Statistics for Business and Economics

Paul Newbold, William Carlson, Betty Thorne

Chapter 1

Using Graphs to Describe Data - all with Video Answers

Educators

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Chapter Questions

Problem 1

A mortgage company randomly samples accounts of their time-share customers. State whether each of the following variables is categorical or numerical. If categorical, give the level of measurement. If numerical, is it discrete or continuous?
a. The original purchase price of a customer's time-share unit
b. The state (or country) of residence of a time-share owner
c. A time-share owner's satisfaction level with the maintenance of the unit purchased (1: very dissatisfied to 5: very satisfied)
d. The number of times a customer's payment was late

Christopher Stanley

Christopher Stanley

Numerade Educator

Problem 2

Visitors to a supermarket in Singapore were asked to complete a customer service survey. Are the answers to the following survey questions categorical or numerical? If an answer is categorical, give the level of measurement. If an answer is numerical, is it discrete or continuous?
a. Have you visited this store before?
b. How would you rate the level of customer service you received today on a scale from 1 (very poor) to 5 (very good)?
c. How much money did you spend in the store today?

Christopher Stanley

Christopher Stanley

Numerade Educator

Problem 3

A questionnaire was distributed at a large university to find out the level of student satisfaction with various activities and services. For example, concerning parking availability, students were asked to indicate their level of satisfaction on a scale from 1 (very dissatisfied) to 5 (very satisfied). Is a student's response to this question numerical or categorical? If numerical, is it discrete or continuous? If categorical, give the level of measurement.

Christopher Stanley

Christopher Stanley

Numerade Educator

Problem 4

Faculty at one university were asked a series of questions in a recent survey. State the type of data for each question.
a. Indicate your level of satisfaction with your teaching load (very satisfied, moderately satisfied, neutral, moderately dissatisfied, or very dissatisfied).
b. How many of your research articles were published in refereed journals during the last 5 years?
c. Did you attend the last university faculty meeting?
d. Do you think that the teaching evaluation process needs to be revised?

Christopher Stanley

Christopher Stanley

Numerade Educator

Problem 5

A number of questions were posed to a random sample of visitors to a London tourist information center. For each question below, describe the type of data obtained.
a. Are you staying overnight in London?
b. How many times have you visited London previously?
c. Which of the following attractions have you visited?
Tower of London
Buckingham Palace
Big Ben
Covent Garden
Westminster Abbey
d. How likely are you to visit London again in the next 12 months: (1) unlikely, (2) likely, (3) very likely?

Christopher Stanley

Christopher Stanley

Numerade Educator

Problem 6

Residents in one housing development were asked a series of questions by their homeowners' association. Identify the type of data for each question.
a. Did you play golf during the last month on the development's new golf course?
b. How many times have you eaten at the country club restaurant during the last month?
c. Do you own a camper?
d. Rate the new security system for the development (very good, good, poor, or very poor).

Christopher Stanley

Christopher Stanley

Numerade Educator

Problem 7

The supervisor of a very large plant obtained the times (in seconds) to complete a task for a random sample of employees. This information and other data about the employees are stored in the data file Completion Times.
a. Give an example of a categorical variable with ordinal responses.
b. Give an example of a categorical variable with nominal responses.
c. Give an example of a numerical variable.

Jessica Waggener

Jessica Waggener

Numerade Educator

Problem 8

The U.S. Department of Agriculture (USDA) Center for Nutrition Policy and Promotion (CNPP) developed and administered the Healthy Eating Index-2005 to measure how well the population follows the recommendations of the 2005 Dietary Guidelines for Americans. The data are contained in the data file HEI Cost Data Variable Subset.
a. Give an example of a categorical variable with ordinal responses.
b. Give an example of a categorical variable with nominal responses.
c. Give an example of a numerical variable with continuous responses.
d. Give an example of a numerical variable with discrete responses.

Lucas Finney

Numerade Educator

Problem 9

A university administrator requested a breakdown of travel expenses for faculty to attend various professional meetings. It was found that $31 \%$ of the travel expenses was spent for transportation costs, $25 \%$ was spent for lodging, $17 \%$ was spent for food, and $20 \%$ was spent for conference registration fees; the remainder was spent for miscellaneous costs.
a. Construct a pie chart.
b. Construct a bar chart.

