Chapter 1, Data and Statistics Video Solutions, Statistics For Business & Economics | Numerade (2024)

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

Tablet PC Comparison provides a wide variety of information about tablet computers. The company's 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 PC Comparison website, February 28, 2013).
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?

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?

Table 1.7 shows data for eight cordless telephones (Consumer Reports, November 2012). The Overall Score, a measure of the overall quality for the cordless telephone, 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 handset 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, Handset on Base, and Talk Time, which variables are categorical and which variables are quantitative?
c. What scale of measurement is used for each variable?

Refer to the data set in Table 1.7.
a. What is the average price for the cordless telephones?
b. What is the average talk time for the cordless telephones?
c. What percentage of the cordless telephones have a voice quality of excellent?
d. What percentage of the cordless telephones have a handset on the base?

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, May 2012.
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 miles per gallon?
c. What is your overall rating of your new vehicle? (1- to 10 -point scale with 1 Unacceptable and 10 Truly Exceptional)
Comment on whether each question provides categorical or quantitative data.

The Kroger Company is one of the largest grocery retailers in the United States, with over 2000 grocery stores across the country. Kroger uses an online customer opinion questionnaire to obtain performance data about its products and services and learn about what motivates its customers (Kroger website, April 2012). In the survey, Kroger customers were asked if they would be willing to pay more for products that had each of the following four characteristics. The four questions were: Would you pay more for
products that have a brand name?
products that are environmentally friendly?
products that are organic?
products that have been recommended by others?
For each question, the customers had the option of responding Yes if they would pay more or No if they would not pay more.
a. Are the data collected by Kroger in this example categorical or quantitative?
b. What measurement scale is used?

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, February 15, 2013).
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?

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

The Bureau of Transportation Statistics Omnibus Houschold 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 (Bureau of Transportation website, August 2010).
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?

In a Gallup telephone survey conducted on April 9-10, 2013, the person being interviewed was asked if he would vote for a law in his state that would increase the gas tax up to 20 cents a gallon, with the new gas tax money going to improve roads and bridges and build more mass transportation in his state. Possible responses were vote for, vote against, and no opinion. Two hundred ninety five respondents said they would vote for the law, 672 said they would vote against the law, and 51 said they had no opinion (Gallup website, June 14, 2013).
a. Do the responses for this question provide categorical or quantitative data?
b. What was the sample size for this Gallup poll?
c. What percentage of respondents would vote for a law increasing the gas tax?
d. Do the results indicate general support for or against increasing the gas tax to improve roads and bridges and build more mass transportation?

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.
- This trip to Hawaii is my: 1st, 2nd, 3rd, 4th, etc.
- 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)
- 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.

Figure 1.7 provides a bar chart showing the annual revenue for Google from 2004 to 2014. (The Wall Street Journal, August 19, 2014).
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 Google revenue over time.

The following data show the number of rental cars in service for three rental car companies: Hertz, Avis, and Dollar. The data are for the years 2007-2010 and are in thousands of vehicles (Auto Rental News website, May 15, 2011 ).
a. Construct a time series graph for the years 2007 to 2010 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 2010 . Is this chart based on cross-sectional or time series data?

Every year, the U.S. Coust Guard collects data and compiles statistics on reported recreational boating accidents. These statistics are derived from accident reports that are filed by the owners/operators of recreational vessels involved in accidents. In 2009, 4730 recreational boating accident reports were filed. Figure 1.8 provides a bar chart summarizing the number of accident reports that were filed each month (U.S. Coast Guard's Boating Safety Division website, August 2010).
a. Are the data categorical or quantitative?
b. Are the data time series or cross-sectional?
c. In what month were the most accident reports filed? Approximately how many?
d. There were 61 accident reports filed in January and 76 accident reports filed in December. What percentage of the total number of accident reports for the year were filed in these two months? Does this seem reasonable?
e. Comment on the overall shape of the bar graph.

The Energy Information Administration of the U.S. Department of Energy provided time series data for the U.S. average price per gallon of conventional regular gasoline between January 2007 and February 2014 (Energy Information Administration website, March 2014). Use the Internet to obtain the average price per gallon of conventional regular gasoline since February 2014.
a. Extend the graph of the time series shown in Figure 1.1.
b. What interpretations can you make about the average price per gallon of conventional regular gasoline since February 2014 ?
c. Does the time series continue to show a summer increase in the average price per gallon? Explain.

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?

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 (CompleteTax Tax Prep Survey 2010).
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 is 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?

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.

A survey of 131 investment managers in Barron's Big Money poll revealed the following:
- $43 \%$ of managers classified themselves as bullish or very bullish on the stock market.
- The average expected return over the next 12 months for equities was $11.2 \%$.
- $21 \%$ selected health care as the sector most likely to lead the market in the next 12 months.
- 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.

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 3980 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 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?

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, September 26, 2013). 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?

Pew Research Center is a nonpartisan polling organization that provides information about issues, attitudes, and trends shaping America. In a poll, Pew researchers found that $47 \%$ of American adult respondents reported getting at least some local news on their cell phone or tablet computer (Pew Research website, May 14, 2011). Further findings showed that $42 \%$ of respondents who own cell phones or tablet computers use those devices to check local weather reports and $37 \%$ use the devices to find local restaurants or other businesses.
a. One statistic concemed using cell phones or tablet computers for local news. What population is that finding applicable to?
b. Another statistic concerned using cell phones or tablet computers to check local weather reports and to find local restaurants. What population is this finding applicable to?
c. Do you think the Pew researchers conducted a census or a sample survey to obtain their results? Why?
d. If you were a restaurant owner, would you find these results interesting? Why? How could you take advantage of this information?

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 .

Table 1.8 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. The data set is also on the website that accompanies the text in the DATAfile named Shadow02.
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 graph similar to Figure 1.4 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 1.5.
e. What is the average price/earnings ratio?