Statistical Techniques in
BUSINESS & ECONOMICS SIXTEENTH
DOUGLAS A. LIND Coastal Carolina University and The University of Toledo
WILLIAM G. MARCHAL The University of Toledo
SAMUEL SAMU EL A. WA WATHEN Coastal Carolina University
STATISTICAL TECHNIQUES IN BUSINESS & ECONOMICS, SIXTEENTH EDITION STATISTICAL Published by McGraw-Hill Education, 2 Penn Plaza, New York, NY 10121. Copyright © 2015 by McGraw-Hill Education. All rights reserved. Printed in the United States of America. Previous editions © 2012, 2010, and 2008. No part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the pr ior written consent of McGraw-Hill Education, including, but not limited to, in any network or other electronic storage or transmission, or broadcast for distance learning. Some ancillaries, including electronic and print components, may not be available to customers outside the United States. This book is pri nted on acid-free paper. 1 2 3 4 5 6 7 8 9 0 DOW/DOW 1 0 9 8 7 6 5 4 ISBN 978-0-07-802052-0 MHID 0-07-802052-2 Senior Vice President, Products & Markets: Kurt Markets: Kurt L. Strand Kimberly Meriwether David Vice President, Content Production & Technology Technology Services: Ser vices: Kimberly Managing Director: Douglas Director: Douglas Reiner Senior Brand Manager: Thomas Hayward Executive Director of Development: Ann Development: Ann Torbert Torbert Development Editor: Kaylee Putbrese Director of Digital Content: Doug Ruby Digital Development Editor: Meg Editor: Meg B. Maloney Senior Marketing Manager: Heather A. Kazakoff Content Project Manager: Diane L. Nowaczyk Content Project Manager: Brian Nacik Senior Buyer: Carol A. Bielski Jana Singer Design: Jana Design: Cover Image: Adrianna Image: Adrianna Williams/The Williams/The Image Bank/Getty Bank/Getty Images Lead Content Licensing Specialist: Keri Johnson Typeface: 9.5/11 Helvetica Neue 55 Compositor: Aptara®, Compositor: Aptara®, Inc. Inc. Printer: R. R. Donnelley All credits appearing on page or at the end of the book are considered considered to be an extension of the the copyright page. Library of Congress Cataloging-in-Publication Data Lind, Douglas A. Statistical techniques in business & economics / Douglas A. Lind, Coastal Carolina University and The University of Toledo, Toledo, William Willia m G. Marchal, The University of Toledo, Samuel A. Wathen, Wathen, Coastal Carolina University University.. — Sixteenth edition. pages cm. — (The McGraw-H McGraw-Hill/Irwin ill/Irwin series in operations and decision sciences) Includes index. ISBN 978-0-07-802052-0 (alk. paper) — ISBN 0-07-802052-2 (alk. paper) 1. Social sciences—Statistical methods. 2. Economics—Statistical Economics—Statistical methods. 3. Commercial statistics. I. Marchal, William G. II. Wathen, Samuel Adam. III. Title. IV IV.. Title: Statistical techniques in business and economics. HA29.M268 2015 519.5—dc23 2013035290
The Internet addresses listed in the text were accurate at the time of publication. The inclusion of a website does not indicate an endorsement by the authors or McGraw-Hill Education, Education, and McGraw-Hill Education does not guarantee the accuracy of the information presented at these sites.
To Jane, my wife and best friend, and our sons, their wives, and our grandchildren: Mike and Sue (Steve and Courtney), Steve and Kathr yn (Kennedy, Jake, and Brady), and Mark and Sarah (Jared, Drew, and Nate). Douglas A. Lind To my newest grandchildren (George Orn Marchal, Liam Brophy Horowitz, and Eloise Larae Marchal Murray), newest son-in-law (James Miller Nicholson), and newest wife (Andrea). William G. Marchal To my wonderful family: Isaac, Hannah, and Barb. Samuel A. Wathen
A NOTE FROM THE AUTHORS
Over the years, we have received many compliments on this text and understand that it’s a favorite among students. We accept that as the highest compliment and continue to work very hard to maintain that status. The objective of Statistical Techniques in Business and Economics is to provide students majoring in management, marketing, finance, accounting, economics, and other fields of business administration with an introductory survey of the many applications of descriptive and inferential statistics. We focus on business applications, but we also use many exercises and examples that relate to the current world of the college student. A previous course in statistics is not necessary, and the mathematical requirement is first-year algebra. In this text, we show beginning students every step needed to be successful in a basic statistics course. This step-by-step approach enhances performance, accelerates preparedness, and significantly improves motivation. Understanding the concepts, seeing and doing plenty of examples and exercises, and comprehending the application of statistical methods in business and economics are the focus of this book. The first edition of this text was published in 1967. At that time, locating relevant business data was difficult. That has changed! Today, locating data is not a problem. The number of items you purchase at the grocery store is automatically recorded at the checkout counter. Phone companies track the time of our calls, the length of calls, and the identity of the person called. Credit card companies maintain information on the number, time and date, and amount of our purchases. Medical devices automatically monitor our heart rate, blood pressure, and temperature from remote locations. A large amount of business information is recorded and reported almost instantly. CNN, USA Today, and MSNBC, for example, all have websites that track stock prices with a delay of less than 20 minutes. Today, skills are needed to deal with a large volume of numerical information. First, we need to be critical consumers of information presented by others. Second, we need to be able to reduce large amounts of information into a concise and meaningful form to enable us to make effective interpretations, judgments, and decisions. All students have calculators and most have either personal computers or access to personal computers in a campus lab. Statistical software, such as Microsoft Excel and Minitab, is available on these computers. The commands necessary to achieve the software results are available in Appendix C at the end of the book. We use screen captures within the chapters, so the student becomes familiar with the nature of the software output. Because of the availability of computers and software, it is no longer necessary to dwell on calculations. We have replaced many of the calculation examples with interpretative ones, to assist the student in understanding and interpreting the statistical results. In addition, we now place more emphasis on the conceptual nature of the statistical topics. While making these changes, we still continue to present, as best we can, the key concepts, along with supporting interesting and relevant examples.
