Chapter 1 Data and Statistics - Solution Manual

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Chapter 1 Data and Statistics Learning Objectives 1. Obtain an appreciation for the breadth of statistical applications in business and economics. 2. Understand the meaning of the terms elements, variables, and observations as they are used in

statistics. 3. Obtain an understanding of the difference between categorical, quantitative, crossectional and time

series data. 4. Learn about the sources of data for statistical analysis, both internal and external, to the firm. 5. Be aware of how errors can arise in data. 6. Know the meaning of descriptive statistics and statistical inference. 7. Be able to distinguish between a population and a sample. 8. Understand the role a sample plays in making statistical inferences about the population. 9. Know the meaning of the term data mining. 10. Be aware of ethical guidelines for statistical practice.

Chapter 1



Solutions: 1. Statistics can be referred to as numerical facts. In a broader sense, statistics is the field of study

dealing with the collection, analysis, presentation and interpretation of data. 2. a. The ten elements are the ten tablet computers b. 5 variables: Cost ($), Operating System, Display Size (inches), Battery Life (hours), CPU

Manufacturer c. Categorical variables: Operating System and CPU Manufacturer

Quantitative variables: Cost ($), Display Size (inches), and Battery Life (hours)

d. Variable Measurement Scale Cost ($) Ratio Operating System Nominal Display Size (inches) Ratio Battery Life (hours) Ratio CPU Manufacturer Nominal

3. a. Average cost = 5829/10 = $582.90 b. Average cost with a Windows operating system = 3616/5 = $723.20 Average cost with an Android operating system = 1714/4 = $428.5 The average cost with a Windows operating system is much higher. c. 2 of 10 or 20% use a CPU manufactured by TI OMAP d. 4 of 10 or 40% use an Android operating system

4. a. There are eight elements in this data set; each element corresponds to one of the eight models of

cordless telephones b. Categorical variables: Voice Quality and Handset on Base Quantitative variables: Price, Overall Score, and Talk Time c. Price – ratio measurement Overall Score – interval measurement Voice Quality – ordinal measurement Handset on Base – nominal measurement Talk Time – ratio measurement 5. a. Average Price = 545/8 = $68.13 b. Average Talk Time = 71/8 = 8.875 hours

c. Percentage rated Excellent: 2 of 8 2/8 = .25, or 25%

d. Percentage with Handset on Base: 4 of 8 4/8 = .50, or 50%

Data and Statistics



6. a. Categorical b. Quantitative c. Categorical

d. Quantitative e. Quantitative 7. a. Each question has a yes or no categorical response. b. Yes and no are the labels for the customer responses. A nominal scale is being used. 8. a. 762 b. Categorical c. Percentages

d. .67(762) = 510.54 510 or 511 respondents said they want the amendment to pass.

9. a. Categorical b. 30 of 71; 42.3% 10. a. Categorical b. Percentages c. 44 of 1080 respondents or approximately 4% strongly agree with allowing drivers of motor vehicles

to talk on a hand-held cell phone while driving. d. 165 of the 1080 respondents or 15% of said they somewhat disagree and 741 or 69% said they

strongly disagree. Thus, there does not appear to be general support for allowing drivers of motor vehicles to talk on a hand-held cell phone while driving.

11. a. Categorical

b. 295 + 672 + 51 = 1018

c. (295/1018)100 = 29% d. Support against; (672/1018)100 = 66% said they would vote against the law. 12. a. The population is all visitors coming to the state of Hawaii. b. Since airline flights carry the vast majority of visitors to the state, the use of questionnaires for

passengers during incoming flights is a good way to reach this population. The questionnaire actually appears on the back of a mandatory plants and animals declaration form that passengers must complete during the incoming flight. A large percentage of passengers complete the visitor information questionnaire.

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c. Questions 1 and 4 provide quantitative data indicating the number of visits and the number of days in Hawaii. Questions 2 and 3 provide categorical data indicating the categories of reason for the trip and where the visitor plans to stay.