Christopher Stanley

Christopher Stanley

Numerade Educator

Problem 10

A company has determined that there are seven possible defects for one of its product lines. Construct a Pareto diagram for the following defect frequencies:
$$
\begin{array}{cc}
\hline \text { Defect Code } & \text { Frequency } \\
\hline \text { A } & 10 \\
\text { B } & 70 \\
\text { C } & 15 \\
\text { D } & 90 \\
\text { E } & 8 \\
\text { F } & 4 \\
\text { G } & 3 \\
\hline
\end{array}
$$

Shafiq Rehman

Numerade Educator

Problem 11

Bank clients were asked to indicate their level of satisfaction with the service provided by the bank's tellers. Responses from a random sample of customers were as follows: 69 were very satisfied, 55 were moderately satisfied, 5 had no opinion, 3 were moderately dissatisfied, and 2 were very dissatisfied.
a. Construct a bar chart.
b. Construct a pie chart.

Christopher Stanley

Christopher Stanley

Numerade Educator

Problem 12

The supervisor of a plant obtained a random sample of employee experience (in months) and times to complete a task (in minutes). Graph the data with a component bar chart.
$$
\begin{array}{lccc}
\hline & \text { Less } & \text { 5 Minutes to } & \text { 10 Minutes to } \\
\text { Experience/ } & \text { Than } & \text { Less Than } & \text { Less Than } \\
\text { Time } & 5 \text { Minutes } & \text { 10 Minutes } & 15 \text { Minutes } \\
\hline \text { Less than } & 10 & 13 & 25 \\
3 \text { months } & & & \\
3<6 \text { months } & 10 & 13 & 12 \\
6<9 \text { months } & 9 & 22 & 8 \\
9<12 \text { months } & 5 & 18 & 19 \\
\hline
\end{array}
$$

Shafiq Rehman

Numerade Educator

Problem 13

Suppose that an estimate of U.S. federal spending showed that $46 \%$ was for entitlements, $18 \%$ was for defense, $15 \%$ was for grants to states and localities, $14 \%$ was for interest on debt, $6 \%$ was for other federal operations, and $1 \%$ was for deposit insurance. Construct a pie chart to show this information.

Christopher Stanley

Christopher Stanley

Numerade Educator

Problem 14

The Statistical Abstract of the United States provides a reliable and complete summary of statistics on the political, social, and economic organization of the United States. The following table gives a partial list of the number of endangered wildlife species both inside and outside the United States as of April 2010 (Table 383, Statistical Abstract of the United States 2011):
$$
\begin{array}{lcc}
\hline & \text { Endangered } & \text { Endangered Wildlife } \\
& \text { Wildlife Species } & \text { Species Outside the } \\
\text { Item } & \text { in United States } & \text { United States } \\
\hline \text { Mammals } & 70 & 255 \\
\text { Birds } & 76 & 182 \\
\text { Reptiles } & 13 & 66 \\
\text { Amphibians } & 14 & 8 \\
\text { Fishes } & 74 & 11 \\
\hline
\end{array}
$$
a. Construct a bar chart of the number of endangered wildlife species in the United States.
b. Construct a bar chart of the number of endangered wildlife species outside the United States.
c. Construct a bar chart to compare the number of endangered species in the United States to the number of endangered species outside the United States.

Shafiq Rehman

Numerade Educator

Problem 15

Jon Payne, tennis coach, kept a record of the most serious type of errors made by each of his players during a 1-week training camp. The data are stored in the data file Tennis.
a. Construct a Pareto diagram of total errors committed by all players.
b. Construct a Pareto diagram of total errors committed by male players.
c. Construct a Pareto diagram of total errors committed by female players.
d. Construct a component bar chart showing type of error and gender of the player.

Prabhu Ramji

Numerade Educator

Problem 16

On what type of Internet activity do you spend the most time? The responses from a random sample of 700 Internet users were banking online, 40 ; buying a product, 60 ; getting news, $150 ;$ sending or reading e-mail, 200; buying or making a reservation for travel, 75 ; checking sports scores or information, 50 ; and searching for an answer to a question, 125 . Describe the data graphically.

Christopher Stanley

Christopher Stanley

Numerade Educator

Problem 17

A random sample of 100 business majors was asked a series of demographic questions including major, gender, age, year in school, and current grade point average (GPA). Other questions were also asked for their levels of satisfaction with campus parking, campus housing, and campus dining. Responses to these satisfaction questions were measured on a scale from 1 to 5 , with 5 being the highest level of satisfaction. Finally, these students were asked if they planned to attend graduate school within 5 years of their college graduation (0: no; 1: yes). These data are contained in the data file Finstad and Lie Study.
a. Construct a cluster bar chart of the respondents' major and gender.
b. Construct a pie chart of their majors.

Shu Naito

Numerade Educator

Problem 18

The Healthy Eating Index-2005 measures how well the population follows the recommendations of the 2005 Dietary Guidelines for Americans. Table $1.2$ is a frequency distribution of males and females in each of three activity level lifestyles: sendentary, active, and very active. This activity level was taken at the first interview $($ daycode $=1)$.
a. Use the data in Table $1.2$ or data (coded daycode $=1$ ) contained in the data file HEI Cost Data Variable Subset to construct a pie chart of the percent of males in each of the activity level categories.
b. Use the data in Table $1.2$ or data (coded daycode $=1$ ) contained in the data file HEI Cost Data Variable Subset to construct a pie chart of the percent of females in each of the activity level categories.