WHAT’S NEW IN THIS SIXTEENTH EDITION? We have made changes to this edition that we think you and your students will find useful and timely. • We reorganized the chapters so that each section corresponds to a learning objective. The learning objectives have been revised. • We expanded the hypothesis testing procedure in Chapter 10 to six steps, emphasizing the interpretation of test results.
• We have revised example/solution sections in various chapters: • Chapter 5 now includes a new example/solution used to demonstrate contingency tables and tree diagrams. Also the example/solution demonstrating the combination formula has been revised. • Chapter 6 includes a revised example/solution demonstrating the binomial distribution. • Chapter 15 includes a new example/solution demonstrating contingency table analysis. • We have revised the simple regression example in Chapter 13 and increased the number of observations to better illustrate the principles of simple linear regression. • We have reordered the nonparametric chapters to follow the traditional statistics chapters. • We moved the sections on one- and two-sample tests of proportions, placing all analysis of nominal data in one chapter: Nonparametric Methods: Nominal Level Hypothesis Tests. • We combined the answers to the Self-Review Exercises into a new appendix. • We combined the Software Commands into a new appendix. • We combined the Glossaries in the section reviews into a single Glossary that follows the appendices at the end of the text. • We improved graphics throughout the text.
HOW ARE CHAPTER S ORGANIZ ED TO ENGAGE STUDENTS AND PROMOTE LEARNING?
Chapter Learning Objectives Each chapter begins with a set of learning objectives designed to provide focus for the chapter and motivate student learning. These objectives, located in the margins next to the topic, indicate what the student should be able to do after completing each section in the chapter. MERRILL LYNCH recently completed LEARNING OBJECTIVES a study of online investment portfo-
When you have completed this chapter, you will be able to:
Chapter Opening Exercise
lios for a sample of clients. For the
Summarize qualitative variables with frequency and relative frequency tables.
A representative exercise opens the chapter and shows how the chapter content can be applied to a real-world situation.
these data into a frequency distribu-
Display a frequency table using a bar or pie chart.
Summarize quantitative variables with frequency and relative frequency distributions.
Display a frequency distribution using a histogram or frequency polygon.
Introduction to the Topic Each chapter starts with a review of the important concepts of the previous chapter and provides a link to the material in the current chapter. This step-by-step approach increases comprehension by providing continuity across the concepts.
70 participants in the study, organize tion. (See Exercise 43 and LO2-3.)
INTRODUCTION Chapter 2 began our study of descriptive statistics. To summarize raw data into a meaningful form, we organized qualitative data into a frequency table and portrayed the results in a bar chart. In a similar fashion, we organized quantitative data into a frequency distribution and portrayed the results in a histogram. We also looked at other graphical techniques such as pie charts to portray qualitative data and frequency polygons to portray quantitative data. This chapter is concerned with two numerical ways of describing quantitative variables, namely, measures of location and measures of dispersion. Measures of location are often referred to as averages. The purpose of a measure of location is to pinpoint the center of a distribution of data. An
E X A M P L E
After important concepts are introduced, a solved example is given. This example provides a how-to illustration and shows a relevant business application that helps students answer the question, “What will I use this for?”
The service departments at Tionesta Ford Lincoln Mercury and Sheffield Motors Inc., two of the four Applewood Auto Group dealerships, were both open 24 days last month. Listed below is the number of vehicles serviced last month at the two dealerships. Construct dot plots and report summary statistics to compare the two dealerships. Tionesta Ford Lincoln Mercury Monday
Self-Reviews Self-Reviews are interspersed throughout each chapter and closely patterned after the preceding examples. They help students monitor their progress and provide immediate reinforcement for that particular technique.
The Quality Control department of Plainsville Peanut Company is responsible for checking the weight of the 8-ounce jar of peanut butter. The weights of a sample of nine jars p roduced last hour are: S E L F � R E V I E W 7.69
4�2 (a) (b)
What is the median weight? Determine the weights corresponding to the first and third quartiles.
Statistics in Action Statistics in Action articles are scattered throughout the text, usually about two per chapter. They provide unique and interesting applications and historical insights in the field of statistics.
STATISTICS I N ACTION
If you wish to get some attention at the next gathering you attend, announce that you believe that at least two people present were born on the same date—that is, the same day of the year but not necessarily the same year. If there are 30 people in the room,
Definitions Definitions of new terms or terms unique to the study of statistics are set apart from the text and highlighted for easy reference and review. They also appear in the Glossary at the end of the book.
JOINT PROBABILITY A probability that measures the likelihood two or more events will happen concurrently.
Formulas Formulas that are used for the first time are boxed and numbered for reference. In addition, a formula card is bound into the back of the text that lists all the key formulas.
Exercises Exercises are included after sections within the chapter and at the end of the chapter. Section exercises cover the material studied in the section.
E X E R C I S E S
SPECIAL RULE OF MULTIPLICATION
P( A and B )
P( A )P( B )
.60, P ( A2 ) .40, P ( B1 ƒ A1 ) .05, and P ( B1 ƒ A2 ) .10. Use Bayes’ theorem to determine P ( A1 ƒ B1 ). .10. 34. P ( A1 ) .20, P ( A2 ) .40, P ( A3 ) .40, P ( B1 ƒ A1 ) .25, P ( B1 ƒ A2 ) .05, and P ( B1 ƒ A3 ) Use Bayes’ theorem to determine P ( A3 ƒ B1 ). 35. The Ludlow Wildcats baseball team, a minor league team in the Cleveland Indians organization, plays 70% of their games at night and 30% during the day. The team wins 50% of their night games and 90% of their day games. According to today’s newspaper, they won yesterday. What is the probability the game was played at night? 36. Dr. Stallter has been teaching basic statistics for many years. She knows that 80% of the students will complete the assigned problems. She has also determined that among those who do their assignments, 90% will pass the course. Among those students who do not do 33.
P ( A1 )
Computer Output The text includes many software examples, using Excel, MegaStat®, and Minitab.
HOW DOES THIS TEXT RE INFORC E STUDENT LEARNING?
BY CHAPTE R
I. A random variable is a numerical value determined by the outcome of an experiment. II. A probability distribution is a listing of all possible outcomes of an experiment and the prob-
ability associated with each outcome.
