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S t a t i s t i c a l T e c h n i q u e s i n

Business & Economics F i f t e e n t h E d i t i o n

Douglas A. Lind Coastal Carolina University and The University of Toledo

William G. Marchal The University of Toledo

Samuel A. Wathen Coastal Carolina University

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STATISTICAL TECHNIQUES IN BUSINESS & ECONOMICS

Published by McGraw-Hill/Irwin, a business unit of The McGraw-Hill Companies, Inc., 1221Avenue of the Americas, New York, NY, 10020. Copyright © 2012, 2010, 2008, 2005, 2002, 1999, 1996, 1993, 1990, 1986, 1982, 1978, 1974, 1970, 1967 by The McGraw-Hill Companies, Inc. All rights reserved. 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 prior written consent of The McGraw-Hill Companies, Inc., 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 printed on acid-free paper.

1 2 3 4 5 6 7 8 9 0 RJE/RJE 1 0 9 8 7 6 5 4 3 2 1

ISBN 978-0-07-340180-5 (student edition) MHID 0-07-340180-3 (student edition) ISBN 978-0-07-732701-9 (instructor’s edition) MHID 0-07-732701-2 (instructor’s edition)

Vice president and editor-in-chief: Brent Gordon Editorial director: Stewart Mattson Publisher: Tim Vertovec Executive editor: Steve Schuetz Executive director of development: Ann Torbert Senior development editor: Wanda J. Zeman Vice president and director of marketing: Robin J. Zwettler Marketing director: Brad Parkins Marketing manager: Katie White Vice president of editing, design, and production: Sesha Bolisetty Senior project manager: Diane L. Nowaczyk Senior buyer: Carol A. Bielski Interior designer: JoAnne Schopler Senior photo research coordinator: Keri Johnson Photo researcher: Teri Stratford Lead media project manager: Brian Nacik Media project manager: Ron Nelms Typeface: 9.5/11 Helvetica Neue 55 Compositor: Aptara®, Inc. Printer: R. R. Donnelley

Library of Congress Cataloging-in-Publication Data Lind, Douglas A.

Statistical techniques in business & economics / Douglas A. Lind, William G. Marchal, Samuel A. Wathen. — 15th ed.

p. cm. — (The McGraw-Hill/Irwin series operations and decision sciences) Includes index. ISBN-13: 978-0-07-340180-5 (student ed. : alk. paper) ISBN-10: 0-07-340180-3 (student ed. : alk. paper) ISBN-13: 978-0-07-732701-9 (instructor’s ed. : alk. paper) ISBN-10: 0-07-732701-2 (instructor’s ed. : alk. paper) 1. Social sciences—Statistical methods. 2. Economics—Statistical methods. 3. Commercial

statistics. I. Marchal, William G. II. Wathen, Samuel Adam. III. Title. IV. Title: Statistical techniques in business and economics. HA29.M268 2012 519.5—dc22

2010045058

www.mhhe.com

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To Jane, my wife and best friend, and our sons, their wives, and our grandchildren: Mike and Sue (Steve and Courtney), Steve and Kathryn (Kennedy and Jake), and Mark and Sarah (Jared, Drew, and Nate).

Douglas A. Lind

To John Eric Mouser, his siblings, parents, and Granny.

William G. Marchal

To my wonderful family: Isaac, Hannah, and Barb.

Samuel A. Wathen

Dedication

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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 high- est 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 infer- ential statistics. We focus on business applications, but we also use many exercises and examples that relate to the current world of the col- lege 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 suc- cessful in a basic statistics course. This step-by-step approach enhances performance, accelerates preparedness, and significantly improves moti- vation. 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, locat- ing relevant business data was difficult. That has changed! Today, locat- ing data is not a problem. The number of items you purchase at the gro- cery store is automatically recorded at the checkout counter. Phone companies track the time of our calls, the length of calls, and the iden- tity 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 tem- perature 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 pre- sented 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 cal- culators 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 a special section at the end of each chapter. 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 Ionger necessary to dwelI on calculations. We have replaced many of the calcu- lation examples with interpretative ones, to assist the student in under- standing 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.