13. a. Google revenue in billions of dollars

b. Quantitative c. Time series d. Google revenue is increasing over time. 14. a. The graph of the time series follows:

b. In 2007 and 2008 Hertz was the clear market share leader. In 2009 and 2010 Hertz and Avis have

approximately the same market share. The market share for Dollar appears to be declining. c. The bar chart for 2010 is shown below.

0

50

100

150

200

250

300

350

2006 2007 2008 2009 2010 2011

Cars in Service (1000s)

Year

Hertz

Dollar

Avis

Data and Statistics



This chart is based on cross-sectional data. 15. a. Quantitative – number of recreational boating accidents b. Time series c. July; 1100 d. 2.9%; Yes, because most recreational boating takes place during the summer months. e. The bar graph follows the shape of a bell curve. 16. The answers to this exercise depend on updating the time series of the average price per gallon of

conventional regular gasoline as shown in Figure 1.1. Contact the website www.eia.doe.gov to obtain the most recent time series data. The answers should focus on the most recent changes or trend in the average price per gallon.

17. Internal data on salaries of other employees can be obtained from the personnel department.

External data might be obtained from the Department of Labor or industry associations.

18. a. 684/1021; or approximately 67% b. 612 c. Categorical 19. a. All subscribers of Business Week in North America at the time the survey was conducted. b. Quantitative c. Categorical (yes or no) d. Crossectional - all the data relate to the same time. e. Using the sample results, we could infer or estimate 59% of the population of subscribers have an

annual income of $75,000 or more and 50% of the population of subscribers have an American Express credit card.

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50

100

150

200

250

300

350

Hertz Dollar Avis

Cars in Service (1000s)

Company

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20. a. 43% of managers were bullish or very bullish. 21% of managers expected health care to be the leading industry over the next 12 months. b. We estimate the average 12-month return estimate for the population of investment managers to be

11.2%. c. We estimate the average over the population of investment managers to be 2.5 years. 21. a. The two populations are the population of women whose mothers took the drug DES during

pregnancy and the population of women whose mothers did not take the drug DES during pregnancy.

b. It was a survey. c. 63 / 3.980 = 15.8 women out of each 1000 developed tissue abnormalities. d. The article reported “twice” as many abnormalities in the women whose mothers had taken DES

during pregnancy. Thus, a rough estimate would be 15.8/2 = 7.9 abnormalities per 1000 women whose mothers had not taken DES during pregnancy.

e. In many situations, disease occurrences are rare and affect only a small portion of the population.

Large samples are needed to collect data on a reasonable number of cases where the disease exists. 22. a. The population consists of all clients that currently have a home listed for sale with the agency or

have hired the agency to help them locate a new home. b. Some of the ways that could be used to collect the data are as follows:

A survey could be mailed to each of the agency’s clients.

Each client could be sent an email with a survey attached.

The next time one of the firm’s agents meets with a client they could conduct a personal interview to obtain the data.

23. a. This finding is applicable to the population of all American adults. b. This finding is applicable to the population of American adults that own a cellphone and/or a tablet

computer. c. They conducted a sample survey. It would be way too costly to survey all American adults or all

American adults who own cellphones and/or tablet computers. As we will see later in the text, very good results can be obtained using a sample survey.

d. These results should be quite interesting to restaurant owners. It suggests that it would be

worthwhile for them to have a website and to consider advertising through an internet search company, such as Google.

24. a. This is a statistically correct descriptive statistic for the sample. b. An incorrect generalization since the data was not collected for the entire population. c. An acceptable statistical inference based on the use of the word “estimate.”

