Cheng-Few Lee • John C. Lee • Alice C. Lee*
Statistics for Businessand Financial Economics
Third Edition
*Disclaimer: Any views or opinions presented in this publication are solely those of the authors
and do not necessarily represent those of State Street Corporation. State Street Corporation is not
associated in any way with this publication and accepts no liability for the contents of this
publication.
Cheng-Few LeeDepartment of Finance and EconomicsRutgers University Business SchoolPiscataway, New JerseyUSA
John C. LeeCenter for PBBEF ResearchMorrisplains, New JerseyUSA
Alice C. LeeState Street CorporationBoston, MassachusettsUSA
ISBN 978-1-4614-5896-8 ISBN 978-1-4614-5897-5 (eBook)DOI 10.1007/978-1-4614-5897-5Springer New York Heidelberg Dordrecht London
Library of Congress Control Number: 2012951347
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Springer is part of Springer Science+Business Media (www.springer.com)
We like to dedicate this book toSchwinne C. Lee, Jennifer Lee, Michael Lee,and Michelle Lee.
Cheng-Few Lee, John C. Lee,and Alice C. Lee
About the Authors
Cheng-Few Lee is a Distinguished Professor of Finance at Rutgers Business
School, Rutgers University and was chairperson of the Department of Finance
from 1988–1995. He has also served on the faculty of the University of Illinois
(IBE Professor of Finance) and the University of Georgia. He has maintained
academic and consulting ties in Taiwan, Hong Kong, China and the United States
for the past three decades. He has been a consultant to many prominent groups
including, the American Insurance Group, the World Bank, the United Nations and
The Marmon Group Inc., Wintek Corporation and Polaris Financial Group, etc.
Professor Lee founded the Review of Quantitative Finance and Accounting
(RQFA) in 1990 and the Review of Pacific Basin Financial Markets and Policies
(RPBFMP) in 1998, and serves as managing editor for both journals. He was also
a co-editor of the Financial Review (1985–1991) and the Quarterly Review of
Economics and Business (1987–1989).
In the past thirty-nine years, Dr. Lee has written numerous textbooks ranging
in subject matter from financial management to corporate finance, security
analysis and portfolio management to financial analysis, planning and forecasting,
and business statistics. Dr. Lee has also published more than 200 articles in more
than twenty different journals in finance, accounting, economics, statistics, and
management. Professor Lee has been ranked the most published finance professor
worldwide during 1953–2008.
Alice C. Lee is currently a vice president in finance at State Street Corporation,
heading up a group that provides analytics and valuations in support to the corpo-
rate Chief Accounting Officer. She was also previously a Vice President in the
Model Validation Group, Enterprise Risk Management, at State Street Corporation.
Her career spans over 20 years of experience, with a diverse background that
includes academia, engineering, sales, and management consulting. Her primary
areas of expertise and research are corporate finance and financial institutions. She
is coauthor of Statistics for Business and Financial Economics, 2nd ed and 3rd ed
(with Cheng F. Lee and John C. Lee), Financial Analysis, Planning and Forecasting,
2nd ed (with Cheng F. Lee and John C. Lee), and Security Analysis, Portfolio
Management, and Financial Derivatives (with Cheng F. Lee, Joseph Finnerty,
vii
John C. Lee and Donald Wort). In addition, she has coedited other annual
publications including Advances in Investment Analysis and Portfolio Manage-
ment (with Cheng F. Lee).
John C. Lee is a Microsoft Certified Professional in Microsoft Visual Basic and
Microsoft Excel VBA. He has a Bachelor and Masters degree in accounting from
the University of Illinois at Urbana-Champaign. John has worked over 20 years in
both the business and technical fields as an accountant, auditor, systems analyst and
as a business software developer. He is the author of the book on how to use
MINITAB and Microsoft Excel to do statistical analysis which is a companion text
to Statistics of Business and Financial Economics, of which he is one of the co-
authors. In addition, he also published Financial Analysis, Planning and
Forecasting, 2ed. (with Cheng F. Lee and Alice C. Lee) , and Security Analysis,
Portfolio Management, and Financial Derivatives (with Cheng F. Lee, Joseph
Finnerty, Alice C. Lee and Donald Wort). John has been a Senior Technology
Officer at the Chase Manhattan Bank, Assistant Vice President at Merrill Lynch
and Associated Director at UBS. Currently, he is the Director of the Center for
PBBEF Research.
viii About the Authors
Preface to the Third Edition
Since the first edition of this book was published in 1993, and the second edition
was published in 2000, it has been widely used in universities in the United States,
Asia, Europe, and other countries. The following universities had adopted this book
as a course text (Here is a partial list of the schools that have adopted this statistics
book. However, it is not a full list because publishers do not have access to the
wholesaler’s list of schools that purchase this book):
Aarhus School of Business, Denmark State University of New York – Binghamton
University, USA
University of Alabama, USA Norwegian School of Economics & Business
Administration, Norway
Aoyama Gakun University, Japan University of North Carolina at Greensboro,
USA
University of Arkansas, USA University of Notre Dame, USA
Bogazici University, Turkey Reading University, England, UK
University of California, Los Angeles, USA Rutgers University, USA
Carnegie Mellon University, USA San Francisco State University, USA
Chaminade University of Honolulu, USA St Joseph’s College-Suffolk Campus, USA
Catholic University of America, USA University of St. Thomas, USA
National Cheng Kung University, Taiwan Suffolk University, USA
Cleary University, USA National Taiwan University, Taiwan
National Chiao Tung University, Taiwan Virginia Polytechnic & State University, USA
University of Gothenburg, Sweden Washington University, USA
City University of Hong Kong, China Western Kentucky University, USA
University of Hartford, USA Western Washington University, USA
University of Illinois at Chicago, USA
University of Illinois Medical Center, USA
Kainan University, Taiwan
Northern Illinois University, USA
Monmouth University, USA
New York University, USA
ix
We appreciate the schools that use the Second Edition and who have given us
useful suggestions to improve this book. To the best of our knowledge, this is the
only business statistics book that uses finance, economic, and accounting data
throughout the entire book. Therefore, this book gives students an understanding
of how to apply the methodology of statistics to real-world situations. In particular,
this book shows how descriptive statistics, probability, statistical distributions,
statistical inference, regression methods, and statistical decision theory can be
used to analyze individual stock price, stock index, stock rate of return, market
rate of return, and decision making. In addition, this book also shows how time-
series analysis and the statistical decision theory method can be used to analyze
accounting and financial data.
How This Edition Has Been Revised
In this edition, we first update the real-world examples and revise some sections to
improve the ease understanding the topics. The auto companies, GM and Ford, used
in empirical section of each chapter are replaced by two pharmaceutical firms,
Johnson & Johnson and Merck. We update the data of stock price, dividend per
share, earnings per share, and financial ratios of Johnson & Johnson and Merck until
2010. The annual macroeconomic data, such as prime rate, GDP, CPI, 3-month
T-Bill rate, are updated to 2009. The EPS, DPS, and PPS for Dow Jones 30 Indus-
trial Firms used in the project are also updated to 2009. The time aggregation and
the estimation of the market model are added in example 16.8. The questions added
to this edition are as follows:
Chapter Problems
1 28, 29, 30, 31
2 52, 53, 54, 55
3 50, 51, 52, 53
4 63, 64, 65, 66, 67, 68, 69, 70
5 83, 84, 85, 86
6 75, 76, 77, 78
7 70, 71, 72, 73
8 88, 89, 90, 91, 92
9 68, 69, 70, 71
10 102, 103, 104, 105
11 100, 101,102,103, 104
12 99, 100, 101, 102
13 77, 78, 79, 80, 81
14 70, 71, 72, 73, 74
15 66, 67, 68, 69, 70
16 72, 73, 74, 75, 76
17 82, 83, 84, 85, 86
18 77, 78, 79, 80, 81
(continued)
x Preface to the Third Edition
Chapter Problems
19 64, 65, 66, 67, 68
20 86, 87, 88, 89, 90
21 68, 69, 70, 71, 72, 73
Alternative Ways to Use the Text
There are five alternative approaches to use the new edition of this book. They can
be described as follows:
A. Traditional ApproachThe goal of this approach is to demonstrate to the students the basic applications
of statistics in general business, economics, and finance. This goal can be
achieved by skipping all appendices, technical footnotes, optional sections,
and other sections at the instructor’s discretion. Using this alternative, students
need only basic algebra, geometry, and business and economic common sense
to understand how statistics can be used in general business, economics, and
finance applications.