Shafiq Rehman

Numerade Educator

Problem 19

Internet Explorer (IE) dropped below $50 \%$ of the worldwide market for the first time in September 2010 (StatCounter Global Stats Microsoft 2010). IE's worldwide market share continued to decrease over the next several months. Worldwide market share data from January 2010 through February 2011 for IE, Firefox, Chrome, Safari, and Opera are contained in the data file Browser Wars.
a. Depict the worldwide market shares for February 2011 for the data contained in the data file Browser Wars using a pie chart.
b. Use a pie chart to depict the current market shares for these Internet browsers (Source: gs.statcounter.com).
c. Select a country or region from the list provided by StatCounter Global Stats and depict the market shares for the current time period with a pie chart (Source: gs.statcounter.com).

Lucas Finney

Numerade Educator

Problem 20

Construct a time-series plot for the following number of customers shopping at a new mall during a given week.

Shafiq Rehman

Numerade Educator

Problem 21

The number of males and females enrolled in colleges (undergraduate and postbaccalaureate) in the United States from 2000 through 2008 is given here. Graphically present these data with a time-series plot.
$$
\begin{array}{crr}
\hline \begin{array}{c}
\text { College Enrollment } \\
\text { (in thousands) }
\end{array} & \text { Males } & \text { Females } \\
\hline 2000 & 6,721.8 & 8,590.5 \\
2001 & 6,960.8 & 967.2 \\
2002 & 7,202.1 & 9,409.6 \\
2003 & 7,255.6 & 9,644.9 \\
2004 & 7,387.3 & 9,884.4 \\
2005 & 7,455.9 & 10,031.6 \\
2006 & 7,574.8 & 10,184.1 \\
2007 & 7,815.9 & 10,432.2 \\
2008 & 8,188.9 & 10,913.9 \\
\hline
\end{array}
$$

Shafiq Rehman

Numerade Educator

Problem 22

From the data file Macro 2009 use a time plot to graph both gross domestic investment and gross private savings in billions of real 2005 dollars.

Narayan Hari

Numerade Educator

Problem 23

Information about the GDP in the area of manufacturing of durable and nondurable goods is important to business owners and economists.
a. Use a time-series plot to graph the GDP in manufacturing in current and real $(2005)$ dollars by industry for durable goods (such as wood products, furniture and related products, motor vehicles, and equipment) from 2000 to 2009 . Data are in billions of dollars (Source: Table 1002. 2011. Statistical $\mathrm{Ab}$ stract of the United States).
b. Use a time-series plot to graph the GDP in manufacturing in real dollars (2005) by industry for nondurable goods (such as food, apparel, and leather products) from 2000 to 2009 . Data are in billions of dollars (Source: Table 1002 2011).

Amy Jiang

Numerade Educator

Problem 24

In Example $1.6$ we plotted the USD to 1 EUR for a 6-month time period.
a. Use a time-series plot to graphically display the currency conversion from the EUR to 1 USD. The data are contained in the data file Currency Exchange Rates.
b. Use a time-series plot to graphically display the currency conversion from the GBP to 1 USD. The data are contained in the data file Currency Exchange Rates.
c. Compare your currency with an appropriate world currency for the last 30 days.

Hossam Mohamed

Numerade Educator

Problem 25

Market shares for a period of 14 months for various Internet providers are contained in the data file Browser Wars.
a. Use a time-series plot to graphically display the worldwide market shares of IE, Firefox, Chrome, Safari, and Opera.
b. Use a time-series plot to graphically display the European market shares of IE, Firefox, Chrome, Safari, and Opera.
c. Use a time-series plot to graphically display the North American market shares of IE, Firefox, Chrome, Safari, and Opera.

Lucas Finney

Numerade Educator

Problem 26

Select annual returns on a stock market index over 14 years from the Internet. Graph the data with a time-series plot.

Shafiq Rehman

Numerade Educator

Problem 27

The data file Gold Price shows the year-end price of gold (in dollars) over 14 consecutive years. Graph the data with a time-series plot.

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 28

The data file Housing Starts shows private housing units started per thousand persons in the U.S. population over a period of 24 years. Describe the data with a graph.

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 29

Earnings per share of a corporation over a period of 28 years are stored in the data file Earnings per Share. Graph the series and comment on the plot.