Data and Statistics



d. While this statement is true for the sample, it is not a justifiable conclusion for the entire population. e. This statement is not statistically supportable. It is entirely possible and even very likely that at least

some students will be outside the 65 to 90 range of grades. 25. a. There are five variables: Exchange, Ticker Symbol, Market Cap, Price/Earnings Ratio and Gross

Profit Margin. b. Categorical variables: Exchange and Ticker Symbol Quantitative variables: Market Cap, Price/Earnings Ratio, Gross Profit Margin c. Exchange variable:

Exchange Frequency Percent Frequency AMEX 5 (5/25) 20% NYSE 3 (3/25) 12% OTC 17 (17/25) 68% 25

d. Gross Profit Margin variable:

Gross Profit Margin Frequency 0.0 – 14.9 2 15.0 – 29.9 6 30.0 – 44.9 8 45.0 – 59.9 6 60.0 – 74.9 3

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AMEX NYSE OTC

Exchange

Per

cen

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req

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e. Sum the Price/Earnings Ratio data for all 25 companies. Sum = 505.4 Average Price/Earnings Ratio = Sum/25 = 505.4/25 = 20.2

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0.0-14.9 15.0-29.9 30.0-44.9 45.0-59.9 60.0-74.9

Gross Profit Margin

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CP - 1 © 2013 Cengage Learning. All Rights Reserved.


Solutions to

Case Problems

Chapter 2

Descriptive Statistics: Tabular and Graphical Presentations

Case Problem 1: Pelican Stores

1. There were 70 Promotional customers and 30 Regular customers. Because there are 100

observations in the sample, the frequency and percent frequency distribution are the same. Percent

frequency distributions for many of the variables are given.

No. of Items Percent Frequency

1 29

2 27

3 10

4 10

5 9

6 7

7 or more 8

Total: 100

Net Sales Percent Frequency

0.00 - 24.99 9

25.00 - 49.99 30

50.00 - 74.99 25

75.00 - 99.99 10

100.00 - 124.99 12

125.00 - 149.99 4

150.00 - 174.99 3

175.00 - 199.99 3

200 or more 4

Total: 100

Method of Payment Percent Frequency

American Express 2

Discover 4

MasterCard 14

Proprietary Card 70

Visa 10

Total: 100

Gender Percent Frequency

Female 93

Male 7

Total: 100

Chapter 2 Descriptive Statistics: Tabular and Graphical Presentations



Martial Status Percent Frequency

Married 84

Single 16

Total: 100

Age Percent Frequency

20 - 29 10

30 - 39 30

40 - 49 33

50 - 59 16

60 - 69 7

70 - 79 4

Total: 100

These percent frequency distributions provide a profile of Pelican's customers. Many observations

are possible, including:

A large majority of the customers use National Clothing’s proprietary credit card.

Over half of the customers purchase 1 or 2 items, but a few make numerous purchases.

The percent frequency distribution of net sales shows that 61% of the customers spent $50 or

more.

Customers are distributed across all adult age groups.

The overwhelming majority of customers are female.

Most of the customers are married.

2.

3. A crosstabulation of type of customer versus net sales is shown.

Net Sales

Customer

0-

25

25-

50

50-

75

75-

100

100-

125

125-

175

175-

200

200-

225

225-

250

250-

275

275-

300

Total

Promotional 7 17 17 8 9 3 2 3 1 2 1 70

Regular 2 13 8 2 3 1 1 30

Total 9 30 25 10 12 4 3 3 1 2 1 100

From the crosstabulation it appears that net sales are larger for promotional customers.




4. A scatter diagram of net Sales vs. age is shown below. A trendline has been fitted to the data. From

this, it appears that there is no relationship between net sales and age.

Age is not a factor in determining net sales.

Case Problem 2: The Motion Picture Industry

This case provides the student with the opportunity to use tabular and graphical presentations to analyze

data from the motion picture industry. Developing and interpreting frequency distributions, percent

frequency distributions and scatter diagrams are emphasized. The interpretations and insights can be quite

varied. We illustrate some below.