A. A discrete probability distribution can assume only certain values. The main features are: 1. The sum of the probabilities is 1.00. 2. The probability of a particular outcome is between 0.00 and 1.00. 3. The outcomes are mutually exclusive. B. A continuous distribution can assume an infinite number of values within a specific range.
Each chapter contains a brief summary of the chapter material, including the vocabulary and the critical formulas.
III. The mean and variance of a probability distribution are computed as follows. A. The mean is equal to: m 5 © [ xP ( x ) ]
2 s 5 ©
This tool lists the mathematical symbol, its meaning, and how to pronounce it. We believe this will help the student retain the meaning of the symbol and generally enhance course communications.
The last several exercises at the end of each chapter are based on three large data sets. These data sets are printed in Appendix A in the text and are also on the text’s website. These data sets present the students with real-world and more complex applications.
Software Commands Software examples using Excel, MegaStat®, and Minitab are included throughout the text. The explanations of the computer input commands are placed at the end of the text in Appendix C.
P( A )
Probability of A
P of A
P( A )
Probability of not A
P( A and B )
Probability of A and B
P of A and B
P( A or B )
Probability of A or B
P of A or B
P ( A ƒ B )
Probability of A given B has happened
P of A given B
Permutation of n items selected r at a time
Combination of n items selected r at a time
[ ( x 2 m ) 2P ( )] x
41. The amount of cola in a 12-ounce can is uniformly distributed between 11.96 ounces and
12.05 ounces. a. What is the mean amount per can? b. What is the standard deviation amount per can? c. What is the probability of selecting a can of cola and finding it has less than 12 ounces? d. What is the probability of selecting a can of col a and finding it has more than 11.98 ounces? e. What is the probability of selecting a can of col a and finding it has more than 11.00 ounces? 42. A tube of Listerine Tartar Control toothpaste contains 4.2 ounces. As people use the toothpaste, the amount remaining in any tube is random. Assume the amount of toothpaste remaining in the tube follows a uniform distribution. From this information, we can determine the following information about the amount remaining in a toothpaste tube without invading anyone’s privacy. a. How much toothpaste would you expect to be remaining in the tube? b. What is the standard deviation of the amount remaining in the tube? c. What is the likelihood there is less than 3.0 ounces remaining in the tube? d. What is the probability there is more than 1.5 ounces remaining in the tube? 43. Many retail stores offer their own credit cards. At the time of the credit application, the customer is given a 10% discount on the purchase. The time required for the credit application process follows a uniform distribution with the times ranging from 4 minutes to 10 minutes. a. What is the mean time for the application process? b. What is the standard deviation of the process time? c. What is the likelihood a particular application will take less than 6 minutes?
Generally, the end-of-chapter exercises are the most challenging and integrate the chapter concepts. The answers and worked-out solutions for all odd-numbered exercises are in Appendix D at the end of the text. Many exercises are noted with a data file icon in the margin. For these exercises, there are data files in Excel format located on the text’s website, www .mhhe.com/lind16e . These files help students use statistical software to solve the exercises.
Data Set Exercises
B. The variance is equal to:
(The data for these exercises are available at the text website: www.mhhe.com/lind16e .) 74. Refer to the Real Estate data, which report information on homes sold in the Goodyear,
Arizona, area during the last year. a. The mean selling price (in $ thousands) of the homes was computed earlier to be $221.10, with a standard deviation of $47.11. Use the normal distribution to estimate the percentage of homes selling for more than $280.0. Compare this to the actual results. Does the normal distribution yield a good approximation of the actual results? b. The mean distance from the center of the city is 14.629 miles, with a standard deviation of 4.874 miles. Use the normal distribution to estimate the number of homes 18 o r more miles but less than 22 miles from the center of the city. Compare this to the actual results. Does the normal distribution yield a good approximation of the actual results?
CHAPTER 5 5–1. The Excel Commands to determine the number of permuta-
tions shown on page 164 are: a. Click on the Formulas tab in the top menu, then, on the far left, select Insert Function fx .
b. In the Insert Function box, select Statistical as the category, then scroll down to PERMUT in the Select a function list. Click OK. c. In the PERM box after Number, enter 8 and in the Number_chosen box enter 3. The correct answer of 336
appears twice in the box.
Answers to Self-Review
16–7 a. Rank
The worked-out solutions to the Self-Reviews are provided at the end of the text in Appendix E.
BY SECTIO N
Section Reviews After selected groups of chapters (1–4, 5–7, 8 and 9, 10–12, 13 and 14, 15 and 16, and 17 and 18), a Section Review is included. Much like a review before an exam, these include a brief overview of the chapters and problems for review.
A REVIEW OF CHAPTERS 1�4 This section is a review of the major concepts and terms introduced in Chapters 1–4. Chapter 1 began by describing the meaning and purpose of statistics. Next we described the different types of variables and the four levels of measurement. Chapter 2 was concerned with describing a set of observations by organizing it into a frequency distribution and then portraying the frequency distribution as a histogram or a frequency polygon. Chapter 3 began by describing measures of location, such as the mean, weighted mean, median, geometric mean, and mode. This chapter also included measures of dispersion, or spread. Discussed in this section were the range, variance, and standard deviation. Chapter 4 included several graphing techniques such as dot plots, box plots, and scatter diagrams. We also discussed the coefficient of skewness, which reports the lack of symmetry in a set of data.
C A S E S A. Century National Bank
The review also includes continuing cases and several small cases that let students make decisions using tools and techniques from a variety of chapters.
The following case will appear in subsequent review sections. Assume that you work in the Planning Department of the Century National Bank and report to Ms. Lamberg. You will need to do some data analysis and prepare a short written report. Remember, Mr. Selig is the president of the bank, so you will want to ensure that your report is complete and accurate. A copy of the data appears in Appendix A.6 . Century National Bank has offices in several cities in the Midwest and the southeastern part of the United States. Mr. Dan Selig, president and CEO, would like to know the characteristics of his checking account customers. What is the balance of a typical customer? How many other bank services do the checking account customers use? Do the customers use the ATM service and, if so, how often? What about debit cards? Who uses them, and how often are they used?
balances for the four branches. Is there a difference among the branches? Be sure to explain the difference between the mean and the median in your report. 3. Determine the range and the standard deviation of the checking account balances. What do the first and third quartiles show? Determine the coefficient of skewness and indicate what it shows. Because Mr. Selig does not deal with statistics daily, include a brief description and interpretation of the standard deviation and other measures.