B. Accounting and Financial Data Analysis ApproachThe goal of this approach is not only to illustrate basic overall business, eco-
nomic, and finance applications but to show how to use statistics in accounting
and financial data analysis and decision making. This goal can be achieved by
omitting all the technical appendices, technical footnotes, and most optional
sections but covering all or most of the following topics:
Chapter Topic
2 Appendices 2 and 3 on stock market rates of return and on financial statements and
financial ratio analysis
4 Appendix 3, financial ratios for two pharmaceutical firms
6 Appendix 2, applications of the binomial distribution to evaluate call options
7 Appendix 2, cumulative normal distribution function and the option pricing model
9 Section 9.8, analyzing the first four moments of rates of return of the 30 DJI firms
10 Appendix 1, a control chart approach for cash management
13 Appendix 1, derivation of normal equations and optimal portfolio weights
13 Appendix 4, American call option and bivariate normal CDF
16 Appendix 1, dynamic ratio analysis; Appendix 2, term structure of interest rate
19 Section 19.5, stock market indexes; Appendix 1, options on stock indexes and
currencies; Appendix 2, index futures and hedge ratio
21 Sections 21.7 and 21.8 on mean and variance trade-off analysis and the mean and
variance method for capital budgeting decisions; Appendices 2, 3, and 4 on the
graphical derivation of the standard deviation for NPV
(continued)
Preface to the Third Edition xi
C. Project ApproachBased upon all five projects, the instructor can use the project approach to teach
the course. Under this approach, the instructor can ask students to write a term
project by using accounting, economic, and financial data collected from Yahoo
Finance and St. Louis Federal Reserve Bank. The five projects are as follows:
Project I: Project for descriptive statistics
Project II: Project for probability and important distributions
Project III: Project for statistical inferences based on samples
Project IV: Project for regression and correlation analyses
Project V: Project for selected topics in statistical analysis
D. Calculus ApproachThe objective of the fourth approach is to show students how calculus can be
used in statistical analysis. To achieve this goal, the instructor can try to cover
all optional sections and as many of the technical footnotes and appendices as
possible. To do this, of course, the instructor may have to skip many application
examples, such as the finance applications discussed in Approach B.
E. Financial Analysis, Planning and Forecasting ApproachThis book can be used for a course entitled Financial Analysis, Planning and
Forecasting by covering every topic presented in Chapters 2, 3, 4, 6, 7, 9, 13, 14,
15, 16, 18, 19, and 21.
In addition to using this book as a textbook, it can also be very useful as a
reference book for managers who deal with accounting and financial data analysis.
We would like to recommend that the instructor consider requiring students
to solve the following problems by using either MINITAB, Microsoft Excel, or
SAS programs:
Chapter Problems
2 7, 23
3 22, 25, 30, 50, 51, 53
4 4, 6, 7, 8, 27, 38, 39, 40, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 64
6 8, 12, 73, 74
7 5, 43
8 7, 85, 86, 87
9 35, 39, 48
10 27, 28, 55, 104, 105
11 5, 9, 46, 98, 99
12 3, 20, 21, 22, 23, 44, 84, 99, 100, 101, 102
13 5, 10, 23, 47, 48, 49, 50, 51, 63, 64, 65, 66, 67, 68, 69, 70, 78, 79
14 7, 19, 20, 21, 23, 24, 25, 26, 27, 28, 29, 30, 31, 33, 34, 35, 40, 65, 70, 74
15 10, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 70
16 27, 28, 31, 34, 35, 38, 41, 42, 43, 44, 45, 66, 67, 68, 75, 76
17 17, 19, 39, 40, 41, 42, 63
18 7, 34, 35, 36, 37, 38, 39, 40, 41, 42, 50, 60, 61, 62, 64, 68, 69, 76, 77, 78, 79, 80, 81
19 62, 63, 68
20 72, 73
21 12, 65
xii Preface to the Third Edition
Supplementary Materials
Study Guide, by Li-Shya Chen, National Chengchi University, Taiwan, Lie-Jane
Kao, Kainan University, Taiwan, and Ronald L. Moy, St. John’s University. This
fine workbook encourages learning by doing. Each chapter begins with a section
describing the basic concept of that chapter in intuitive terms. Then, the student
goes on to a formal review of the chapter and several worked-out problems that
show in details how the solution is obtained. A variety of multiple-choice, true-
false, and open-ended questions and problems follows. All answers are included at
the end of each chapter.
Data Sets. A wide variety of macroeconomic, financial, and accounting data is
available on computer disks to facilitate student practice. A complete listing of
these data sets is given at the end of this book. The disks themselves are free of
charge.
Instructor’s Guide. The three main parts of the Instructor’s Guide are the Overview
and Objectives; the complete solutions to the text problems by Cheng F. Lee,
John C. Lee, Li-Shya Chen, Lie-Jane Kao; and the Test Bank, with more than
1,000 multiple-choice and true-false problems, by Alice C. Lee, Li-Shya Chen, and
Lie-Jane Kao. Most instructors will find the Instructor’s Guide indispensable.
Computerized Testing Program. With the Test Bank on CD-ROM for notebook
or desktop computers, instructors can select, rearrange, edit, or add problems as
they wish.
New Jersey, USA Cheng-Few Lee
Preface to the Third Edition xiii
Acknowledgments
For the third edition, we appreciate our secretaries, staff, and my assistants,
including Ms. Miranda Mei-Lan Luo, Tzu Tai, Hong-Yi Chen, Anthony Gallo,
for being very helpful in updating and typing the text for the new edition and the
instructor’s manual for this book. Finally, we like to thank the Wintek Corporation
and APEX International Financial Engineering Res. & Tech. Co., Ltd for the
financial support that allowed us to write this book.
Cheng F. Lee
John C. Lee
Alice C. Lee
xv
Preface to the Second Edition
Since the first edition of this book was published in 1993, it has been widely used
in universities in the United States, Asia, and Europe. The following universities
had adopted this book as a course text:
Aarhus School of Business
University of Alabama
Aoyama Gakun University
University of Arkansas
University of California, Los Angeles
Carnegie Mellon University
Catholic University of America
National Cheng Kung University
City University of Hong Kong
University of Hartford
University of Illinois Medical Center
Northern Illinois University
Monmouth University
New York University
Norwegian School of Economics & Business Administration
University of North Carolina at Greensboro
University of Notre Dame
Reading University
Rutgers University
San Francisco State University
University of St. Thomas
Suffolk University
National Taiwan University
Virginia Polytechnic & State University
Washington University
Western Kentucky University
Western Washington University
xvii
How This Edition Has Been Revised
In addition to correction of errors, the new edition uses the most updated real-world
data on accounting, finance, and economics. The most recent version of MINITAB
(Version 12) has been used for most of the empirical examples. In addition,
Microsoft Excel 97 has been explicitly introduced in this book. The new material
added to this edition is briefly described as follows:
Appendix 2A Microsoft Excel to Draw Graphs
Appendix 2B Stock Rates of Return and Market Rates of Return
Appendix 2C Financial Statements and Financial Ratio Analysis
Appendix 3A Financial Ratio Analysis
Appendix 4C Financial Ratio Analysis for Three Auto Firms
Appendix 7A Mean and Variance for Continuous Random Variables
Appendix 7B Cumulative Normal Distribution Function and the Option Pricing
Model
Appendix 7C Lognormal Distribution Approach to Derive the Option Pricing
Model
Section 9.4 The Chi-Square Distribution and the Distribution of Sample
Variance
Section 9.8 Analyzing the First Four Moments of Rates of Return of the 30 DJI
Firms
Appendix 9E Noncentral χ2 and Option Pricing Model
Section 10.9 Control Charts for Quality Control
Section 11.3 Hypothesis Test Construction and Testing Procedure
Appendix 11A The Power of a Test, the Power Function, and the Operating-
Characteristic Curve
Appendix 12A ANOVA and Statistical Quality Control
Appendix 13D American Call Option and Bivariate Normal CDF
Appendix 16A Dynamic Ratio Analysis
Appendix 16B Term Structure of Interest Rate
Application 19.3 CPI, Inflation Rate, and Interest Rate
Appendix 19A Options on Stock Indexes and Currencies
Appendix 19B Index Futures and Hedge Ratio
Section 21.7 Mean and Variance Trade-Off Analysis
Appendix E Useful Formula in Statistics
Appendix F Important Finance Topics
In addition, a real-world application project is added to the end of each part to
show how the topics discussed can be applied in analyzing the real-world financial
data. They are:
Project I: Project for Descriptive Statistics
Project II: Project for Probability and Important Distributions
Project III: Project for Statistical Inferences Based on Samples
Project IV: Project for Regression and Correlation Analyses
Project V: Project for Selected Topics in Statistical Analysis
xviii Preface to the Second Edition
Alternative Ways to Use the Text
There are five alternative approaches to use the new edition of this book. They can
be described as follows:
A. Traditional ApproachThe goal of this approach is to demonstrate to the students the basic applications
of statistics in general business, economics, and finance. This goal can be
achieved by skipping all appendices, technical footnotes, optional sections,
and other sections at the instructor’s discretion. Using this alternative, students
need only basic algebra, geometry, and business and economic common sense
to understand how statistics can be used in general business, economics, and
finance applications.