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 30

Use the Quick Guide to find an approximate number of classes for a frequency distribution for each sample size.
a. $n=47$
b. $n=80$
c. $n=150$
d. $n=400$
e. $n=650$

Rashmi Sinha

Numerade Educator

Problem 31

Determine an appropriate interval width for a random sample of 110 observations that fall between and include each of the following:
a. 20 to 85
b. 30 to 190
c. 40 to 230
d. 140 to 500

James Kiss

Numerade Educator

Problem 31

Determine an appropriate interval width for a random sample of 110 observations that fall between and include each of the following:
a. 20 to 85
b. 30 to 190
c. 40 to 230
d. 140 to 500

James Kiss

Numerade Educator

Problem 32

Consider the following data:
$$
\begin{array}{llll}
\hline 17 & 62 & 15 & 65 \\
28 & 51 & 24 & 65 \\
39 & 41 & 35 & 15 \\
39 & 32 & 36 & 37 \\
40 & 21 & 44 & 37 \\
59 & 13 & 44 & 56 \\
12 & 54 & 64 & 59 \\
\hline
\end{array}
$$
a. Construct a frequency distribution.
b. Construct a histogram.
c. Construct an ogive.
d. Construct a stem-and-leaf display.

Shafiq Rehman

Numerade Educator

Problem 33

Construct a stem-and-leaf display for the hours that 20 students spent studying for a marketing test.
$$
\begin{array}{cccccccccc}
\hline 3.5 & 2.8 & 4.5 & 6.2 & 4.8 & 2.3 & 2.6 & 3.9 & 4.4 & 5.5 \\
5.2 & 6.7 & 3.0 & 2.4 & 5.0 & 3.6 & 2.9 & 1.0 & 2.8 & 3.6 \\
\hline
\end{array}
$$

Shafiq Rehman

Numerade Educator

Problem 34

Consider the following frequency distribution:
$$
\begin{array}{rc}
\hline {\text { Class }} & \text { Frequency } \\
\hline 0<10 & 8 \\
10<20 & 10 \\
20<30 & 13 \\
30<40 & 12 \\
40<50 & 6 \\
\hline
\end{array}
$$
a. Construct a relative frequency distribution.
b. Construct a cumulative frequency distribution.
c. Construct a cumulative relative frequency distribution.

Shafiq Rehman

Numerade Educator

Problem 35

Prepare a scatter plot of the following data:
$$
\begin{array}{llllll}
(5,53) & (21,65) & (14,48) & (11,66) & (9,46) & (4,56) \\
(7,53) & (21,57) & (17,49) & (14,66) & (9,54) & (7,56) \\
(9,53) & (21,52) & (13,49) & (14,56) & (9,59) & (4,56)
\end{array}
$$

Christopher Stanley

Christopher Stanley

Numerade Educator

Problem 36

The following table shows the ages of competitors in a charity tennis event in Rome:
$$
\begin{array}{cc}
\hline \text { Age } & \text { Percent } \\
\hline 18-24 & 18.26 \\
25-34 & 16.25 \\
35-44 & 25.88 \\
45-54 & 19.26 \\
55+ & 20.35 \\
\hline
\end{array}
$$
a. Construct a relative cumulative frequency distribution.
b. What percent of competitors were under the age of 35 ?
c. What percent of competitors were 45 or older?

Donna Densmore

Numerade Educator

Problem 37

The demand for bottled water increases during the hurricane season in Florida. The manager at a plant that bottles drinking water wants to be sure that the process to fill 1-gallon bottles (approximately $3.785$ liters) is operating properly. Currently, the company is testing the volumes of 1-gallon bottles. A random sample of 75 bottles is tested. Study the filling process for this product and submit a report of your findings to the operations manager. Construct a frequency distribution, cumulative frequency distribution, histogram, and a stemand-leaf display. Incorporate these graphs into a well-written summary. How could we apply statistical thinking in this situation? The data are stored in the data file Water.

Nick Johnson

Numerade Educator

Problem 38

Percentage returns for the 25 largest U.S. common stock mutual funds for a particular day are stored in the data file Returns.
a. Construct a histogram to describe the data.
b. Draw a stem-and-leaf display to describe the data.

Jerelyn Nevil

Numerade Educator

Problem 39

Ann Thorne, the operations manager at a suntan lotion manufacturing plant, wants to be sure that the filling process for 8-oz ( $237 \mathrm{~mL}$ ) bottles of SunProtector is operating properly. Suppose that a random sample of 100 bottles of this lotion is selected, the contents are measured, and the volumes (in $\mathrm{mL}$ ) are stored in the data file Sun. Describe the data graphically.