B. Wildcat Plumbing Supply Inc.: Do We Have Gender Differences? Wildcat Plumbing Supply has served the plumbing needs of Southwest Arizona for more than 40 years. The company was founded by Mr. Terrence St. Julian and is run today by
Practice Test The Practice Test is intended to give students an idea of content that might appear on a test and how the test might be structured. The Practice Test includes both objective questions and problems covering the material studied in the section.
P R A C T I C E
T E S T
There is a practice test at the end of each review section. The tests are in two parts. The first part contains several objective questions, usually in a fill-in-the-blank format. The second part is problems. In most cases, it should take 30 to 45 minutes to complete the test. The problems require a calculator. Check the answers in the Answer Section in the back of the book.
Part 1—Objective 1. The science of collecting, organizing, presenting, analyzing, and interpreting data to assist in
making effective decisions is called
2. Methods of organizing, summarizing, and presenting data in an informative way are
3. The entire set of individuals or objects of interest or the measurements obtained from all
individuals or objects of interest are called the 4. List the two types of variables.
W H AT T E C H N O L O G Y C O N N E C T S S T U D E N T S TO BUSINESS STATISTICS?
MCGRAW�HILL CONNECT® BUSINESS STATISTICS
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forming, allowing for more productive use of lecture and office hours. The progress-tracking function enables you to • View scored work immediately and track individual or group performance with assignment and grade reports. • Access an instant view of student or class performance relative to learning objectives. • Collect data and generate reports required by many accreditation organizations, such as AACSB and AICPA.
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TEGRIT Y CAMPUS: LECTURES 24/7 Tegrity Campus is a service that makes class time available 24/7 by automatically capturing every lecture in a searchable format for students to review when they study and complete assignments. With a simple one-click start-and-stop process, you capture all computer screens and corresponding audio. Students can replay any part of any class with easy-to-use browser-based viewing on a PC or Mac. Educators know that the more students can see, hear, and experience class resources, the better they learn. In fact, studies prove it. With Tegrity Campus, students quickly recall key moments by using Tegrity Campus’s unique search feature. This search helps students efficiently find what they need, when they need it, across an entire semester of class recordings. Help turn all your students’ study time into learning moments immediately supported by your lecture. To learn more about Tegrity watch a two-minute Flash demo at http://tegritycampus.mhhe.com .
ASSURANCE OF LEARNING READY Many educational institutions today are focused on the notion of assurance of learning, an important element of some accreditation standards. Statistical Techniques in Business & Economics is designed specifically to support your assurance of learning initiatives with a simple, yet powerful solution. Each test bank question for Statistical Techniques in Business & Economics maps to a specific chapter learning objective listed in the text. You can use our test bank software, EZ Test and EZ Test Online, or Connect ® Busi ness Statistics to easily query for learning objectives that directly relate to the lear ning objectives for your course. You can then use the reporting features of EZ Test to aggregate student results in similar fashion, making the collection and presentation of assurance of learning data simple and easy.
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WHAT SOFTWARE I S AVAILABLE WITH THIS TEXT?
MEGASTAT® FOR MICROSOFT EXCEL® MegaStat ® by J. B. Orris of Butler University is a full-featured Excel statistical analysis add-in that is available on the MegaStat website at www.mhhe.com/megastat (for purchase). MegaStat works with recent versions of Microsoft Excel® (Windows and Mac OS X). See the website for details on supported versions. Once installed, MegaStat will always be available on the Excel add-ins ribbon with no expiration date or data limitations. MegaStat performs statistical analyses within an Excel workbook. When a MegaStat menu item is selected, a dialog box pops up for data selection and options. Since MegaStat is an easy-to-use extension of Excel, students can focus on learning statistics without being distracted by the software. Ease-of-use features include Auto Expand for quick data selection and Auto Label detect. MegaStat does most calculations found in introductory statistics textbooks, such as descriptive statistics, frequency distributions, and probability calculations as well as hypothesis testing, ANOVA chi-square, and regression (simple and multiple). MegaStat output is carefully formatted and appended to an output worksheet. Video tutorials are included that provide a walkthrough using MegaStat for typical business statistics topics. A context-sensitive help system is built into MegaStat and a User’s Guide is included in PDF format.
MINITAB®/SPSS®/JMP® Minitab® Student Version 14, SPSS ® Student Version 18.0, and JMP ® Student Edition Version 8 are software tools that are available to help students solve the business statistics exercises in the text. Each can be packaged with any McGraw-Hill business statistics text.
W H AT R E S O U R C E S A R E A VA I L A B L E F O R I N S T R U C T O R S ?
ONLINE LEARNING CENTER: www.mhhe.com/lind16e The Online Learning Center (OLC) provides the instructor with a complete Instructor’s Manual in Word format, the complete Test Bank in both Word files and computerized EZ Test format, Instructor PowerPoint slides, text art files, an introduction to ALEKS ®, an introduction to McGraw-Hill Connect Business StatisticsTM, and more.
All test bank questions are available in an EZ Test electronic format. Included are a number of multiple-choice, true/false, and short-answer questions and problems. The answers to all questions are given, along with a rating of the level of difficulty, chapter goal the question tests, Bloom’s taxonomy question type, and the AACSB knowledge category.
WebCT/Blackboard/eCollege All of the material in the Online Learning Center is also available in portable WebCT, Blackboard, or eCollege content “cartridges” provided free to adopters of this text.
W H AT R E S O U R C E S A R E AVA I L A B L E F O R S T U D E N T S ?
ALEKS is an assessment and learning program that provides individualized instruction in Business Statistics, Business Math, and Accounting. Available online, ALEKS interacts with students much like a skilled human tutor, with the ability to assess precisely a student’s knowledge and provide instruction on the exact topics the student is most ready to learn. By providing topics to meet individual students’ needs, allowing students to move between explanation and practice, correcting and analyzing errors, and defining terms, ALEKS helps students to master course content quickly and easily. ALEKS also includes a new instructor module with powerful, assignment-driven features and extensive content flexibility. ALEKS simplifies course management and allows instructors to spend less time with administrative tasks and more time directing student learning. To learn more about ALEKS, visit www.aleks.com.