B. Accounting and Financial Data Analysis ApproachThe goal of this approach is not only to illustrate basic overall business,
economic, and finance applications but to show how to use statistics in account-
ing and financial data analysis and decision making. This goal can be achieved
by omitting all the technical appendices, technical footnotes, and most optional
sections but covering all or most of the following topics:
Chapter Topic
2 Appendices 2 and 3 of Chap. 2 on stock market rates of return
and on financial statements and financial ratio analysis
3 Appendix 1 of Chap. 3, financial ratio analysis
4 Appendix 3 of Chap. 4, financial ratios for three auto firms
6 Appendix 2 of Chap. 6, applications of the binomial distribution
to evaluate call options
7 Appendix 2 of Chap. 7, cumulative normal distribution function
and the option pricing model
9 Section 9.8, analyzing the first four moments of rates of return
of the 30 DJI firms
10 Appendix 1 of Chap. 10, a control chart approach for cash
management
Appendix 1 of Chap. 13 Derivation of normal equations and optimal portfolio weights
Appendix 4 of Chap. 13 American call option and bivariate normal CDF
16 Appendix 1 of Chap. 16, dynamic ratio analysis and Appendix
2 of Chap. 16, term structure of interest rate
19 Section 19.5, stock market indexes and Appendix 1 of Chap. 19,
options on stock indexes and currencies. Appendix 2 of
Chap. 19, index futures and hedge ratio
21 Sections 21.7 and 21.8 on mean and variance trade-off analysis
and the mean and variance method for capital budgeting
decisions; Appendices 2, 3, and 4 of Chap. 21 on the
graphical derivation of the standard deviation for NPV
C. Project ApproachBased upon all five projects, the instructor can use the project approach to teach
the course. Under this approach, the instructor can ask students to write a term
project by using accounting, economic, and financial data.
Preface to the Second Edition xix
D. Calculus ApproachThe objective of the fourth approach is to show students how calculus can be
used in statistical analysis. To achieve this goal, the instructor can try to cover
all optional sections and as many of the technical footnotes and appendices as
possible. To do this, of course, the instructor may have to skip many application
examples, such as the finance applications discussed in Approach B.
E. Financial Analysis, Planning and Forecasting ApproachThis book can be used for a course entitled Financial Analysis, Planning andForecasting by covering every topic presented in Chaps. 2, 3, 4, 6, 7, 9, 13, 14,
15, 16, 18, 19 and 21.
In addition to using this book as a textbook, it can also be very useful as a
reference book for managers who deal with accounting and financial data analysis.
We would like to recommend that the instructor consider requiring students to
solve the following problems by using either MINITAB, Microsoft Excel, or SAS
programs:
Chapter Problems
2 7, 23
3 22, 25, 30
4 4, 6, 7, 8, 27, 38, 39, 40, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54
6 8, 12, 73, 74
7 5, 43
8 7, 85, 86, 87
9 35, 39, 48
10 27, 28, 55
11 5, 9, 46, 98, 99
12 3, 20, 21, 22, 23, 44, 84
13 5, 10, 23, 47, 48, 49, 50, 51, 63, 64, 65, 66, 67, 68, 69, 70
14 7, 19, 20, 21, 23, 24, 25, 26, 27, 28, 29, 30, 31, 33, 34, 35, 40, 65
15 10, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37
16 27, 28, 31, 34, 35, 38, 41, 42, 43, 44, 45, 66, 67, 68
17 17, 19, 39, 40, 41, 42, 63
18 7, 34, 35, 36, 37, 38, 39, 40, 41, 42, 50, 60, 61, 62, 64, 68, 69, 76
19 62, 63
20 72, 73
21 12, 65
Supplementary Materials
Study Guide, by Ronald L. Moy, St. John’s University. This fine workbook
encourages learning by doing. Each chapter begins with a section describing the
basic concept of that chapter in intuitive terms. Then, the student goes on to a
formal review of the chapter and several worked-out problems that show in details
xx Preface to the Second Edition
how the solution is obtained. A variety of multiple-choice, true-false, and
open-ended questions and problems follows. All answers are included at the end
of each chapter.
MINITAB and Microsoft Excel Book, by John C. Lee, Chase Manhattan Bank.
The book, which follows the textbook chapter by chapter, is designed to help
students use MINITAB and (or) Microsoft Excel throughout the course. Each
chapter includes a variety of specific applications and ends with a statistical
summary.
Data Sets. A wide variety of macroeconomic, financial, and accounting data is
available on computer disks to facilitate student practice. A complete listing of
these data sets is given at the end of this book. The disks themselves are free of
charge.
Instructor’s Guide. The three main parts of the Instructor’s Guide are the Overview
and Objectives; the complete solutions to the text problems by Cheng F. Lee,
John C. Lee, and Edward Bubnys; and the Test Bank, with more than 1,000
multiple-choice and true-false problems, by Alice C. Lee, Pricewaterhouse
Coopers. Most instructors will find the Instructor’s Guide indispensable.
Computerized Testing Program. With the Test Bank on disk for either IBM or
Macintosh computers, instructors can select, rearrange, edit, or add problems as
they wish.
New Jersey, USA Cheng-Few Lee
New Jersey, USA John C. Lee
Massachusetts, USA Alice C. Lee
Preface to the Second Edition xxi
Acknowledgments
For this new edition, suggestions from Professors Richard T. Baillie, Abdul Basti,
Y. C. Chang, Dongcheol Kim, Ron Moy, Terry G. Seaks, Ed Bubnys, Chin-Chen
Chien, and others are most appreciated. In addition, Ta-Peng Wu and Chingfu
Chang’s help is also appreciated.
My secretarial staff, including Gerry Leo, Bertha Martinez, and Nikki Lewis,
have been very helpful in typing the text for the new edition and the instructor’s
manual for this book.
Cheng F. Lee
John C. Lee
Alice C. Lee
xxiii
Preface to the First Edition
When I first began writing Statistics for Business and Financial Economics, my
goal was to develop a text that would give my students at the University of Illinois
and at Rutgers University the basic statistical tools they need not only for a general
business school education but also for the statistics that a finance major needs. Over
time, that original purpose has evolved into a broad statistical approach that
integrates concepts, methods, and applications. The scope has widened to include
all students of business and economics, especially upper-level undergraduates and
MBA students, who want a clear and comprehensive introduction to statistics. This
book is written for them.
A distinguishing feature of the text is the creative ways in which it weaves useful
and interesting concepts from general business (accounting, marketing, manage-
ment, and quality control), economics, and finance into the text. It actively shows
how various statistical methods can be applied in business and financial economics.
More specifically, the text incorporates the following pedagogical features:
Usefulness of statistical methods. This text features an unusually large number of
real-life examples that show students how statistical methods can help them.
Non-calculus approach. Extensive use of examples and applications (more than
500) in the text and problem sets at the end of the chapters (more than 1,500) shows
students how statistical methodology can be effectively implemented and applied.
All the examples, applications, and problems can be worked out using only high-
school algebra and geometry. Calculus, which offers an alternative and intellectually
satisfying perspective, is presented only in footnotes and appendixes.
Emphasis on data analysis. Most statistics texts, in their justifiable need to demon-
strate to students how to use the various statistical tests, focus all too often on the
mechanical aspects of problem solving. Lost is the simple but important notion that
statistics is the study of data. Data analysis is an important theme of this text. In
particular, one set of financial economic data for GM and Ford is used continuously
throughout the text for various types of statistical analysis.
xxv
Use of computers. After students understand the step-by-step processes, the text
shows how computers can make statistical analysis more efficient and less time
consuming. Examples utilizing MINITAB, Lotus 1-2-3, and SAS are shown, and a
supplementary manual based entirely on MINITAB is available.
Straightforward language. Not least, the text employs clear and simple language to
guide the reader to a knowledge of the basic statistical methods used in business
decision making and financial economics.
Additionally, this text explores in slightly greater depth many of the standard
statistical topics: There is more coverage of regression analysis than in other texts
(see Chaps. 13, 14, 15, and 16 and part of Chaps. 18, 19, 20, and 21). Quality control
is explicitly integrated with point and interval estimation (Chap. 10). Stock market
indexes and the index of leading economic indicators are both treated as an
expanded portion of regular index numbers (Chap. 19).
Many chapters have appendixes that develop useful financial applications of the
standard topics found in the chapter body. Some appendixes may be used as case
studies and the following will especially serve the purpose:
Financial Statements and Financial Ratio Analysis (Appendix 3 of Chap. 2,
Appendix 1 of Chap. 3, and Appendix 3 of Chap. 4 may be used together as a
single case study)
Applications of the Binomial Distribution to Evaluate Call Options (Appendix 2
of Chap. 6)
Cumulative Normal Distribution Function and the Option Pricing Model (Appendix
2 of Chap. 7)
Control Chart Approach for Cash Management (Appendix 1 of Chap. 10)
Organization of the Text
The text has 21 chapters divided into five parts. Part I, Introduction and Descriptive
Statistics, consists of four chapters. Following the introductory chapter, Chap. 2
addresses Data Collection and Presentation. Chapter 3 delves into Frequency
Distributions and Data Analyses. It is followed by Numerical Summary Measures in
Chap. 4.
Probability and Important Distributions, Part II, includes five chapters, the first
of which, Chap. 5, is entitled Probability Concepts and Their Analysis. Discrete
Random Variables and Probability Distributions are discussed in Chap. 6, after
which Chap. 7 covers The Normal and Lognormal Distributions. Sampling and
Sampling Distributions are covered in Chap. 8. Chapter 9 closes Part II of the text
by discussing Other Continuous Distributions and Moments for Distributions.
Part III, Statistical Inferences Based on Samples, comprises three chapters.