Frequency Distribution and Percent Frequency Distribution

The choice of the classes for frequency distributions or percent frequency distributions can be expected to

vary. The frequency distributions we developed are as follows:

Opening Gross Sales

(Millions)

Frequency

(or Percentage)

$0 – 9.99 70

10 – 19.99 15

20 – 29.99 8

30 – 39.99 2

40 – 49.99 1

50 – 59.99 1

60 – 69.99 0

70 – 79.99 1

80 – 89.99 0

90 – 99.99 0

100 – 109.99 2

Total 100

0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

0 10 20 30 40 50 60 70 80 90

Net

Sa

les

Age




Total Gross Sales

(Millions)

Frequency

(or Percentage)

$0 – 49.99 77

50 – 99.99 16

100 – 149.99 1

150 – 199.99 1

200 – 249.99 3

250 – 299.99 1

300 – 349.99 0

350 – 399.99 1

Total 100

Number

of Theaters

Frequency

(or Percentage)

0 – 499 51

500 – 999 3

1000 – 1499 6

1500 – 1999 7

2000 – 2499 5

2500 – 2999 6

3000 – 3499 17

3500 – 3999 5

Total 100

Number of

Weeks

in Top 60

Frequency

(or Percentage)

0 – 4 33

5 – 9 28

10 – 14 18

15 – 19 15

20 – 24 5

25 – 29 1

Total 100




Histograms

The following histograms are based on the frequency distributions shown above.

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80

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Opening Weekend Gross Sales (millions)

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10

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30

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60

70

80

90

Fre

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Total Gross Sales (millions)




Interpretation

Opening Weekend Gross Sales. The distribution is skewed to the right. Numerous motion pictures have

somewhat low opening weekend gross sales, while a relatively few (7%) have an opening weekend gross

sales of $30 million or more. Only 2% had opening weekend gross sales of $100 million or more. 70% of

the motion pictures had opening weekend gross sales less than $10 million and 85% of the motion pictures

had opening weekend gross sales less than $20 million. Unless there is something unusually attractive

about the motion picture, an opening weekend gross sales less than $10 million appears typical.

Total Gross Sales. This distribution is also skewed to the right. Again, the majority of the motion pictures

have relatively low total gross sales with 77% less than $50 million and 93% less than $100 million.

Highly successful blockbuster motion pictures are rare. Total gross sales over $200 million occurred only

5% of the time and over $300 million occurred only 1% of the time. No motion picture reported $400

million in total gross sales. Unless there is something unusually attractive about the motion picture, a total

gross sales less than $50 million appears typical.

0

10

20

30

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50

60

Fre

qu

ency

Number of Theaters

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10

15

20

25

30

35

0-4 5–9 10–14 15–19 20–24 25–29

Fre

qu

ency

Number of Weeks in the Top 60




Number of Theaters. This distribution is skewed to the right, but not so much as sales data distributions.

The number of theaters range from less than 500 to almost 4000. 51% of the motion pictures had the

smaller market exposure with the number of theaters less than 500. Interestingly enough, 22% of the

motion pictures had the widest market exposure, appearing in over 3000 theaters. 3000 to 4000 theaters is

typical for a highly promoted motion picture.

Number of Weeks in Top 60. This distribution is skewed to the right, but not as much as the other

distributions. In appears that almost all newly released movies initially make it into the top 60, with 67%

staying in the top 60 for 5 or more weeks. Even motion pictures with relative low gross sales can appear in

the top 60 motion pictures for a month or more. Almost 40% of the motion pictures are in the top 60 for 10

or more weeks, with 6% of the motion pictures in the top 60 for 20 or more weeks.

General Observations. The data show that there are relative few high-end, highly successful motion

pictures. The financial rewards are there for the pictures that make the blockbuster level. But the majority

of motion pictures will have low opening weekend gross sales and low total gross sales. Motion pictures

being shown in less than 1500 theaters and motion pictures less than 10 weeks in the top 60 are common.

Scatter Diagrams

Three scatter diagrams are suggested to show how Total Gross Sales is related to each of the other three

variables.