ONLINE LEARNING CENTER: www.mhhe.com/lind16e The Online Learning Center (OLC) provides students with the following content: • Quizzes • PowerPoints • Data sets/files • Appendixes • Chapter 20
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This edition of Statistical Techniques in Business and Economics is the product of many people: students, colleagues, reviewers, and the staff at McGraw-Hill/Irwin. We thank them all. We wish to express our sincere gratitude to the survey and focus group participants, and the reviewers:
Sung K. Ahn Washington State University– Pullman Vaughn S. Armstrong Utah Valley University Scott Bailey Troy University Douglas Barrett University of North Alabama Arnab Bisi Purdue University Pamela A. Boger Ohio University–Athens Emma Bojinova Canisius College Ann Brandwein Baruch College Giorgio Canarella California State University–Los Angeles Lee Cannell El Paso Community College James Carden University of Mississippi Mary Coe St. Mary College of California Anne Davey Northeastern State University Neil Desnoyers Drexel University Nirmal Devi Embry Riddle Aeronautical University David Doorn University of Minnesota–Duluth Ronald Elkins Central Washington University Vickie Fry Westmoreland County Community College Xiaoning Gilliam Texas Tech University
Mark Gius Quinnipiac University Clifford B. Hawley West Virginia University Peter M. Hutchinson Saint Vincent College Lloyd R. Jaisingh Morehead State University Ken Kelley University of Notre Dame Mark Kesh University of Texas Melody Kiang California State University–Long Beach Morris Knapp Miami Dade College David G. Leupp University of Colorado–Colorado State Teresa Ling Seattle University Cecilia Maldonado Georgia Southwestern State University John D. McGinnis Pennsylvania State–Altoona Mary Ruth J. McRae Appalachian State University Jackie Miller The Ohio State University Carolyn Monroe Baylor University Valerie Muehsam Sam Houston State University Tariq Mughal University of Utah Elizabeth J. T. Murff Eastern Washington University Quinton Nottingham Virginia Polytechnic Institute and State University René Ordonez Southern Oregon University
Ed Pappanastos Troy University Michelle Ray Parsons Aims Community College Robert Patterson Penn State University Joseph Petry University of Illinois at UrbanaChampaign Germain N. Pichop Oklahoma City Community College Tammy Prater Alabama State University Michael Racer University of Memphis Darrell Radson Drexel University Steven Ramsier Florida State University Emily N. Roberts University of Colorado–Denver Christopher W. Rogers Miami Dade College Stephen Hays Russell Weber State University Martin Sabo Community College of Denver Farhad Saboori Albright College Amar Sahay Salt Lake Community College and University of Utah Abdus Samad Utah Valley University Nina Sarkar Queensborough Community College Roberta Schini West Chester University of Pennsylvania Robert Smidt California Polytechnic State University Gary Smith Florida State University
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Survey and Focus Group Participants
Nawar Al-Shara American University Charles H. Apigian Middle Tennessee State University Nagraj Balakrishnan Clemson University
Philip Boudreaux University of Louisiana at Lafayette Nancy Brooks University of Vermont Qidong Cao Winthrop University Margaret M. Capen East Carolina University Robert Carver Stonehill College Jan E. Christopher Delaware State University James Cochran Louisiana Tech University Farideh Dehkordi-Vakil Western Illinois University Brant Deppa Winona State University Bernard Dickman Hofstra University Casey DiRienzo Elon University Erick M. Elder University of Arkansas at Little Rock Nicholas R. Farnum California State University–Fullerton K. Renee Fister Murray State University Gary Franko Siena College Maurice Gilbert Troy State University Deborah J. Gougeon University of Scranton Christine Guenther Pacific University Charles F. Harrington University of Southern Indiana Craig Heinicke Baldwin-Wallace College George Hilton Pacific Union College Cindy L. Hinz St. Bonaventure University Johnny C. Ho Columbus State University
Shaomin Huang Lewis-Clark State College J. Morgan Jones University of North Carolina at Chapel Hill Michael Kazlow Pace University John Lawrence California State University–Fullerton Sheila M. Lawrence Rutgers, The State University of New Jersey Jae Lee State University of New York at New Paltz Rosa Lemel Kean University Robert Lemke Lake Forest College Francis P. Mathur California State Polytechnic University, Pomona Ralph D. May Southwestern Oklahoma State University Richard N. McGrath Bowling Green State University Larry T. McRae Appalachian State University Dragan Miljkovic Southwest Missouri State University John M. Miller Sam Houston State University Cameron Montgomery Delta State University Broderick Oluyede Georgia Southern University Andrew Paizis Queens College Andrew L. H. Parkes University of Northern Iowa Paul Paschke Oregon State University Srikant Raghavan Lawrence Technological University Surekha K. B. Rao Indiana University Northwest
Timothy J. Schibik University of Southern Indiana Carlton Scott University of California, Irvine Samuel L. Seaman Baylor University Scott J. Seipel Middle Tennessee State University Sankara N. Sethuraman Augusta State University Daniel G. Shimshak University of Massachusetts, Boston Robert K. Smidt California Polytechnic State University
William Stein Texas A&M University Robert E. Stevens University of Louisiana at Monroe Debra Stiver University of Nevada–Reno Ron Stunda Birmingham-Southern College Edward Sullivan Lebanon Valley College Dharma Thiruvaiyaru Augusta State University Daniel Tschopp Daemen College Bulent Uyar University of Northern Iowa
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Their suggestions and thorough reviews of the previous edition and the manuscript of this edition make this a better text. Special thanks go to a number of people. Professor Malcolm Gold, Avila University, reviewed the page proofs and the solutions manual, checking text and exercises for accuracy. Professor Jose Lopez–Calleja, Miami Dade College–Kendall, prepared the test bank. Professor Vickie Fry, Westmoreland County Community College, accuracy checked the Connect exercises. We also wish to thank the staff at McGraw-Hill. This includes Thomas Hayward, Senior Brand Manager; Kaylee Putbrese, Development Editor; Diane Nowaczyk, Content Project Manager; and others we do not know personally, but who have made valuable contributions.