Chapter 10 covers Estimation and Statistical Quality Control. Chapter 11 explores
Hypothesis Testing and Chap. 12 provides an Analysis of Variance and Chi-Square
Tests.
xxvi Preface to the First Edition
Chapters 13, 14, 15, and 16 make up Part IV, which is entitled Regression and
Correlation: Relating Two or More Variables. The first of these chapters is Simple
Linear Regression and the Correlation Coefficient. From a discussion of Simple
Linear Regression and Correlation: Analyses and Applications in Chap. 14, this
book moves on to address Multiple Linear Regression in Chap. 15. Finally,
Chap. 16 closes Part IV with a look at Other Topics in Applied Regression
Analysis.
The last part of the text, Part V, considers Selected Topics in Statistical Analysis
for Business and Economics. Nonparametric Statistics is the subject of Chap. 17,
which is followed by an exploration of Time Series: Analysis, Model, and
Forecasting in Chap. 18. Chapters 19 and 20 discuss Index Numbers and Stock
Market Indexes, and Sampling Surveys: Methods and Applications, respectively.
Statistical Decision Theory: Methods and Applications is the topic of the final
chapter, Chap. 21.
There are four appendixes. Appendix A provides 14 statistical tables. Appendix 1
gives a full description of the data sets available on a computer disk. Appendix 2
briefly describes the use of MINITAB, especially the microcomputer version,
and Appendix 3 introduces the microcomputer version of SAS. Finally, to make
sure they are on the right track in working the problems, students can consult the
section at the end of this book that gives short Answers to Selected Odd-Numbered
Questions and Problems. (Full solutions are given in the Instructor’s Guide.)
About This First Edition
One legitimate concern with a new statistics text is that the first edition will contain
errors (too many errors!) that must await correction only in the second edition. We
have taken action to confront this problem by carrying out a thorough and detailed
accuracy check of the entire text: Every problem in the text has been reworked by
“outsiders” to the project. So confident are we that this is an error-free book that the
publisher is willing to pay $10 for the first report (in writing) of each substantive
error.
Alternative Ways to Use the Text
Based upon my own teaching experience, I would like to suggest three alternative
ways to use this textbook.
Alternative One: The goal of this alternative is to demonstrate to students the basic
applications of statistics in general business, economics, and finance. This goal can be
achieved by skipping all appendixes, technical footnotes, optional sections, and other
sections at the instructor’s discretion. Using this alternative, the student needs only
Preface to the First Edition xxvii
basic algebra, geometry, and business and economic common sense to understand
how statistics can be used in general business, economics, and finance applications.
Alternative Two: The goal of this alternative is not only to illustrate basic overall
business, economic, and finance applications but to show how to use statistics in
financial analysis and decision making. This goal can be achieved by omitting all
the technical appendixes, technical footnotes, and most optional sections but
covering all or most of the following topics:
Chapter Topic
2 Appendices 2 and 3 of Chap. 2 on stock and market rates of return and on financial
statements and financial ratio analysis
3 Appendix 1 of Chap. 3, financial ratio analysis
4 Appendix 3 of Chap. 4, financial ratios for three auto firms. As mentioned earlier,
Appendix 3 of Chap. 2, Appendix 1 of Chap. 3, and Appendix 3 of Chap. 4 can
be treated as a single case study
6 Appendix 2 of Chap. 6, applications of the binomial distribution to evaluate call
options
7 Appendix 2 of Chap. 7, cumulative normal distribution function and the option pricing
model
9 Section 9.8, analyzing the first four moments of rates of return of the 30 DJI firms
10 Appendix 1 of Chap. 10, a control chart approach for cash management
19 Section 19.5, stock market indexes
21 Sections 21.7 and 21.8 on mean and variance trade-off analysis and the mean
and variance method for capital budgeting decisions; Appendices 2, 3, and 4 of
Chap. 21 on the graphical derivation of the capital market line, present value and
net present value, and derivation of the standard deviation for NPV
Alternative Three: The objective of the third approach is to show students how
calculus can be used in statistical analysis. To achieve this goal, the instructor can
try to cover all optional sections and as many of the technical footnotes and
appendixes as possible. To do this, of course, the instructor may have to skip
many application examples, such as the finance applications discussed in Alterna-
tive Two.
Supplementary Materials
Study Guide, by Ahyee Lee, Monmouth College, and Ronald L. Moy, St. John’s
University. This fine workbook encourages learning by doing. Each chapter begins
with a section describing the basic import of each chapter in intuitive terms. Then,
the student goes on to a formal review of the chapter and several worked-out
problems that show in detail how the solution is obtained. A variety of multiple-
choice, true-false, and open-ended questions and problems follows, and finally a
brief sample test is given. All answers are included at the end of each chapter.
xxviii Preface to the First Edition
M1N1TAB Manual, by John C. Lee, University of Illinois. This manual, keyed to
the text chapter by chapter, is designed to help students use M1NITAB throughout
the course. Each chapter includes a variety of specific applications and ends with
both a statistical summary and a summary of MINITAB commands.
Data Sets. A wide variety of macroeconomic, financial, and accounting data is
available on computer disks to facilitate student practice. A complete listing of
these data sets is given at the end of this book. The disks themselves are free of
charge.
Instructor’s Guide. The three main parts of the Instructor’s Guide are the Overview
and Objectives by Cheng F. Lee; the complete Solutions to the text problems by
Ahyee Lee and Ronald L. Moy; and the Test Bank, with more than 1,000 multiple-
choice and true-false problems, by Alice C. Lee, University of Pennsylvania. Most
instructors will find the Instructor’s Guide indispensable.
Computerized Testing Program. With the Test Bank on disk for either IBM or
Macintosh computers, instructors can select, rearrange, edit, or add problems as
they wish.
New Jersey, USA Cheng-Few Lee
Preface to the First Edition xxix
Acknowledgments
I am very grateful to my colleagues across the country who have contributed to the
development of this book. In particular, I would like to thank Kent Becker, Temple
University, and Edward L. Bubnys, Suffolk University, who not only reviewed
parts of the manuscript but also class-tested several chapters; John Burr, Mobil
Oil Company; H. H. Liao, my research assistant at Rutgers; D. Y. Huang and
C. C. Young, both of National Taiwan University; and Kimberly Catucci, my
editorial assistant.
I am also indebted to many other people who reviewed all or part of the
manuscript:
Richard T. Baillie Supriya Lahiri
Michigan State University University of Lowell
Abdul Basti Leonard Lardaro
Northern Illinois University The University of Rhode Island
Philip Bobko Ahyee Lee
Rutgers University Monmouth College
Warren Boe Keh Shin Lii
University of Iowa University of California
Y. C. Chang Pi-Erh Lin
University of Notre Dame Florida State University
Shaw K. Chen Chao-nan Liu
The University of Rhode Island Trenton State College
Whewon Cho Tom Mathew
Tennessee Technological University The Troy State University in Montgomery
Daniel S. Christiansen Richard McGowan
Portland State University Boston College
James S. Ford Ronald L. Moy
University of Southern California St. John’s University
(continued)
xxxi
Mel H. Friedman Hassan Pourbabaee
Kean College University of Central Oklahoma
R. A. Holmes Jean D. Powers
Simon Fraser University The Ohio State University
James Freeland William E. Stein
Horrell University of Oklahoma Texas A&M University
Der Ann Hsu William Wei
University of Wisconsin-Milwaukee Temple University
Dongcheol Kim Jeffrey M. Wooldridge
Rutgers University Massachusetts Institute of Technology
Bharat Kolluri Gili Yen
University of Hartford National Central University, Taiwan
Not least, I would like to thank and salute my family—my wife, Schwinne, for
her good humor and patience, and my two children, John and Alice, whose
contributions are described elsewhere in this preface.