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250.00

300.00

350.00

400.00

0.00 20.00 40.00 60.00 80.00 100.00 120.00

Opening Weekend Gross Sales

Tota

l G

ross

Sale

s

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50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

0 500 1,000 1,500 2,000 2,500 3,000 3,500 4,000 4,500

Number of Theaters

To

tal G

ross

Sa

les




Interpretation

Opening Weekend Gross Sales. The scatter plot of total gross sales and opening weekend gross sales

shows a strong positive relationship. Motion pictures with the highest total gross sales were the motion

pictures with the highest opening weekend gross sales. How the motion picture does during its opening

weekend should be a very good predictor of how the motion picture will do in terms of total gross sales.

Note in the scatter diagram that the majority of the motion pictures show a low opening weekend gross

sales and a low total gross sales.

Number of Theaters. The scatter plot of the total gross sales and number of theaters also shows a positive

relationship. For motion pictures playing in less than 3000 theaters, the total gross sales has a positive

relationship with the number of theaters. If the motion picture is shown in more theaters, higher total gross

sales are anticipated. For motion pictures playing in more than 3000 theaters, the relationship is not as

strong. 3000 to 4000 represents the maximum number of theaters possible. If a motion picture is shown in

this many theaters, 15 motion pictures did slightly better in terms of total gross sales. However, the

blockbuster motion pictures in this category showed extremely high total gross sales for the number of

theaters where the motion picture was shown.

Number of Weeks in Top 60. The scatter plot of the total gross sales and number of weeks in the top 60

shows a positive relationship, but this relationship appears to be the weakest of the three relationships

studied. Generally, the more successful, higher gross sales motion pictures are in the top 60 for more

weeks. However, this is not always the case. Four of the six motion pictures with the highest total gross

sales appeared in the top 60 less than 20 weeks. At the same time, four motion pictures with 20 or more

weeks in the top 60 did not have unusually high total gross sales. This suggests that in some cases

blockbuster movies with high gross sales may run their course quickly and not have an excessively long run

on the top 60 motion picture list. At the same time, perhaps quality motion pictures with a limited audience

may not generate the high total gross sales but may still show a run of 20 or more weeks on the top 60

motion picture list. The number of weeks in the top 60 does not appear to the best predictor of total gross

sales.

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300.00

350.00

400.00

0 5 10 15 20 25 30

Number of Weeks in the Top 60

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tal G

ross

Sa

les




Case Problem 3: Queen City

This case provides the student with the opportunity to use basic tabular and graphical presentations to

describe data from the annual expenditures for the city of Cincinnati, Ohio. The data set is large relative to

others in the text. It contains 5,427 records of expenditures. As such, one point of this case is to expose

students to a larger data set and help them understand that the pivot tables and charts can be used on a

larger data set. In some cases, the student will have to copy, paste, and aggregate data to create the desired

tables and charts. Style of presentation may vary by student (for example, vertical versus horizontal bar

charts may be used). We illustrate with results and comments below.

Expenditures by Category

The pivot table shows expenditures and percentage of total expenditures by category. The bar chart shows

percentage of total expenditures by category (both the table and the bar chart are sorted in descending

order). Capital expenditures and payroll account for over 50% of all expenditures. Total expenditures are

over $660 million. Debt Service seems somewhat high, as it is over 10% of total expenditures.

Category Total Expenditures % of Total Expenditures

Capital $198,365,854 29.98%

Payroll $145,017,555 21.92%

Debt Service $86,913,978 13.14%

Contractual Services $85,043,249 12.85%

Fringe Benefits $66,053,340 9.98%

Fixed Costs $53,732,177 8.12%

Materials and Supplies $19,934,710 3.01%

Inventory $6,393,394 0.97%

Payables $180,435 0.03%

Grand Total $661,634,693 100.0%

0.00% 5.00% 10.00% 15.00% 20.00% 25.00% 30.00%

Payables

Inventory

Materials and Supplies

Fixed Costs

Fringe Benefits

Contractual Services

Debt Service

Payroll

Capital

% of Total Expenditures

Category




Expenditures by Department

The following table and bar chart show the percentages of total expenditures incurred by department. Note

that we have combined all departments that individually incurred less than 1% of the total expenditures.