ENHANCEMENTS TO STATISTICAL TECHNIQUES I N B U S I N E S S & E C O N O M I C S , 16 E
MAJOR CHANGES MADE TO INDIVIDUAL CHAPTERS: CHAPTER 1 What Is Statistics? • New photo and chapter opening exercise on th e Nook Color sold by Barnes & Noble.
• Revised Self-Review 6–4 applying the binomial distribution. • New exercise 10 using the number of “underwater” loans. • New exercise using a raffle at a local golf club to demonstrate probability and expected returns.
CHAPTER 7 Continuous Probability Distributions
• New introduction with new graphic showing the increasing amount of information collected and processed with new technologies.
• Updated Statistics in Action.
• New ordinal scale example based on rankings of states based on business climate.
• Revised explanation of the Empirical Rule as it relates to the normal distribution.
• Revised Self-Review 7–2 based on daily personal water consumption.
• The chapter includes several new examples. • Chapter is more focused on the revised learning objectives and improving the chapter’s flow. • Revised exercise 17 is based on economic data.
CHAPTER 2 Describing Data: Frequency
Tables, Frequency Distributions, and Graphic Presentation • Revised Self-Review 2–3 to include data. • Updated the company list in revised exercise 38. • New or revised exercises 45, 47, and 48.
CHAPTER 8 Sampling Methods and the Central Limit Theorem • New example of simple random sampling and the application of the table of random numbers. • The discussions of systematic random, stratified random, and cluster sampling have been revised. • Revised exercise 44 based on the price of a gallon of milk.
CHAPTER 9 Estimation and Confidence Intervals • New Statistics in Action describing EPA fuel economy. • New separate section on point estimates.
CHAPTER 3 Describing Data: Numerical
• Integration and application of the central limit theorem.
• A revised simul ation demons tratin g the inter pretat ion of confidence level.
• Reorganized chapter based on revised learning objectives. • Replaced the mean deviation with more emphasis on the variance and standard deviation. • Updated statistics in action.
• New presentation on using the t table to find z values. • A revised discussion of determining th e confidence i nterval for the population mean. • Expanded section on calculating sample size.
CHAPTER 4 Describing Data: Displaying and
Exploring Data • Updated exercise 22 with 2012 New York Yankee player salaries.
CHAPTER 5 A Survey of Probability Concepts • New explanation of odds compared to probabilities. • New exercise 21. • New example/solution for demonstrating contingency tables and tree diagrams.
• New exercise 12 (milk consumption).
CHAPTER 10 One-Sample Tests of Hypothesis • New example/solution involving airport parking. • Revised software solution and explanation of p-values. • New exercises 17 (daily water consumption) and 19 (number of text messages by teenagers). • Conducting a test of hypothesis about a population proportion is moved to Chapter 15.
• New contingency table exercise 31.
• New example introducing the concept of hypothesis testing.
• Revised example/solution demonstrating the combination formula.
• Sixth step added to the hypothesis testing procedure emphasizing the interpretation of the hypothesis test results.
CHAPTER 6 Discrete Probability Distributions
CHAPTER 11 Two-Sample Tests of Hypothesis
• Revised the section on the binomial distribution.
• New introduction to the chapter.
• Revised example/solution demonstrating the binomial distribution.
• Section of two-sample tests about proportions moved to Chapter 15.
• Changed subscripts in example/solution for easier understanding. • Updated exercise with 2012 New York Yankee player salaries. CHAPTER 12
Analysis of Variance
• New introduction to the chapter. • New exercise 24 using the speed of browsers to search the Internet. • Revised exercise 33 comparing learning in traditional versus online courses. • New section on Comparing Two Population Variances. • New example illustrating the comparison of variances. • Revised section on two-way ANOVA with interaction with new examples and revised example/solution. • Revised the names of the airlines in the one-way ANOVA example. • Changed the subscripts in example/solution for easier understanding. • New exercise 30 (flight times between Los Angeles and San Francisco). CHAPTER 13
Correlation and Linear Regression
Nonparametric Methods: Nominal Level Hypothesis Tests CHAPTER 15
• Moved and renamed ch apter. • Moved one-sample and two-sample tests of proportions from Chapters 10 and 11 to Chapter 15. • New example introducing goodness-of-fit tests. • Removed the graphical methods to evaluate normality. • Revised section on contingency table analysis with a new example/solution. • Revised Data Set exercises.
Nonparametric Methods: Analysis of Ordinal Data CHAPTER 16
• Moved and renamed ch apter. • New example/solution and self-review demonstrating a hypothesis test about the median. • New example/solution demonstrating the rank-order correlation. CHAPTER 17
• Moved chapter to follow nonparametric statistics. • Updated dates, illustrations, and examples.
• Rewrote the introduction section to the chapter.
• Revised example/solution demonstrating the use of the Production Price Index to deflate sales dollars.
• The data used as the basis for the North American Copier Sales example/solution used throughout the chapter has been changed and expanded to 15 observations to more clearly demonstrate the chapter’s learning objectives.
• Revised example/solution demonstrating the comparison of the Dow Jones Industrial Average and the Nasdaq using indexing.
• Revised section on transforming data using the economic relationship between price and sales. • New exercises 35 (transforming data), 36 (Masters prizes and scores), 43 (2012 NFL points scored versus points allowed), 44 (store size and sales), and 61 (airline distance and fare). CHAPTER 14
Multiple Regression Analysis
• Rewrote the section on evaluating the multiple regression equation. • More emphasis on the regression ANOVA table. • Enhanced the discussion of the p-value in decision making. • More emphasis on calculating the variance inflation factor to evaluate multicollinearity.
• New self-review about using indexes to compare two different measures over time. • Revised Data Set Exercise. CHAPTER 18
Time Series and Forecasting
• Moved chapter to follow nonparametric statistics and index numbers. • Updated dates, illustrations, and examples. • Revised section on the components of a time series. • Revised graphics for better illustration.