A Note from

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the Authors

What’s New in This Fifteenth Edition? We have made changes to this edition that we think you and your stu- dents will find useful and timely.

• We have revised the learning objectives so they are more specific, added new ones, identified them in the margin, and keyed them directly to sections within the chapter.

• We have replaced the key example in Chapters 1 to 4. The new example includes more variables and more observations. It presents a realistic business situation. It is also used later in the text in Chap- ter 13.

• We have added or revised several new sections in various chapters: � Chapter 7 now includes a discussion of the exponential distribution. � Chapter 9 has been reorganized to make it more teachable and

improve the flow of the topics. � Chapter 13 has been reorganized and includes a test of hypothe-

sis for the slope of the regression coefficient. � Chapter 17 now includes a graphic test for normality and the chi-

square test for normality. • New exercises and examples use Excel 2007 screenshots and the lat-

est version of Minitab. We have also increased the size and clarity of these screenshots.

• There are new Excel 2007 software commands and updated Minitab commands at the ends of chapters.

• We have carefully reviewed the exercises within the chapters, those at the ends of chapters, and in the Review Section. We have added many new or revised exercises throughout. You can still find and assign your favorites that have worked well, or you can introduce fresh examples.

• Section numbers have been added to more clearly identify topics and more easily reference them.

• The exercises that contain data files are identified by an icon for easy identification.

• The Data Exercises at the end of each chapter have been revised. The baseball data has been updated to the most current completed season, 2009. A new business application has been added that refers to the use and maintenance of the school bus fleet of the Buena School District.

• There are many new photos throughout, with updated exercises in the chapter openers.

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How Are Chapters Organized to

3 Learning Objectives When you have completed this chapter, you will be able to:

LO1 Explain the concept of central tendency.

LO2 Identify and compute the arithmetic mean.

LO3 Compute and interpret the weighted mean.

LO4 Determine the median.

LO5 Identify the mode.

LO6 Calculate the geometric mean.

LO7 Explain and apply mea- sures of dispersion.

LO8 Compute and explain the variance and the standard deviation.

LO9 Explain Chebyshev’s Theorem and the Empirical Rule.

LO10 Compute the mean and standard deviation of grouped data.

Describing Data: Numerical Measures

The Kentucky Derby is held the first Saturday in May at Churchill

Downs in Louisville, Kentucky. The race track is one and one-quarter

miles. The table in Exercise 82 shows the winners since 1990, their

margin of victory, the winning time, and the payoff on a $2 bet.

Determine the mean and median for the variables winning time and

payoff on a $2 bet. (See Exercise 82 and LO2 and LO4.)

Introduction to the Topic Each chapter starts with a review of the impor- tant concepts of the previous chapter and pro- vides a link to the material in the current chapter. This step-by-step approach increases com- prehension by providing continuity across the concepts.

2.1 Introduction The highly competitive automobile retailing industry in the United States has changed dramatically in recent years. These changes spurred events such as the:

• bankruptcies of General Motors and Chrysler in 2009. • elimination of well-known brands such as Pontiac and

Saturn. • closing of over 1,500 local dealerships. • collapse of consumer credit availability. • consolidation dealership groups.

Traditionally, a local family owned and operated the com- munity dealership, which might have included one or two man- ufacturers or brands, like Pontiac and GMC Trucks or Chrysler and the popular Jeep line. Recently, however, skillfully managed and well-financed companies have been acquiring local dealer-

Example

Solution

Layton Tire and Rubber Company wishes to set a minimum mileage guarantee on its new MX100 tire. Tests reveal the mean mileage is 67,900 with a stan- dard deviation of 2,050 miles and that the distribu- tion of miles follows the normal probability distrib- ution. Layton wants to set the minimum guaranteed mileage so that no more than 4 percent of the tires will have to be replaced. What minimum guaranteed mileage should Layton announce?