Cheng F. Lee
(continued)
xxxii Acknowledgments
Brief Contents
Part I Introduction and Descriptive Statistics
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 Data Collection and Presentation . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3 Frequency Distributions and Data Analyses . . . . . . . . . . . . . . . . . . . 65
4 Numerical Summary Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
Part II Probability and Important Distributions
5 Probability Concepts and Their Analysis . . . . . . . . . . . . . . . . . . . . . 157
6 Discrete Random Variables and Probability Distributions . . . . . . . . . 211
7 The Normal and Lognormal Distributions . . . . . . . . . . . . . . . . . . . . 271
8 Sampling and Sampling Distributions . . . . . . . . . . . . . . . . . . . . . . . 331
9 Other Continuous Distributions and Moments
for Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 381
Part III Statistical Inferences Based on Samples
10 Estimation and Statistical Quality Control . . . . . . . . . . . . . . . . . . . . 425
11 Hypothesis Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 487
12 Analysis of Variance and Chi-Square Tests . . . . . . . . . . . . . . . . . . . 543
xxxiii
Part IV Regression and Correlation: Relating
Two or More Variables
13 Simple Linear Regression and the Correlation Coefficient . . . . . . . . 615
14 Simple Linear Regression and Correlation: Analyses
and Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 675
15 Multiple Linear Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 739
16 Other Topics in Applied Regression Analysis . . . . . . . . . . . . . . . . . 793
Part V Selected Topics in Statistical Analysis
for Business and Economics
17 Nonparametric Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 877
18 Time Series: Analysis, Model, and Forecasting . . . . . . . . . . . . . . . . 927
19 Index Numbers and Stock Market Indexes . . . . . . . . . . . . . . . . . . . . 973
20 Sampling Surveys: Methods and Applications . . . . . . . . . . . . . . . . . 1019
21 Statistical Decision Theory: Methods and Applications . . . . . . . . . . 1065
Appendix A Statistical Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1125
Appendix B Description of Data Sets . . . . . . . . . . . . . . . . . . . . . . . . 1157
Appendix C Introduction to MINITAB 16 . . . . . . . . . . . . . . . . . . . . 1161
Appendix D Introduction to SAS: Microcomputer Version . . . . . . . 1165
Appendix E Useful Formulas in Statistics . . . . . . . . . . . . . . . . . . . . . 1171
Appendix F Important Finance and Accounting Topics . . . . . . . . . . 1193
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1195
xxxiv Brief Contents
Contents
Part I Introduction and Descriptive Statistics
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1 The Role of Statistics in Business and Economics . . . . . . . . . . 3
1.2 Descriptive Versus Inferential Statistics . . . . . . . . . . . . . . . . . 5
1.3 Deductive Versus Inductive Analysis in Statistics . . . . . . . . . . 10
1.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Questions and Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2 Data Collection and Presentation . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2 Data Collection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3 Data Presentation: Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.4 Data Presentation: Charts and Graphs . . . . . . . . . . . . . . . . . . . 19
2.5 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
Questions and Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
Appendix 1: Using Microsoft Excel to Draw Graphs . . . . . . . . . . . . 45
Appendix 2: Stock Rates of Return and Market Rates of Return . . . . 47
Appendix 3: Financial Statements and Financial Ratio Analysis . . . . 51
3 Frequency Distributions and Data Analyses . . . . . . . . . . . . . . . . . 65
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.2 Tally Table for Constructing a Frequency Table . . . . . . . . . . . 66
3.3 Three Other Frequency Tables . . . . . . . . . . . . . . . . . . . . . . . . 70
3.4 Graphical Presentation of Frequency Distribution . . . . . . . . . . 72
3.4.1 Histograms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
3.4.2 Stem-and-Leaf Display . . . . . . . . . . . . . . . . . . . . . . . . 76
3.4.3 Frequency Polygon . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
3.4.4 Pie Chart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
xxxv
3.5 Further Economic and Business Applications . . . . . . . . . . . . . 82
3.5.1 Lorenz Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
3.5.2 Stock and Market Rate of Return . . . . . . . . . . . . . . . . . 84
3.5.3 Interest Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
3.5.4 Quality Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
3.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
Questions and Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
4 Numerical Summary Measures . . . . . . . . . . . . . . . . . . . . . . . . . . 95
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
4.2 Measures of Central Tendency . . . . . . . . . . . . . . . . . . . . . . . . 96
4.2.1 The Arithmetic Mean . . . . . . . . . . . . . . . . . . . . . . . . . 97
4.2.2 The Geometric Mean . . . . . . . . . . . . . . . . . . . . . . . . . 98
4.2.3 The Median . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
4.2.4 The Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
4.3 Measures of Dispersion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
4.3.1 The Variance and the Standard Deviation . . . . . . . . . . . 102
4.3.2 The Mean Absolute Deviation . . . . . . . . . . . . . . . . . . . 105
4.3.3 The Range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
4.3.4 The Coefficient of Variation . . . . . . . . . . . . . . . . . . . . 107
4.4 Measures of Relative Position . . . . . . . . . . . . . . . . . . . . . . . . . 109
4.4.1 Percentiles, Quartiles, and Interquartile Range . . . . . . . 109
4.4.2 Box and Whisker Plots: Graphical Descriptions
Based on Quartiles . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
4.4.3 Z Scores . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
4.5 Measures of Shape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
4.5.1 Skewness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
4.5.2 Kurtosis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
4.6 Calculating Certain Summary Measures from
Grouped Data (Optional) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
4.6.1 The Mean . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
4.6.2 The Median . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
4.6.3 The Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
4.6.4 Variance and Standard Deviation . . . . . . . . . . . . . . . . . 120
4.6.5 Percentiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
4.7 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
4.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
Questions and Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
Project I: Project for Descriptive Statistics . . . . . . . . . . . . . . . . . . . . 146
Appendix 1: Shortcut Formulas for Calculating Variance
and Standard Deviation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
Appendix 2: Shortcut Formulas for Calculating Group
Variance and Standard Deviation . . . . . . . . . . . . . . . . . . . . . . . . 148
Appendix 3: Financial Ratio Analysis for Two
Pharmaceutical Firms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
xxxvi Contents
Part II Probability and Important Distributions
5 Probability Concepts and Their Analysis . . . . . . . . . . . . . . . . . . . 157
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
5.2 Random Experiment, Outcomes, Sample Space, Event,
and Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
5.2.1 Properties of Random Experiments . . . . . . . . . . . . . . . 159
5.2.2 Sample Space of an Experiment and the
Venn Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
5.2.3 Probabilities of Outcomes . . . . . . . . . . . . . . . . . . . . . . 161
5.2.4 Subjective Probability . . . . . . . . . . . . . . . . . . . . . . . . . 165
5.3 Alternative Events and Their Probabilities . . . . . . . . . . . . . . . . 166
5.3.1 Probabilities of Union and Intersection of Events . . . . . 166
5.3.2 Partitions, Complements, and Probability
of Complements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
5.3.3 Using Combinatorial Mathematics to Determine
the Number of Simple Events . . . . . . . . . . . . . . . . . . . 173
5.4 Conditional Probability and Its Implications . . . . . . . . . . . . . . 174
5.4.1 Basic Concept of Conditional Probability . . . . . . . . . . . 174
5.4.2 Multiplication Rule of Probability . . . . . . . . . . . . . . . . 176
5.5 Joint Probability and Marginal Probability . . . . . . . . . . . . . . . 177
5.5.1 Joint Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
5.5.2 Marginal Probabilities . . . . . . . . . . . . . . . . . . . . . . . . . 179
5.6 Independent, Dependent, and Mutually Exclusive Events . . . . . 182
5.7 Bayes’ Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
5.8 Business Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
5.9 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
Questions and Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
Appendix 1: Permutations and Combinations . . . . . . . . . . . . . . . . . . 204
6 Discrete Random Variables and Probability Distributions . . . . . . 211
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212
6.2 Discrete and Continuous Random Variables . . . . . . . . . . . . . . 212
6.3 Probability Distributions for Discrete Random Variables . . . . . 213
6.3.1 Probability Distribution . . . . . . . . . . . . . . . . . . . . . . . . 213
6.3.2 Probability Function and Cumulative
Distribution Function . . . . . . . . . . . . . . . . . . . . . . . . . 216
6.4 Expected Value and Variance for Discrete
Random Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
6.5 The Bernoulli Process and the Binomial
Probability Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221
6.5.1 The Bernoulli Process . . . . . . . . . . . . . . . . . . . . . . . . . 221
6.5.2 Binomial Distribution . . . . . . . . . . . . . . . . . . . . . . . . . 222
6.5.3 Probability Function . . . . . . . . . . . . . . . . . . . . . . . . . . 224
6.5.4 Mean and Variance . . . . . . . . . . . . . . . . . . . . . . . . . . . 228
Contents xxxvii