Statistical Process Control and Quality Management CHAPTER 19
• Updated 2012 Malcolm Baldrige National Quality Award winners.
1 What Is Statistics?
2 Describing Data: Frequency Tables, Frequency Distributions, and
3 Describing Data: Numerical Measures
4 Describing Data: Displaying and Exploring Data 5 A Survey of Probability Concepts
6 Discrete Probability Distributions
7 Continuous Probability Distributions
8 Sampling Methods and the Central Limit Theorem 9 Estimation and Confidence Intervals
10 One-Sample Tests of Hypothesis
11 Two-Sample Tests of Hypothesis
12 Analysis of Variance
13 Correlation and Linear Regression 14 Multiple Regression Analysis
15 Nonparametric Methods: Nominal Level Hypothesis Tests 16 Nonparametric Methods: Analysis of Ordinal Data 17 Index Numbers
18 Time Series and Forecasting
19 Statistical Process Control and Quality Management 20 An Introduction to Decision Theory
Photo Credits Index
On the website: www.mhhe.com/lind16e
Appendixes: Data Sets, Tables, Software Commands, Answers
A Note from the Authors
What Is Statistics?
Introduction 2 Why Study Statistics?
What Is Meant by Statistics? Types of Statistics
Levels of Measurement
Data Set Exercises
Describing Data: Numerical Measures
Constructing Frequency Tables
The Weighted Mean
Graphic Presentation of Qualitative Data 24
Population Variance 73 Population Standard Deviation
Sample Variance and Standard Deviation 76 Software Solution 77 EXERCISES
Graphic Presentation of a Frequency Distribution 32
Interpretation and Uses of the Standard Deviation 78
Chebyshev’s Theorem 78 The Empirical Rule 79
Cumulative Frequency Distributions
Why Study Dispersion?
Relative Frequency Distribution
The Geometric Mean
Constructing Frequency Distributions
Range 69 Variance 70
Relative Class Frequencies 20
Histogram 32 Frequency Polygon
The Relative Positions of the Mean, Median, and Mode 61
The Median 56 The Mode 58
Describing Data: Frequency Tables, Frequency Distributions, and Graphic Presentation 17
Data Set Exercises
The Population Mean 52 The Sample Mean 53 Properties of the Arithmetic Mean
Computer Software Applications
Measures of Location
Ethics and Statistics
Nominal-Level Data 7 Ordinal-Level Data 8 Interval-Level Data 9 Ratio-Level Data 10 EXERCISES
Descriptive Statistics 4 Inferential Statistics 5 Types of Variables
The Mean and Standard Deviation of Grouped Data 81
Classical Probability 135 Empirical Probability 136 Subjective Probability 138
Arithmetic Mean of Grouped Data 81 Standard Deviation of Grouped Data 82 EXERCISES
Data Set Exercises
Special Rule of Multiplication 146 General Rule of Multiplication 147 Contingency Tables Tree Diagrams
Describing the Relationship between Two Variables 114 Contingency Tables EXERCISES
Data Set Exercises
A REVIEW OF CHAPTERS 1–4
Data Set Exercises
Discrete Probability Distributions 173 What Is a Probability Distribution? Random Variables
Discrete Random Variable 177 Continuous Random Variable 177 The Mean, Variance, and Standard Deviation of a Discrete Probability Distribution 178
Mean 178 Variance and Standard Deviation
PROBLEMS 126 CASES
The Multiplication Formula 160 The Permutation Formula 161 The Combination Formula 163
Quartiles, Deciles, and Percentiles 102 Box Plots
Principles of Counting
Measures of Position
Rules of Multiplication to Calculate Probability 146
Introduction 94 Stem-and-Leaf Displays
Special Rule of Addition 140 Complement Rule 142 The General Rule of Addition 143 EXERCISES
Describing Data: Displaying and Exploring Data Dot Plots
Rules of Addition for Computing Probabilities
Ethics and Reporting Results
Introduction 132 What Is a Probability? 133 Approaches to Assigning Probabilities
Binomial Probability Distribution
A Survey of Probability Concepts 131
How Is a Binomial Probability Computed? Binomial Probability Tables 185 EXERCISES
Cumulative Binomial Probability Distributions 189 EXERCISES
Hypergeometric Probability Distribution
Poisson Probability Distribution EXERCISES
Simple Random Sampling 249 Systematic Random Sampling 252 Stratified Random Sampling 252 Cluster Sampling 253
19 4 194
Data Set Exercises
Sampling Distribution of the Sample Mean
The Central Limit Theorem
Using the Sampling Distribution of the Sample Mean 269
The Family of Normal Probability Distributions 211 The Standard Normal Probability Distribution
Applications of the Standard Normal Distribution 215 The Empirical Rule 215 EXERCISES
21 7 22 1
Data Set Exercises
Estimation and Confidence Intervals Point Estimate for a Population Mean
23 0 23 5
Data Set Exercises
Sampling Methods and the Central Limit Theorem 247 248
Data Set Exercises
A REVIEW OF CHAPTERS 8–9 PROBLEMS CASE
Finite-Population Correction Factor EXERCISES
Sample Size to Estimate a Population Mean Sample Size to Estimate a Population Proportion 302 EXERCISES
Reasons to Sample
Choosing an Appropriate Sample Size
A REVIEW OF CHAPTERS 5–7
A Confidence Interval for a Population Proportion 297 EXERCISES
Population Standard Deviation, 229
The Family of Exponential Distributions
Population Standard Deviation, Known A Computer Simulation 286
Continuity Correction Factor 227 How to Apply the Correction Factor
Confidence Intervals for a Population Mean
The Normal Approximation to the Binomial
Finding Areas under the Normal Curve EXERCISES
Continuous Probability Distributions 206 The Family of Uniform Probability Distributions 207
One-Sample Tests of Hypothesis 315
Comparing Dependent and Independent Samples 368
Data Set Exercises
What Is a Hypothesis?
What Is Hypothesis Testing?