Emily Himsel

Numerade Educator

Problem 40

A company sets different prices for a particular DVD system in eight different regions of the country. The accompanying table shows the numbers of units sold and the corresponding prices (in dollars). Plot the data using a scatter plot with sales as the dependent variable and price as the independent variable.
$$
\begin{array}{ccccccccc}
\hline \text { Sales } & 420 & 380 & 350 & 400 & 440 & 380 & 450 & 420 \\
\hline \text { Price } & 104 & 195 & 148 & 204 & 96 & 256 & 141 & 109 \\
\hline
\end{array}
$$

Shafiq Rehman

Numerade Educator

Problem 41

A corporation administers an aptitude test to all new sales representatives. Management is interested in the possible relationship between test scores and the sales representatives' eventual success. The accompanying table records average weekly sales (in thousands of dollars) and aptitude test scores for a random sample of eight representatives. Construct a scatter plot with weekly sales as the dependent variable and test scores as the independent variable.
$$
\begin{array}{lllllllll}
\hline \text { Weekly sales } & 10 & 12 & 28 & 24 & 18 & 16 & 15 & 12 \\
\hline \text { Test score } & 55 & 60 & 85 & 75 & 80 & 85 & 65 & 60 \\
\hline
\end{array}
$$

Shafiq Rehman

Numerade Educator

Problem 42

Doctors are interested in the possible relationship between the dosage of a medicine and the time required for a patient's recovery. The following table shows, for a sample of 10 patients, dosage levels (in grams) and recovery times (in hours).
These patients have similar characteristics except for medicine dosages. Describe the data graphically with a scatter plot.
$$
\begin{array}{lrrrrrrrrrr}
\hline \text { Dosage level } & 1.2 & 1.3 & 1.0 & 1.4 & 1.5 & 1.8 & 1.2 & 1.3 & 1.4 & 1.3 \\
\hline \text { Recovery time } & 25 & 28 & 40 & 38 & 10 & 9 & 27 & 30 & 16 & 18 \\
\hline
\end{array}
$$

Shafiq Rehman

Numerade Educator

Problem 43

Bishop's supermarket records the actual price for consumer food products and the weekly quantities sold. Use the data file Bishop to obtain the scatter plot for the actual price of a gallon of orange juice and the weekly quantities sold at that price. Does the scatter plot follow the pattern from economic theory?

Charles Carter

Numerade Educator

Problem 44

A Hong Kong snack-food vendor offers 3 types of boxed "lunches to go," priced at $$\$ 3$$, $$\$ 5$$, and $$\$ 10$$, respectively. The vendor would like to establish whether there is a relationship between the price of the boxed lunch and the number of sales achieved per hour. Consequently, over a 15 -day period the vendor records the number of sales made for each of the 3 types of boxed lunches. The following data show the boxed-lunch price $(x)$ and the number sold (y) during each of the 15 lunch hours.
$$
\begin{aligned}
&(3,7)(5,5)(10,2)(3,9)(5,6)(10,5)(3,6)(5,6) \\
&(10,1)(3,10)(5,7)(10,4)(3,5)(5,6)(10,4)
\end{aligned}
$$
Prepare a scatter plot of the points and comment on the relationship between the price of the boxed lunches and the numbers sold each lunchtime.

Shafiq Rehman

Numerade Educator

Problem 45

Sales revenue totals (in dollars) by day of the week are contained in the data file Stordata. Prepare a cross table that contains the days of the week as rows and the four sales quartile intervals as columns.
a. Compute the row percentages.
b. What are the major differences in sales level by day of the week as indicated by the row percentages?
c. Describe the expected sales volume patterns over the week based on this table.

Brandon Cleary

Numerade Educator

Problem 46

6 Many small cities make significant efforts to attract commercial operations such as shopping centers and large retail stores. One of the arguments is that these facilities will contribute to the property that can be taxed and thus provide additional funds for local government needs. The data stored in the data file Citydatr come from a study of municipal revenue-generation capability. Prepare a scatter plot of "taxbase"-the assessed value of all city property in millions of dollarsversus "comper" -the percent of assessed property value that is commercial property. What information does this scatter plot provide about the assessable tax base and percent of commercial property in the city?

Nick Johnson

Numerade Educator

Problem 47

A supervisor of a plant kept records of the time (in seconds) that employees needed to complete a particular task. The data are summarized as follows:
$$
\begin{array}{lcccccc}
\hline \text { Time } & 30<40 & 40<50 & 50<60 & 60<80 & 8<100 & 100<150 \\
\hline \text { Number } & 10 & 15 & 20 & 30 & 24 & 20 \\
\hline
\end{array}
$$
a. Graph the data with a histogram.
b. Discuss possible errors.