6.6 The Hypergeometric Distribution (Optional) . . . . . . . . . . . . . . 229
6.6.1 The Hypergeometric Formula . . . . . . . . . . . . . . . . . . . 230
6.6.2 Mean and Variance . . . . . . . . . . . . . . . . . . . . . . . . . . . 231
6.7 The Poisson Distribution and Its Approximation
to the Binomial Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . 232
6.7.1 The Poisson Distribution . . . . . . . . . . . . . . . . . . . . . . . 233
6.7.2 The Poisson Approximation to the
Binomial Distribution . . . . . . . . . . . . . . . . . . . . . . . . . 235
6.8 Jointly Distributed Discrete Random Variables (Optional) . . . . 237
6.8.1 Joint Probability Function . . . . . . . . . . . . . . . . . . . . . . 237
6.8.2 Marginal Probability Function . . . . . . . . . . . . . . . . . . . 238
6.8.3 Conditional Probability Function . . . . . . . . . . . . . . . . . 239
6.8.4 Independence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240
6.9 Expected Value and Variance of the Sum
of Random Variables (Optional) . . . . . . . . . . . . . . . . . . . . . . . 242
6.9.1 Covariance and Coefficient of Correlation
Between Two Random Variables . . . . . . . . . . . . . . . . . 242
6.9.2 Expected Value and Variance of the Summation
of Random Variables X and Y . . . . . . . . . . . . . . . . . . . 244
6.9.3 Expected Value and Variance of Sums
of Random Variables . . . . . . . . . . . . . . . . . . . . . . . . . 247
6.10 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250
Questions and Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250
Appendix 1: The Mean and Variance of the
Binomial Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259
Appendix 2: Applications of the Binomial Distribution
to Evaluate Call Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260
7 The Normal and Lognormal Distributions . . . . . . . . . . . . . . . . . . 271
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271
7.2 Probability Distributions for Continuous
Random Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272
7.2.1 Continuous Random Variables . . . . . . . . . . . . . . . . . . . 272
7.2.2 Probability Distribution Functions for Discrete
and Continuous Random Variables . . . . . . . . . . . . . . . 273
7.3 The Normal and Standard Normal Distribution . . . . . . . . . . . . 278
7.3.1 The Normal Distribution . . . . . . . . . . . . . . . . . . . . . . . 278
7.3.2 Areas Under the Normal Curve . . . . . . . . . . . . . . . . . . 279
7.3.3 How to Use the Normal Area Table . . . . . . . . . . . . . . . 282
7.4 The Lognormal Distribution and Its Relationship
to the Normal Distribution (Optional) . . . . . . . . . . . . . . . . . . . 286
7.4.1 The Lognormal Distribution . . . . . . . . . . . . . . . . . . . . 286
7.4.2 Mean and Variance of Lognormal Distribution . . . . . . . 286
7.5 The Normal Distribution as an Approximation
to the Binomial and Poisson Distributions . . . . . . . . . . . . . . . . 290
xxxviii Contents
7.5.1 Normal Approximation to the
Binomial Distribution . . . . . . . . . . . . . . . . . . . . . . . . . 290
7.5.2 Normal Approximation to the
Poisson Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . 292
7.6 Business Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293
7.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303
Questions and Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304
Appendix 1: Mean and Variance for Continuous
Random Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315
Appendix 2: Cumulative Normal Distribution Function
and the Option Pricing Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 321
Appendix 3: Lognormal Distribution Approach to Derive
the Option Pricing Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326
8 Sampling and Sampling Distributions . . . . . . . . . . . . . . . . . . . . . 331
8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331
8.2 Sampling from a Population . . . . . . . . . . . . . . . . . . . . . . . . . . 332
8.2.1 Sampling Error and Nonsampling Error . . . . . . . . . . . . 333
8.2.2 Selection of a Random Sample . . . . . . . . . . . . . . . . . . 334
8.3 Sampling Cost Versus Sampling Error . . . . . . . . . . . . . . . . . . 337
8.3.1 Sampling Size and Accuracy . . . . . . . . . . . . . . . . . . . . 338
8.3.2 Time Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339
8.4 Sampling Distribution of the Sample Mean . . . . . . . . . . . . . . . 339
8.4.1 All Possible Random Samples and Their Mean . . . . . . . 340
8.4.2 Mean and Variance for a Sample Mean . . . . . . . . . . . . 345
8.4.3 Sample Without Replacement from
a Finite Sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 346
8.5 Sampling Distribution of the Sample Proportion . . . . . . . . . . . 352
8.6 The Central Limit Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . 354
8.7 Other Business Applications . . . . . . . . . . . . . . . . . . . . . . . . . . 357
8.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 360
Questions and Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 360
Appendix 1: Sampling Distribution from a Uniform
Population Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373
9 Other Continuous Distributions and Moments
for Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 381
9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382
9.2 The Uniform Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . 382
9.3 Student’s t Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385
9.4 The Chi-Square Distribution and the Distribution
of Sample Variance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 388
9.4.1 The Chi-Square Distribution . . . . . . . . . . . . . . . . . . 388
9.4.2 The Distribution of Sample Variance . . . . . . . . . . . . 392
Contents xxxix
9.5 The F Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393
9.6 The Exponential Distribution (Optional) . . . . . . . . . . . . . . . . 396
9.7 Moments and Distributions (Optional) . . . . . . . . . . . . . . . . . . 398
9.7.1 The Second Moment and the Coefficient
of Variation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 398
9.7.2 The Third Moment and the Coefficient
of Skewness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 399
9.7.3 Kurtosis and the Coefficient of Kurtosis . . . . . . . . . . 401
9.7.4 Skewness and Kurtosis for Normal
and Lognormal Distributions . . . . . . . . . . . . . . . . . . 401
9.8 Analyzing the First Four Moments of Rates of Return
of the 30 DJl Firms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403
9.9 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405
Questions and Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405
Project II: Project for Probability and Important Distributions . . . . . 412
Appendix 1: Derivation of the Mean and Variance
for a Uniform Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413
Appendix 2: Derivation of the Exponential Density Function . . . . . . 415
Appendix 3: The Relationship Between the Moment
About the Origin and the Moment About the Mean . . . . . . . . . . . . . 418
Appendix 4: Derivations of Mean, Variance, Skewness,
and Kurtosis for the Lognormal Distribution . . . . . . . . . . . . . . . . 418
Appendix 5: Noncentral �2 and the Option Pricing Model . . . . . . . . 420
Part III Statistical Inferences Based on Samples
10 Estimation and Statistical Quality Control . . . . . . . . . . . . . . . . . . 425
10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 426
10.2 Point Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 426
10.2.1 Point Estimate, Estimator, and Estimation . . . . . . . . 426
10.2.2 Four Important Properties of Estimators . . . . . . . . . . 428
10.2.3 Mean Squared Error for Choosing
Point Estimator . . . . . . . . . . . . . . . . . . . . . . . . . . . . 432
10.3 Interval Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433
10.4 Interval Estimates for μ When σX2 Is Known . . . . . . . . . . . . . 434
10.5 Confidence Intervals for μ When σX2 Is Unknown . . . . . . . . . 440
10.6 Confidence Intervals for the Population Proportion . . . . . . . . 445
10.7 Confidence Intervals for the Variance . . . . . . . . . . . . . . . . . . 447
10.8 An Overview of Statistical Quality Control . . . . . . . . . . . . . . 449
10.8.1 The Sample Size of an Inspection . . . . . . . . . . . . . . 450
10.8.2 Acceptance Sampling and Its
Alternative Plans . . . . . . . . . . . . . . . . . . . . . . . . . . . 450
10.8.3 Process Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . 452
xl Contents
10.9 Control Charts for Quality Control . . . . . . . . . . . . . . . . . . . 452
10.9.1 �X -Chart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453
10.9.2 �R -Chart and S-Chart . . . . . . . . . . . . . . . . . . . . . . . 456
10.9.3 Control Charts for Proportions . . . . . . . . . . . . . . . . 462
10.10 Further Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 464
10.11 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 468
Questions and Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 468
Appendix 1: Control Chart Approach for Cash Management . . . . . . 480
Appendix 2: Using MINITAB to Generate Control Charts . . . . . . . . 483
11 Hypothesis Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 487
11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 488
11.2 Concepts and Errors of Hypothesis Testing . . . . . . . . . . . . . 488
11.2.1 Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 488
11.2.2 Type I and Type II Errors . . . . . . . . . . . . . . . . . . . 490
11.3 Hypothesis Test Construction and Testing Procedure . . . . . . 490
11.3.1 Two Types of Hypothesis Tests . . . . . . . . . . . . . . . 490
11.3.2 The Trade-off Between Type I
and Type II Errors . . . . . . . . . . . . . . . . . . . . . . . . . 493
11.3.3 The P-Value Approach to Hypothesis Testing . . . . . 495
11.4 One-Tailed Tests of Means for Large Samples . . . . . . . . . . . 496
11.4.1 One-Sample Tests of Means . . . . . . . . . . . . . . . . . . 496
11.4.2 The zα-Value Approach . . . . . . . . . . . . . . . . . . . . . 498
11.4.3 The �xα -Value Approach . . . . . . . . . . . . . . . . . . . . 499
11.4.4 The p-Value Approach . . . . . . . . . . . . . . . . . . . . . . 499
11.4.5 Two-Samples Tests of Means . . . . . . . . . . . . . . . . . 500
11.5 Two-Tailed Tests of Means for Large Samples . . . . . . . . . . 504
11.5.1 One-Sample Tests of Means . . . . . . . . . . . . . . . . . 504
11.5.2 Confidence Intervals and Hypothesis Testing . . . . . 506
11.5.3 Two-Samples Tests of Means . . . . . . . . . . . . . . . . 507