Six-Step Procedure for Testing a Hypothesis
Step 1: State the Null Hypothesis ( H0 ) and the Alternate Hypothesis ( H1 ) 318 Step 2: Select a Level of Significance 319 Step 3: Select the Test Statistic 320 Step 4: Formulate the Decision Rule 320 Step 5: Make a Decision 321 Step 6: Interpret the Result 322
Comparing Two Population Variances
33 8 339 34 2
Data Set Exercises
Interaction Plots 404 Testing for Interaction 405 Hypothesis Tests for Interaction
Data Set Exercises
Two-Sample Tests of Hypothesis: Dependent Samples 364
Correlation and Linear Regression 426 Introduction 427
Unequal Population Standard Deviations
Comparing Population Means with Unknown Population Standard Deviations 355
Two-Sample Tests of Hypothesis: Independent Samples 349
A REVIEW OF CHAPTERS 10–12
Two-Sample Pooled Test
Two-Way ANOVA with Interaction
Two-Sample Tests of Hypothesis 348
Two-Way Analysis of Variance
A Software Solution 337
Inferences about Pairs of Treatment Means
Testing for a Population Mean: Population Standard Deviation Unknown 331
ANOVA Assumptions 385 The ANOVA Test 387
p-Value in Hypothesis Testing
Type II Error
ANOVA: Analysis of Variance
A Two-Tailed Test 324 A One-Tailed Test 327
The F Distribution 380 Testing a Hypothesis of Equal Population Variances 381
Testing for a Population Mean: Known Population Standard Deviation 324
Analysis of Variance Introduction 380
One-Tailed and Two-Tailed Tests of Significance 322
What Is Correlation Analysis? 361
The Correlation Coefficient EXERCISES
Testing the Significance of the Correlation Coefficient 437
Variation in Residuals Same for Large and ˆ Values 496 Small y Distribution of Residuals 496 Multicollinearity 497 Independent Observations 499
Least Squares Principle 441 Drawing the Regression Line 443 EXERCISES
Qualitative Independent Variables
Testing the Significance of the Slope EXERCISES
Regression Models with Interaction Stepwise Regression
Evaluating a Regression Equation’s Ability to Predict 450
Relationships among the Correlation Coefficient, the Coefficient of Determination, and the Standard Error of Estimate 453 EXERCISES
Data Set Exercises
Assumptions Underlying Linear Regression Constructing Confidence and Prediction Intervals 456
A REVIEW OF CHAPTERS 13–14
Interval Estimates of Prediction 455
Review of Multiple Regression 508
The Standard Error of Estimate 450 The Coefficient of Determination 451 EXERCISES
Nonparametric Methods: Nominal Level Hypothesis 533 Tests
Test a Hypothesis of a Population Proportion
Data Set Exercises
The ANOVA Table 483 Multiple Standard Error of Estimate 484 Coefficient of Multiple Determination 484 Adjusted Coefficient of Determination 485 48 6
Inferences in Multiple Linear Regression Global Test: Testing the Multiple Regression Model 487 Evaluating Individual Regression Coefficients 489 EXERCISES
Evaluating the Assumptions of Multiple Regression 494 Linear Relationship
Hypothesis Test of Equal Expected Frequencies 543
Evaluating a Multiple Regression Equation 482
Goodness-of-Fit Tests: Comparing Observed and Expected Frequency Distributions 543
Introduction 477 Multiple Regression Analysis
Two-Sample Tests about Proportions
Multiple Regression Analysis 476
Hypothesis Test of Unequal Expected Frequencies 549 Limitations of Chi-Square EXERCISES
Testing the Hypothesis That a Distribution Is Normal 554 EXERCISES
Contingency Table Analysis EXERCISES
Data Set Exercises
Paasche Price Index 618 Fisher’s Ideal Index 619
Nonparametric Methods: Analysis of Ordinal Data
Introduction 571 The Sign Test EXERCISES
571 57 5
Kruskal-Wallis Test: Analysis of Variance by Ranks 589 EXERCISES
Rank-Order Correlation 595 Testing the Significance of r
Data Set Exercise
Time Series and Forecasting 639 Introduction 640
Components of a Time Series
Data Set Exercises
A Moving Average
A REVIEW OF CHAPTERS 15–16
Introduction 609 609
Determining a Seasonal Index
Laspeyres Price Index
The Durbin-Watson Statistic
Simple Average of the Price Indexes Simple Aggregate Index 616 Weighted Indexes
Using Deseasonalized Data to Forecast
Why Convert Data to Indexes? 612 Construction of Index Numbers 612 EXERCISES
Simple Index Numbers
Nonlinear Trends EXERCISES
Least Squares Method
Secular Trend 640 Cyclical Variation 641 Seasonal Variation 642 Irregular Variation 642 Weighted Moving Average
Special Uses of the Consumer Price Index 628 Shifting the Base 630
Wilcoxon Rank-Sum Test for Independent Populations 585 EXERCISES
Consumer Price Index
Wilcoxon Signed-Rank Test for Dependent Populations 580 EXERCISES
Consumer Price Index 623 Producer Price Index 624 Dow Jones Industrial Average (DJIA)
Testing a Hypothesis about a Median EXERCISES
Using the Normal Approximation to the Binomial 576 EXERCISES
Data Set Exercise
A REVIEW OF CHAPTERS 17–18
PROBLEMS 680 PRACTICE TEST
Expected Opportunity Loss EXERCISES
Statistical Process Control and Quality Management 682
Value of Perfect Information
Maximin, Maximax, and Minimax Regret Strategies
A Brief History of Quality Control 683 Six Sigma
Sources of Variation Diagnostic Charts
Pareto Charts 687 Fishbone Diagrams 689 EXERCISES
Purpose and Types of Quality Control Charts Control Charts for Variables Range Charts 694
Attribute Control Charts
p-Charts 699 c-Bar Charts 702 EXERCISES
Appendix D: Answers to Odd-Numbered Chapter Exercises & Review Exercises & Solutions to Practice Tests 756
An Introduction to Decision Theory Introduction Elements of a Decision Decision Making under Conditions of Uncertainty Payoff Table Expected Payoff
Appendix E: Answers to Self-Review
On the website: www.mhhe.com/lind16e
Appendix C: Software Commands 744
Acceptance Sampling EXERCISES
Appendix A: Data Sets Appendix B: Tables
In-Control and Out-of-Control Situations EXERCISES