Khalida Dawar

Numerade Educator

Problem 48

The following table lists the number of daily visitors to the Web site of a new business during its first year.
$$
\begin{array}{cccc}
\hline \text { Month } & \text { Number } & \text { Month } & \text { Number } \\
\hline 1 & 5,400 & 7 & 5,600 \\
2 & 5,372 & 8 & 5,520 \\
3 & 5,265 & 9 & 5,280 \\
4 & 5,250 & 10 & 5,400 \\
5 & 5,289 & 11 & 5,448 \\
6 & 5,350 & 12 & 5,500 \\
\hline
\end{array}
$$
a. Graph the data with a time-series plot using a vertical scale from 5,000 to 5,700 .
b. Graph the data with a time-series plot using a vertical scale from 4,000 to 7,000 .
c. Comment on the difference between these two time-series plots.

Charles Carter

Numerade Educator

Problem 49

The data file Exchange Rate shows an index of the value of the U.S. dollar against trading partners' currencies over 12 consecutive months.
a. Construct a time-series plot of this data using a vertical axis that ranges from 92 to 106 .
b. Construct a time-series plot of this data using a vertical axis that ranges from 75 to 120 .
c. Comment on these two time-series plots.

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 50

The data file Inventory Sales shows the inventory-sales ratio for manufacturing and trade in the United States over a period of 12 years. Construct two time-series plots for this series with different vertical ranges. Comment on your findings.

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 51

Describe graphically the time (in hours) that 20 students studied for a statistics test.
$\begin{array}{llllllllll}6.5 & 5.8 & 4.5 & 6.2 & 4.8 & 7.3 & 4.6 & 3.9 & 4.4 & 5.5 \\ 5.2 & 6.7 & 3.0 & 2.4 & 5.0 & 3.6 & 2.9 & 4.0 & 2.8 & 3.6\end{array}$

Sheryl Ezze

Numerade Educator

Problem 52

A sample of 20 financial analysts was asked to provide forecasts of earnings per share of a corporation for next year. The results are summarized in the following table:
$$
\begin{array}{rc}
\hline \text { Forecast (\$ per share) } & \text { Number of Analysts } \\
\hline 9.95<10.45 & 2 \\
10.45<10.95 & 8 \\
10.95<11.45 & 6 \\
11.45<11.95 & 3 \\
11.95<12.45 & 1 \\
\hline
\end{array}
$$
a. Construct the histogram.
b. Determine the relative frequencies.
c. Determine the cumulative frequencies.
d. Determine and interpret the relative cumulative frequencies.

Sheryl Ezze

Numerade Educator

Problem 53

In one region it was found that $28 \%$ of people with incomes less than $$\$ 50,000$$ use the Internet; $48 \%$ of those with incomes between $$\$ 50,000$$ to $$\$ 74,999$$ use the Internet; and $70 \%$ of those with incomes of at least $$\$ 75,000$$ use the Internet. Use a pie chart or a bar chart to plot this data.

Shafiq Rehman

Numerade Educator

Problem 54

Regulatory agencies and the U.S. Congress are recognizing both the values and emerging issues for small firms as the Sarbanes-Oxley Act of 2002 (SOX) has been implemented. On April 23, 2006, the Advisory Committee on Smaller Public Companies issued a final report to the Security and Exchange Commission assessing the impact of $\mathrm{SOX}$ on smaller public companies (Final Report 2006). A random sample of CEOs, CFOs, and board members of small, medium, and large firms were surveyed and their opinions of the overall impact of $\mathrm{SOX}$ on their firm were:
$$
\begin{array}{lccc}
\hline \text { Impact of Sox } & \text { Small Firms } & \text { Medium Firms } & \text { Large Firms } \\
\hline \text { Little or no impact } & 17 & 13 & 6 \\
\begin{array}{l}
\text { Moderate to very } \\
\text { major impact }
\end{array} & 13 & 41 & 22 \\
\hline
\end{array}
$$
Construct a cluster bar chart of these findings (Michelson, Stryker and Thorne 2009).

Shafiq Rehman

Numerade Educator

Problem 55

A survey of consumers who had recently purchased their first smartphones sought to identify how much these consumers knew about using smartphone technology. The findings were as follows: $90 \%$ could connect to the Internet, $80 \%$ could download an app, $55 \%$ could use Bluetooth, $44 \%$ had set up their phones to receive e-mail, and $5 \%$ knew only how to make and receive voice calls and texts. Present this data graphically.