11.6 Small-Sample Tests of Means with Unknown Population
Standard Deviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 509
11.6.1 One-Sample Tests of Means . . . . . . . . . . . . . . . . . 509
11.6.2 Two-Samples Tests of Means . . . . . . . . . . . . . . . . 510
11.7 Hypothesis Testing for a Population Proportion . . . . . . . . . . 513
11.8 Chi-Square Tests of the Variance
of a Normal Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . 516
11.9 Comparing the Variances of Two Normal Populations . . . . . 518
11.10 Business Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . 518
11.11 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 523
Questions and Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 524
Appendix 1: The Power of a Test, the Power Function,
and the Operating-Characteristic Curve . . . . . . . . . . . . . . . . . . . . 536
Contents xli
12 Analysis of Variance and Chi-Square Tests . . . . . . . . . . . . . . . . . 543
12.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 544
12.2 One-Way Analysis of Variance . . . . . . . . . . . . . . . . . . . . . . 544
12.2.1 Defining One-Way ANOVA . . . . . . . . . . . . . . . . . 545
12.2.2 Specifying the Hypotheses . . . . . . . . . . . . . . . . . . . 545
12.2.3 Generalizing the One-Way ANOVA . . . . . . . . . . . . 546
12.2.4 Between-Treatments and Within-Treatment
Sums of Squares . . . . . . . . . . . . . . . . . . . . . . . . . . 548
12.2.5 Between-Treatments and Within-Treatment
Mean Squares . . . . . . . . . . . . . . . . . . . . . . . . . . . . 551
12.2.6 The Test Statistic . . . . . . . . . . . . . . . . . . . . . . . . . 552
12.2.7 Population Model for One-Way ANOVA . . . . . . . . 553
12.3 Simple and Simultaneous Confidence Intervals . . . . . . . . . . 554
12.3.1 Simple Comparison . . . . . . . . . . . . . . . . . . . . . . . . 554
12.3.2 Scheffe’s Multiple Comparison . . . . . . . . . . . . . . . 556
12.4 Two-Way ANOVA with One Observation
in Each Cell, Randomized Blocks . . . . . . . . . . . . . . . . . . . . 557
12.4.1 Basic Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . 557
12.4.2 Specifying the Hypotheses . . . . . . . . . . . . . . . . . . . 558
12.4.3 Between and Residual Sum of Squares . . . . . . . . . . 558
12.4.4 Between Variance, Error Variance,
and F-Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 560
12.4.5 Population Model for Two-Way ANOVA
with One Observation in Each Cell . . . . . . . . . . . . . 561
12.5 Two-Way ANOVA with More than One
Observation in Each Cell . . . . . . . . . . . . . . . . . . . . . . . . . . 563
12.5.1 Basic Concept and Hypothesis Testing . . . . . . . . . . 563
12.5.2 Generalizing the Two-Way ANOVA . . . . . . . . . . . 566
12.6 Chi-Square as a Test of Goodness of Fit . . . . . . . . . . . . . . . 568
12.7 Chi-Square as a Test of Independence . . . . . . . . . . . . . . . . . 572
12.8 Business Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . 574
12.9 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 582
Questions and Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 582
Project III: Project for Statistical Inferences Based on Samples . . . . . 606
Appendix 1: ANOVA and Statistical Quality Control . . . . . . . . . . . . 607
Part IV Regression and Correlation: Relating Two
or More Variables
13 Simple Linear Regression and the Correlation Coefficient . . . . . . 615
13.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 616
13.2 Population Parameters and the Regression Models . . . . . . . . 616
13.2.1 Data Description . . . . . . . . . . . . . . . . . . . . . . . . . . 617
13.2.2 Building the Population Regression Model . . . . . . . 618
13.2.3 Sample Versus Population Regression Model . . . . . 621
xlii Contents
13.3 The Least-Squares Estimation of α and β . . . . . . . . . . . . . . . 622
13.3.1 Scatter Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . 622
13.3.2 The Method of Least Squares . . . . . . . . . . . . . . . . . . 624
13.3.3 Estimation of Intercept and Slope . . . . . . . . . . . . . . . 625
13.4 Standard Assumptions for Linear Regression . . . . . . . . . . . . . 629
13.5 The Standard Error of Estimate and the Coefficient
of Determination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 631
13.5.1 Variance Decomposition . . . . . . . . . . . . . . . . . . . . . 632
13.5.2 Standard Error of Residuals (Estimate) . . . . . . . . . . . 635
13.5.3 The Coefficient of Determination . . . . . . . . . . . . . . . 635
13.6 The Bivariate Normal Distribution
and Correlation Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 636
13.6.1 The Sample Correlation Coefficient . . . . . . . . . . . . . 638
13.6.2 The Relationship Between r and b . . . . . . . . . . . . . . 639
13.6.3 The Relationship Between r and R2 . . . . . . . . . . . . . 639
13.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 646
Questions and Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 646
Appendix 1: Derivation of Normal Equations and Optimal
Portfolio Weights . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 659
Appendix 2: The Derivation of Equation 13.20 . . . . . . . . . . . . . . . . 661
Appendix 3: The Bivariate Normal Density Function . . . . . . . . . . . . 661
Appendix 4: American Call Option and the Bivariate
Normal CDF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 664
14 Simple Linear Regression and Correlation: Analyses
and Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 675
14.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 675
14.2 Tests of the Significance of α and β . . . . . . . . . . . . . . . . . . . 676
14.2.1 Hypothesis Testing and Confidence Interval
for β and α . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 677
14.2.2 The F-Test Versus the t-Test . . . . . . . . . . . . . . . . . . 682
14.3 Test of the Significance of ρ . . . . . . . . . . . . . . . . . . . . . . . . . 685
14.3.1 t-Test for Testing ρ ¼ 0 . . . . . . . . . . . . . . . . . . . . . 686
14.3.2 z-Test for Testing ρ ¼ 0 or ρ ¼ Constant . . . . . . . . . 687
14.4 Confidence Interval for the Mean Response
and Prediction Interval for the Individual Response . . . . . . . . 688
14.4.1 Point Estimates of the Mean Response
and the Individual Response . . . . . . . . . . . . . . . . . . 688
14.4.2 Interval Estimates of Forecasts under Three
Cases of Estimated Variance . . . . . . . . . . . . . . . . . . 689
14.4.3 Calculating Standard Errors . . . . . . . . . . . . . . . . . . . 691
14.4.4 Confidence Interval for the Mean Response and
Prediction Interval for the Individual Response . . . . . 693
14.4.5 Using MINITAB to Calculate Confidence
Interval and Interval . . . . . . . . . . . . . . . . . . . . . . . . 696
14.5 Business Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 700
Contents xliii
14.6 Using Computer Programs to Do Simple
Regression Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 713
14.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 714
Questions and Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 717
Appendix 1: Impact of Measurement Error and Proxy
Error on Slope Estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 734
Appendix 2: The Relationship Between the F-Testand the t-Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 736
Appendix 3: Derivation of Variance for Alternative Forecasts . . . . . 736
15 Multiple Linear Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 739
15.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 740
15.2 The Model and Its Assumptions . . . . . . . . . . . . . . . . . . . . . . 740
15.2.1 The Multiple Regression Model . . . . . . . . . . . . . . . . 740
15.2.2 The Regression Plane for Two
Explanatory Variables . . . . . . . . . . . . . . . . . . . . . . . 741
15.2.3 Assumptions for the Multiple Regression Model . . . . 742
15.3 Estimating Multiple Regression Parameters . . . . . . . . . . . . . . 744
15.4 The Residual Standard Error and the Coefficient
of Determination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 747
15.4.1 The Residual Standard Error . . . . . . . . . . . . . . . . . . 747
15.4.2 The Coefficient of Determination . . . . . . . . . . . . . . . 748
15.5 Tests on Sets and Individual Regression Coefficients . . . . . . 750
15.5.1 Test on Sets of Regression Coefficients . . . . . . . . . . 750
15.5.2 Hypothesis Tests for Individual
Regression Coefficients . . . . . . . . . . . . . . . . . . . . . . 752
15.6 Confidence Interval for the Mean Response and
Prediction Interval for the Individual Response . . . . . . . . . . . 756
15.6.1 Point Estimates of the Mean and the
Individual Responses . . . . . . . . . . . . . . . . . . . . . . . . 756
15.6.2 Interval Estimates of Forecasts . . . . . . . . . . . . . . . . . 756
15.7 Business and Economic Applications . . . . . . . . . . . . . . . . . . 759
15.8 Using Computer Programs to Do Multiple
Regression Analyses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 766
15.8.1 SAS Program for Multiple Regression Analysis . . . . 766
15.8.2 MINITAB Program for Multiple
Regression Prediction . . . . . . . . . . . . . . . . . . . . . . . 771
15.8.3 Stepwise Regression Analysis . . . . . . . . . . . . . . . . . 772
15.9 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 776
Questions and Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 777
Appendix 1: Derivation of the Sampling Variance
of the Least-Squares Slope Estimations . . . . . . . . . . . . . . . . . . . . 788
Appendix 2: Derivation of Equation 15.30 . . . . . . . . . . . . . . . . . . . . 791
xliv Contents
16 Other Topics in Applied Regression Analysis . . . . . . . . . . . . . . . . 793
16.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 794
16.2 Multicollinearity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 794
16.2.1 Definition and Effect . . . . . . . . . . . . . . . . . . . . . . . 794
16.2.2 Rules of Thumb in Determining the Degree
of Collinearity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 796
16.3 Heteroscedasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 798
16.3.1 Definition and Concept . . . . . . . . . . . . . . . . . . . . . 798
16.3.2 Evaluating the Existence
of Heteroscedasticity . . . . . . . . . . . . . . . . . . . . . . . 800
16.4 Autocorrelation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 804
16.4.1 Basic Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . 804
16.4.2 The Durbin–Watson Statistic . . . . . . . . . . . . . . . . . 805
16.5 Model Specification and Specification
Bias (Optional) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 810
