults (aged 18 and older) was conducted by Opinion Research Corporation on behalf of CompleteTax, an online tax preparation and e-filing service. The survey results showed that 684 of those surveyed planned to file their taxes electronically.
a. Develop a descriptive statistic that can be used to estimate the percentage of all taxpayers who file electronically.
b. The survey reported that the most frequently used method for preparing the tax return was to hire an accountant or professional tax preparer. If $60 \%$ of the people surveyed had their tax return prepared this way, how many people used an accountant or professional tax preparer?
c. Other methods that the person filing the return often used include manual preparation, use of an online tax service, and use of a software tax program. Would the data for the method for preparing the tax return be considered categorical or quantitative?

Jorge Villanueva

Jorge Villanueva

Numerade Educator

Problem 19

Magazine Subscriber Survey. A Bloomberg Businessweek 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 categorical or quantitative variable?
c. Is ownership of an American Express card a categorical or quantitative variable?
d. Does this study involve cross-sectional or time series data?
e. Describe any statistical inferences Bloomberg Businessweek might make on the basis of the survey.

Jorge Villanueva

Jorge Villanueva

Numerade Educator

Problem 20

Investment Manager Survey. A survey of 131 investment managers in Barron's Big Money poll revealed the following:
$\bullet$ Forty-three percent 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 $11.2 \%$ $\bullet$ Twenty-one percent 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.

Jorge Villanueva

Jorge Villanueva

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 compared 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 3,980 women showed that 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 1,000 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 1,000 who would be expected to have tissue abnormalities?
e. Medical studies often use a relatively large sample (in this case, 3,980 ). Why?

Jorge Villanueva

Jorge Villanueva

Numerade Educator

Problem 22

A survey conducted by Better Homes and Gardens Real Estate LLC showed that one in five U.S. homeowners have either moved from their home or would like to move because their neighborhood or community isn't ideal for their lifestyle (Better Homes and Gardens Real Estate website). The top lifestyle priorities of respondents when searching for their next home include ease of commuting by car, access to health and safety services, family-friendly neighborhood, availability of retail stores, access to cultural activities, public transportation access, and nightlife and restaurant access. Suppose a real estate agency in Denver, Colorado, hired you to conduct a similar study to determine the top lifestyle priorities for clients that currently have a home listed for sale with the agency or have hired the agency to help them locate a new home.
a. What is the population for the survey you will be conducting?
b. How would you collect the data for this study?

Emily Himsel

Numerade Educator

Problem 23

Pew Research Center is a nonpartisan polling organization that provides information about issues, attitudes, and trends shaping America. In a 2015 poll, Pew researchers found that $73 \%$ of teens aged $13-17$ have a smartphone, $15 \%$ have a basic phone and $12 \%$ have no phone. The study also asked the respondents how they communicated with their closest friend. Of those with a smartphone, $58 \%$ responded texting, $17 \%$ social media and $10 \%$ phone calls. Of those with no smartphone, $25 \%$ responded texting, $29 \%$ social media and $21 \%$ phone calls (Pew Research Center website).
a. One statistic $(58 \%)$ concerned the use of texting to contact his/her closest friend, if the teen owns a smartphone. To what population is that applicable?
b. Another statistic $(25 \%)$ concerned the use of texting by those who do not own a smartphone. To what population is that applicable?
c. Do you think the Pew researchers conducted a census or a sample survey to obtain their results? Why?

Jorge Villanueva

Jorge Villanueva

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.

Jorge Villanueva

Jorge Villanueva

Numerade Educator

Problem 25

Consumer Reports evaluates products for consumers. The file CompactSUV contains the data shown in Table 1.8 for 15 compact sports utility vehicles (SUVs) from the 2018 model line (Consumer Reports website):
Make-manufacturer Model-name of the model
Overall score-awarded based on a variety of measures, including those in this data set Recommended-Consumer Reports recommends the vehicle or not Owner satisfaction - satisfaction on a five-point scale based on the percentage of owners who would purchase the vehicle again $(--,-, 0,+,++)$ Overall miles per gallon-miles per gallon achieved in a 150 -mile test trip Acceleration $(0-60 \mathrm{sec})$ - time in seconds it takes vehicle to reach 60 miles per hour from a standstill with the engine idling
a. How many variables are in the data set?
b. Which of the variables are categorical, and which are quantitative?
c. What percentage of these 15 vehicles are recommended?
d. What is the average of the overall miles per gallon across all 15 vehicles?
e. For owner satisfaction, construct a bar chart similar to Figure 1.4 .
for the frequency distribution for acceleration using the following intervals:
$7.0-7.9,8.0-8.9,9.0-9.9,$ and $10.0-10.9 .$ Construct a histogram similar to Figure 1.5

Jorge Villanueva

Jorge Villanueva

Numerade Educator