Shafiq Rehman

Numerade Educator

Problem 56

A team of undergraduate business students was asked to recommend improvement to the data entry process at the county appraiser's office. The team identified several types of errors, such as posting an incorrect name or entering an incorrect parcel number. The deed abstractors were asked to keep a record of the errors in data entry that were sent to them. The following table is a frequency distribution of errors:
$$
\begin{array}{lc}
\hline \text { Defect } & \text { Total } \\
\hline \text { Posting error in name } & 23 \\
\text { Posting error in parcel } & 21 \\
\text { Property sold after tax bills were mailed } & 5 \\
\begin{array}{l}
\text { Inappropriate call transfer (not part of deeds/ } \\
\text { mapping) }
\end{array} & 18 \\
\text { Posting error in legal description/incomplete } & 4 \\
\text { legal description } & \\
\text { Deeds received after tax bills printed } & 6 \\
\text { Correspondence errors } & 2 \\
\text { Miscellaneous errors } & 1 \\
\hline
\end{array}
$$
a. Construct a Pareto diagram of these defects in data entry.
b. What recommendations would you suggest to the county appraiser?

James Kiss

Numerade Educator

Problem 57

Groupon, an online Web site, offers its subscribers at least one special deal per day to local businesses in their cities such as places to eat, health-related activities (spas or fitness centers), places to see (museums), a variety of activities such as golfing or sky diving, or other specials (such as a Gap Groupon or a gourmet fruit basket). Since December 2008 , the number of subscribers has increased from 400 to more than 50 million in more than 400 markets, in over 40 countries (Groupon Hits $50 \mathrm{~m}$ Subscribers, 2011). To date, Groupon claims that more than $30 \mathrm{mil}$ lion Groupons have been sold, saving subscribers nearly $\$ 1.3$ billion. From a survey of students at one university, it, was found that during the past week, the following number and category of Groupons were purchased: 230 (activities); 80 (food); 90 (health-related items), and 50 (other).
a. Graph these purchases with a pie chart.
b. Graph these purchases with a bar chart.

Shafiq Rehman

Numerade Educator

Problem 58

For the random sample of Groupon purchases by the university students in Exercise 1.57, the following breakdown by gender was obtained:
$$
\begin{array}{lccc}
\hline & \text { Male } & \text { Female } & \text { Total } \\
\hline \text { Activities } & 140 & 90 & 230 \\
\text { Food } & 45 & 35 & 80 \\
\text { Health related } & 20 & 70 & 90 \\
\text { Other } & 10 & 40 & 50 \\
\text { Total } & 215 & 235 & 450 \\
\hline
\end{array}
$$
a. Graphically depict the type of purchase by gender with a component bar chart.
b. Graphically depict the type of purchase by gender with a cluster bar chart.

Shafiq Rehman

Numerade Educator

Problem 59

What is the relationship between the $\$$ price of paint and the gallon demand for this paint? A random sample of (price, quantity) data for 7 days of operation was obtained. Construct a plot and describe the relationship between quantity and price, with emphasis on any unusual observations.
$$
\begin{aligned}
&(10,100)(8,120)(5,200)(4,200)(10,90) \\
&(7,110)(6,150)
\end{aligned}
$$

Dale Sanford

Numerade Educator

Problem 60

A consumer goods company has been studying the effect of advertising on total profits. As part of this study, data on advertising expenditures $(1,000 \mathrm{~s})$ and total sales $(1,000 \mathrm{~s})$ were collected for a 5-month period and are as follows:
$$
(10,100)(15,200)(7,80)(12,120)(14,150)
$$
The first number is advertising expenditures and the second is total sales. Plot the data.

Shafiq Rehman

Numerade Educator

Problem 61

The president of Floor Coverings Unlimited wants information concerning the relationship between retail experience (years) and weekly sales (in hundreds of dollars). He obtained the following random sample of experience and weekly sales:
$$
\begin{aligned}
&(2,5)(4,10)(3,8)(6,18)(3,6)(5,15) \\
&(6,20)(2,4)
\end{aligned}
$$
The first number for each observation is years of experience and the second is weekly sales. Plot the data.

Shafiq Rehman

Numerade Educator

Problem 62

A Malaysian swimming coach wanted to see if working with a sports psychologist would improve the performance of elite swimmers. A random sample of 12 swimmers took part in the year-long program. The following ordered pairs show the number of sessions each swimmer had with the psychologist and the corresponding improvement in their personal best times (in seconds) for the 800-meter freestyle.
$$
\begin{aligned}
&(9,2.4),(20,5.6),(6,1.8),(12,4.1),(9,2.1) \\
&(15,4.8),(7,2.3),(9,4.3),(18,6.2),(24,7.1) \\
&(9,1.5),(6,2.2)
\end{aligned}
$$
Plot the data and state whether you think the program has been successful.

Shafiq Rehman

Numerade Educator

Problem 63

Four types of checking accounts are offered by one bank. Suppose that recently a random sample of 300 bank customers was surveyed and asked several questions. It was found that $60 \%$ of the respondents preferred Easy Checking; $12 \%$, Intelligent Checking; $18 \%$, Super Checking; and the remainder, Ultimate Checking. Of those who selected Easy Checking, 100 were females; one-third of the respondents who selected Intelligent Checking were males; half of the respondents who selected Super Checking were males; and $80 \%$ of respondents who selected Ultimate Checking were males.
a. Describe the data with a cross table.
b. Describe the data graphically.