16.6 Nonlinear Models (Optional) . . . . . . . . . . . . . . . . . . . . . . . 816
16.6.1 The Quadratic Model . . . . . . . . . . . . . . . . . . . . . . . 816
16.6.2 The Log-Linear and the Log–Log-Linear
Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 819
16.7 Lagged Dependent Variables (Optional) . . . . . . . . . . . . . . . 822
16.8 Dummy Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 832
16.9 Regression with Interaction Variables . . . . . . . . . . . . . . . . . 837
16.10 Regression Approach to Investigating the Effect
of Alternative Business Strategies . . . . . . . . . . . . . . . . . . . . 840
16.11 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 841
Questions and Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 841
Project IV: Project for Regression and Correlation Analyses . . . . . . . 859
Appendix 1: Dynamic Ratio Analysis . . . . . . . . . . . . . . . . . . . . . . . 869
Appendix 2: Term Structure of Interest Rate . . . . . . . . . . . . . . . . . . 870
Part V Selected Topics in Statistical Analysis
for Business and Economics
17 Nonparametric Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 877
17.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 878
17.2 The Matched-Pairs Sign Test . . . . . . . . . . . . . . . . . . . . . . . . 879
17.3 The Wilcoxon Matched-Pairs Signed-Rank Test . . . . . . . . . . 881
17.4 Mann–Whitney U Test (Wilcoxon Rank-Sum Test) . . . . . . . . 884
17.5 Kruskal–Wallis Test for m Independent Samples . . . . . . . . . . 889
17.6 Spearman Rank Correlation Test . . . . . . . . . . . . . . . . . . . . . . 892
17.7 The Number-of-Runs Test . . . . . . . . . . . . . . . . . . . . . . . . . . 894
17.8 Business Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 896
17.9 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 905
Questions and Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 905
Contents xlv
18 Time Series: Analysis, Model, and Forecasting . . . . . . . . . . . . . . 927
18.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 928
18.2 The Classical Time-Series Component Model . . . . . . . . . . . . 928
18.2.1 The Trend Component . . . . . . . . . . . . . . . . . . . . . . . 929
18.2.2 The Seasonal Component . . . . . . . . . . . . . . . . . . . . 929
18.2.3 The Cyclical Component and Business Cycles . . . . . 929
18.2.4 The Irregular Component . . . . . . . . . . . . . . . . . . . . . 932
18.3 Moving Average and Seasonally Adjusted Time Series . . . . . 934
18.3.1 Moving Averages . . . . . . . . . . . . . . . . . . . . . . . . . . 934
18.3.2 Seasonal Index and Seasonally Adjusted
Time Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 935
18.4 Linear and Log-Linear Time Trend Regressions . . . . . . . . . . 941
18.5 Exponential Smoothing and Forecasting . . . . . . . . . . . . . . . . 943
18.5.1 Simple Exponential Smoothing and Forecasting . . . . 943
18.5.2 The Holt–Winters Forecasting Model for
Nonseasonal Series . . . . . . . . . . . . . . . . . . . . . . . . . 947
18.6 Autoregressive Forecasting Model . . . . . . . . . . . . . . . . . . . . 952
18.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 956
Questions and Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 956
Appendix 1: The Holt–Winters Forecasting Model
for Seasonal Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 968
19 Index Numbers and Stock Market Indexes . . . . . . . . . . . . . . . . . 973
19.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 974
19.2 Price Indexes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 974
19.2.1 Simple Aggregative Price Index . . . . . . . . . . . . . . . . 974
19.2.2 Simple Average of Price Relatives . . . . . . . . . . . . . . 976
19.2.3 Weighted Relative Price Index . . . . . . . . . . . . . . . . . 977
19.2.4 Weighted Aggregative Price Index . . . . . . . . . . . . . . 979
19.3 Quantity Indexes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 982
19.3.1 Laspeyres Quantity Index . . . . . . . . . . . . . . . . . . . . 982
19.3.2 Paasche Quantity Index . . . . . . . . . . . . . . . . . . . . . . 983
19.3.3 Fisher’s Ideal Quantity Index . . . . . . . . . . . . . . . . . . 985
19.3.4 FRB Index of Industrial Production . . . . . . . . . . . . . 985
19.4 Value Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 986
19.5 Stock Market Indexes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 986
19.5.1 Market-Value-Weighted Index . . . . . . . . . . . . . . . . . 987
19.5.2 Price-Weighted Index . . . . . . . . . . . . . . . . . . . . . . . 988
19.5.3 Equally Weighted Index . . . . . . . . . . . . . . . . . . . . . 990
19.5.4 Wilshire 5000 Equity Index . . . . . . . . . . . . . . . . . . . 991
19.6 Business and Economic Applications . . . . . . . . . . . . . . . . . . 993
19.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1002
Questions and Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1002
Appendix 1: Options on Stock Indices and Currencies . . . . . . . . . . . 1013
Appendix 2: Index Futures and Hedge Ratio . . . . . . . . . . . . . . . . . . 1016
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20 Sampling Surveys: Methods and Applications . . . . . . . . . . . . . . . 1019
20.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1019
20.2 Sampling and Nonsampling Errors . . . . . . . . . . . . . . . . . . . . 1020
20.3 Simple and Stratified Random Sampling . . . . . . . . . . . . . . . . 1021
20.3.1 Designing the Sampling Study . . . . . . . . . . . . . . . . . 1021
20.3.2 Statistical Inferences in Terms of Simple
Random Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . 1022
20.3.3 Stratified Random Sampling . . . . . . . . . . . . . . . . . . 1027
20.4 Determining the Sample Size . . . . . . . . . . . . . . . . . . . . . . . . 1030
20.4.1 Sample Size for Simple Random Sampling . . . . . . . . 1030
20.4.2 Sample Size for Stratified Random Sampling . . . . . . 1034
20.5 Two-Stage Cluster Sampling . . . . . . . . . . . . . . . . . . . . . . . . 1036
20.6 Ratio Estimates Versus Regression Estimates . . . . . . . . . . . . 1040
20.6.1 Ratio Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1040
20.6.2 Regression Method . . . . . . . . . . . . . . . . . . . . . . . . . 1042
20.6.3 Comparison of the Ratio and Regression Methods . . . 1043
20.7 Business and Economic Applications . . . . . . . . . . . . . . . . . . 1043
20.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1046
Questions and Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1046
Appendix 1: The Jackknife Method for Removing Bias
from a Sample Estimate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1059
21 Statistical Decision Theory: Methods and Applications . . . . . . . . 1065
21.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1066
21.2 Four Key Elements of a Decision . . . . . . . . . . . . . . . . . . . . . 1067
21.3 Decisions Based on Extreme Values . . . . . . . . . . . . . . . . . . . 1068
21.3.1 Maximin Criterion . . . . . . . . . . . . . . . . . . . . . . . . . . 1068
21.3.2 Minimax Regret Criterion . . . . . . . . . . . . . . . . . . . . 1069
21.4 Expected Monetary Value and Utility Analysis . . . . . . . . . . . 1070
21.4.1 The Expected Monetary Value Criterion . . . . . . . . . . 1071
21.4.2 Utility Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1073
21.5 Bayes’ Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1078
21.6 Decision Trees and Expected Monetary Values . . . . . . . . . . . 1080
21.7 Mean and Variance Trade-Off Analysis . . . . . . . . . . . . . . . . . 1085
21.7.1 The Mean–Variance Rule and the
Dominance Principle . . . . . . . . . . . . . . . . . . . . . . . . 1085
21.7.2 The Capital Market Line . . . . . . . . . . . . . . . . . . . . . 1089
21.7.3 The Capital Asset Pricing Model . . . . . . . . . . . . . . . 1090
21.8 The Mean and Variance Method for Capital
Budgeting Decisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1096
21.8.1 Statistical Distribution of Cash Flow . . . . . . . . . . . . 1097
21.9 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1100
Questions and Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1101
Project V: Project for Selected Topics in Statistical Analysis . . . . . . 1115
Contents xlvii
Appendix 1: Using the Spreadsheet in Decision-Tree Analysis . . . . . 1116
Appendix 2: Graphical Derivation of the Capital Market Line . . . . . 1119
Appendix 3: Present Value and Net Present Value . . . . . . . . . . . . . . 1121
Appendix 4: Derivation of Standard Deviation for NPV . . . . . . . . . . 1123
Appendix A Statistical Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1125
Table A.1 Probability function of the binomial distribution . . . . . . . . . . . 1125
Table A.2 Poisson probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1130
Table A.3 The standardized normal distribution . . . . . . . . . . . . . . . . . . . 1135
Table A.4 Critical values of t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1137
Table A.5 Critical values of χ2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1138
Table A.6 Critical values of F . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1140
Table A.7 Exponential function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1147
Table A.8 Random numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1148
Table A.9 Cutoff points for the distribution of the Durbin-Watson
test statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1149
Table A.10 Lower and upper critical values R for the runs test . . . . . . . . 1152
Table A.11 Critical values of W in the Wilcoxon Matched-Pairs
Signed-Rank test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1153
Table A.12 Lower and upper critical values Rn1 and Rn2
of the Wilcoxon Rank-Sum test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1153
Table A.13 Factors for control chart . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1154
Table A.14 Present value of $l . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1155
Appendix B Description of Data Sets . . . . . . . . . . . . . . . . . . . . . . . . 1157
Appendix C Introduction to MINITAB 16 . . . . . . . . . . . . . . . . . . . . 1161
Appendix D Introduction to SAS: Microcomputer Version . . . . . . . 1165
Appendix E Useful Formulas in Statistics . . . . . . . . . . . . . . . . . . . . . 1171
Appendix F Important Finance and Accounting Topics . . . . . . . . . . 1193
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1195
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