There are 119 departments, and 96 each account for less than 1% of the total expenditures. As shown

below, only six individual departments incur 5% or more of the total expenditures. These include, Police,

Sewers, Transportation Engineering (Engineering). Fire, Sewer Debt Service and Finance/Risk

Management. Debt service on sewers as a percentage of total expenditures appears to be very high.

Department

% of Total

Expenditures

Department of Police 9.7%

Department of Sewers 8.8%

Transportation and Engineering, (Engineering) 8.7%

Department of Fire 7.2%

Sewers, Debt Service 6.6%

Finance, Risk Management 5.4%

SORTA Operations 3.6%

Water Works, Debt Service 3.2%

Department of water Works 3.1%

Finance, Treasury 2.8%

Economic Development 2.1%

Division of Parking Services 1.9%

Community Development, Housing 1.7%

Enterprise Technology Solutions 1.7%

Public Services, Fleet Services 1.7%

Finance, Accounts & Audits 1.7%

Transportation and Engineering, Planning 1.6%

Public Services, Neighborhood Operations 1.4%

Sewers, Millcreek 1.3%

Health, Primary Health Care Centers 1.2%

Water Works, Water Supply 1.2%

Public Services, Facilities Management 1.1%

Sewers, Wastewater Administration 1.0%

Other Depts. (< 1% each) 21.2%

Total 100.0%




Expenditures by Fund

The following bar table and bar chart show the percentages of total expenditures charged by fund used to

pay. Note that we have combined those funds that each cover less than 1% of the total expenditures. There

are 129 funds in the data base, and 117 of these funds each account for less than 1% of total expenditures.

Fund % of Total Expenditures

Covered

050 - GENERAL FUND 25.5%

980 - CAPITAL PROJECTS 16.0%

701 - METROPOLITAN SEWER DISTRICT OF GREATER CINCINNATI 12.7%

704 - METROPOLITAN SEWER DISTRICT CAPITAL IMPROVEMENTS 8.8%

101 - WATER WORKS 7.9%

711 - RISK MANAGEMENT 4.9%

759 - INCOME TAX – TRANSIT 3.7%

151 - BOND RETIREMENT – CITY 2.4%

202 - FLEET SERVICES 1.7%

898 - WATER WORKS IMPROVEMENT 12 1.3%

897 - WATER WORKS IMPROVEMENT 11 1.3%

302 - INCOME TAX – INFRASTRUCTURE 1.1%

Other (< 1 % each). 12.9%

Total 100.0%

0% 5% 10% 15% 20% 25%

Sewers, Wastewater Administration

Public Services, Facilities Management

Water Works, Water Supply

Health, Primary Health Care Centers

Sewers, Millcreek

Public Services, Neighborhood Operations

Transportation and Engineering, Planning

Finance, Accounts & Audits

Public Services, Fleet Services

Enterprise Technology Solutions

Community Development, Housing

Division of Parking Services

Economic Development

Finance, Treasury

Department of water Works

Water Works, Debt Service

SORTA Operaitions

Finance, Risk Management

Sewers, Debt Service

Department of Fire

Transportation and Engineering, Engineering

Department of Sewers

Department of Police

Other Depts (< 1% each)

Percentage of Total Expenditures

Department




Other Points: There are 5,427 records of expenditures in the data base, of which 235 (4.3%) are negative.

0.00% 5.00% 10.00% 15.00% 20.00% 25.00% 30.00%

302 - INCOME TAX - INFRASTRUCTURE

897 - WATER WORKS IMPROVEMENT 11

898 - WATER WORKS IMPROVEMENT 12

202 - FLEET SERVICES

151 - BOND RETIREMENT - CITY

759 - INCOME TAX - TRANSIT

711 - RISK MANAGEMENT

101 - WATER WORKS

704 - METROPOLITAN SEWER DISTRICT …

701 - METROPOLITAN SEWER DISTRICT OF …

Other (< 1 % each)

980 - CAPITAL PROJECTS

050 - GENERAL FUND

% of Total Spending

Fund

Chapter 1 Data and Statistics - Solution Manual

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