statistics for business and financial economics978-1-4614-5897-5/1.pdfstatistics for business and...

Statistics for Business and Financial Economics

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

# Springer Science+Business Media New York 2013This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or partof the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations,recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission orinformation storage and retrieval, electronic adaptation, computer software, or by similar or dissimilarmethodology now known or hereafter developed. Exempted from this legal reservation are brief excerptsin connection with reviews or scholarly analysis or material supplied specifically for the purpose of beingentered and executed on a computer system, for exclusive use by the purchaser of the work. Duplicationof this publication or parts thereof is permitted only under the provisions of the Copyright Law of thePublisher’s location, in its current version, and permission for use must always be obtained fromSpringer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center.Violations are liable to prosecution under the respective Copyright Law.The use of general descriptive names, registered names, trademarks, service marks, etc. in thispublication does not imply, even in the absence of a specific statement, that such names are exemptfrom the relevant protective laws and regulations and therefore free for general use.While the advice and information in this book are believed to be true and accurate at the date ofpublication, neither the authors nor the editors nor the publisher can accept any legal responsibility forany errors or omissions that may be made. The publisher makes no warranty, express or implied, withrespect to the material contained herein.

Printed on acid-free paper

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


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


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.




charge.


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 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.


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.


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.




charge.


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.


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


19.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1002


Appendix 1: Options on Stock Indices and Currencies . . . . . . . . . . . 1013

Appendix 2: Index Futures and Hedge Ratio . . . . . . . . . . . . . . . . . . 1016

xlvi Contents

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


20.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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


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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