Shafiq Rehman

Numerade Educator

Problem 64

How did people first learn about a new product? A random sample of 200 shoppers at a particular store was asked their age and whether they heard about the product from a friend or through a local newspaper advertisement. The results indicated that 50 respondents were under 21 years of age, 90 people were in the age group between 21 and 35, and 60 respondents were older than 35 years of age. Of those under 21 years old, 30 heard about the product from a friend, and the remainder learned about the product through an advertisement in the local paper. One-third of the people in the age category from 21 to 35 first learned about the product from the local newspaper advertisement; the remainder of this age group learned about the product from a friend. A friend informed $30 \%$ of the people in the over-35 age category about the product; the remainder learned about it from the local newspaper advertisement.
a. Describe the data with a cross table.
b. Describe the data graphically.

Shafiq Rehman

Numerade Educator

Problem 65

A random sample of customers was asked to select their favorite soft drink from a list of five brands. The results showed that 30 preferred Brand A, 50 preferred Brand B, 46 preferred Brand C, 100 preferred Brand D, and 14 preferred Brand $\mathrm{E}$.
a. Construct a pie chart.
b. Construct a bar chart.

Shafiq Rehman

Numerade Educator

Problem 66

The owner of Snappy Lawn Care thinks that the time it takes to mow a yard may be related to the temperatures at the time of mowing. He randomly sampled several yards of the same size and collected data on temperature and time it takes to mow. The data are in the data file Snappy Lawn Care. Plot the data with a scatter plot and comment on your findings.

Sisi Gao

Numerade Educator

Problem 67

Construct a time-series plot of population growth for the state of New York from 2002 to the present. (Hint: Check www.census.gov.)

Yifan Xu

Numerade Educator

Problem 68

Florin, owner of Florin's Flower Mart, randomly sampled 124 customers in order to obtain data such as a customer's method of payment (Visa, MasterCard, American Express, cash, or some other method) and the day of the week that the customer made the purchase (except for when the store is closed on Sundays). The data are contained in the data file Florin. Construct the following:
a. A cross table of the variables method of payment and day of purchase
b. A pie chart of day of purchase

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 69

A random sample of 50 employees working for a large international bank in Hong Kong was interviewed to establish whether there was a link between the jobs of employees in the bank and where they normally ate at lunchtime-either in the canteen or at their desks. The results of this research showed that $75 \%$ of staff in clerical roles normally ate in the office canteen and $54 \%$ of managers normally ate lunch at their desks. Compile a cross table and bar chart to display this information,

Sheryl Ezze

Numerade Educator

Problem 70

The closing costs of shares of Apple Inc. (AAPL) stock from January 3,2011 , through February 21 , 2011, are contained in the data file Apple Stock Prices.
a. Construct a time series plot of the closing costs.
b. Obtain closing costs of Apple stock for the most recent 30-day period.

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 71

RELEVANT Magazine keeps records of traffic (such as the weekly number of new visitors) to its Web site from various social networks, such as Facebook and Twitter (Butcher 2011). Use a time-series plot to graph the number of unique page views by weekly new visitors to RELEVANT Magazine's Web site by Facebook users over a recent 9-week period. The data are stored in the data file RELEVANT Magazine.

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 72

How much time (in minutes) do people spend on a typical visit to a local mall? A random sample of $n=104$ shoppers was timed and the results (in minutes) are stored in the data file Shopping Times.
a. Construct a histogram of these shopping times.
b. Construct a stem-and-leaf display of these shopping times.

Wendi Zhao

Numerade Educator

Problem 73

The data file Grade Point Averages contains a random sample of 156 grade point averages for students at one university. Construct a stem-and-leaf display of the data.

Maxime Rossetti

Maxime Rossetti

Numerade Educator

Problem 74

A corporation administers an aptitude test to all new sales representatives. Management is interested in the extent to which this test is able to predict weekly sales of new representatives. Aptitude test scores range from 0 to 30 with greater scores indicating a higher aptitude. Weekly sales are recorded in hundreds of dollars. Construct a scatter plot of the following test scores and weekly sales for a random sample of 10 representatives.
$$
\begin{array}{lllllllllll}
\hline \text { Test Score, } x & 12 & 30 & 15 & 24 & 14 & 18 & 28 & 26 & 19 & 27 \\
\hline \text { Weekly Sales, } y & 20 & 60 & 27 & 50 & 21 & 30 & 61 & 54 & 32 & 57 \\
\hline
\end{array}
$$

Shafiq Rehman

Numerade Educator