The facets of this case are shown in the following diagram, where X represents the minimum guaran- teed mileage.

Self-Review 3–6 The weights of containers being shipped to Ireland are (in thousands of pounds):

95 103 105 110 104 105 112 90

(a) What is the range of the weights? (b) Compute the arithmetic mean weight. (c) Compute the mean deviation of the weights.

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 the chapter.

Chapter Opening Exercise A representative exercise opens the chapter and shows how the chapter content can be applied to a real-world situation.

Example/Solution After important concepts are introduced, a solved example is given to provide a how-to illustration for students and to show a relevant business or economics-based application that helps answer the question, “What will I use this for?” All examples provide a realistic scenario or application and make the math size and scale reasonable for introductory students.

Self-Reviews Self-Reviews are interspersed through- out each chapter and closely patterned after the preceding Examples. They help students monitor their progress and provide immediate reinforcement for that particular technique.

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Engage Students and Promote Learning?

Statistics in Action Statistics in Action articles are scattered through- out the text, usually about two per chapter. They provide unique and interesting applications and historical insights in the field of statistics.

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.

The equation for the trend line is:

The slope of the trend line is .08991. This shows that over the 24 quarters the deseasonalized sales increased at a rate of 0.08991 ($ million) per quarter, or $89,910 per quarter. The value of 8.109 is the intercept of the trend line on the Y-axis (i.e., for t � 0).

Ŷ � 8.109 � .08991t

Statistics in Action

Forecasts are not al- ways correct. The re- ality is that a forecast may just be a best guess as to what will happen. What are the reasons forecasts are not correct? One expert lists eight common errors:

Margin Notes There are more than 300 concise notes in the margin. Each is aimed at reemphasizing the key concepts presented immediately adja- cent to it.

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.

Population Variance The formulas for the population variance and the sample variance are slightly different. The population variance is considered first. (Recall that a population is the totality of all observations being studied.) The population variance is found by:

Variance and standard deviation are based on squared deviations from the mean.

STANDARD DEVIATION The square root of the variance.

The variance is non-negative and is zero only if all observations are the same.

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, which lists all the key formulas.

POPULATION VARIANCE [3–8]�2 � �(X � �)2

N

Exercises For Exercises 35–38, calculate the (a) range, (b) arithmetic mean, (c) mean deviation, and (d) interpret the values.

35. There were five customer service representatives on duty at the Electronic Super Store during last weekend’s sale. The numbers of HDTVs these representatives sold are: 5, 8, 4, 10, and 3.

36. The Department of Statistics at Western State University offers eight sections of basic statistics. Following are the numbers of students enrolled in these sections: 34, 46, 52, 29, 41, 38, 36, and 28.

Computer Output The text includes many software examples, using Excel, MegaStat®, and Minitab.

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BY CHAPTER Chapter Summary Each chapter contains a brief summary of the chapter material, including the vocabulary and the critical formulas.

How Does This Text

Chapter Summary I. A dot plot shows the range of values on the horizontal axis and the number of observa-

tions for each value on the vertical axis. A. Dot plots report the details of each observation. B. They are useful for comparing two or more data sets.

II. A stem-and-leaf display is an alternative to a histogram. A. The leading digit is the stem and the trailing digit the leaf. B. The advantages of a stem-and-leaf display over a histogram include:

Pronunciation Key This tool lists the mathematical symbol, its mean- ing, and how to pronounce it. We believe this will help the student retain the meaning of the symbol and generally enhance course communications.

Pronunciation Key SYMBOL MEANING PRONUNCIATION

Location of percentile L sub p

First quartile Q sub 1

Third quartile Q sub 3Q3

Q1

Lp

Chapter Exercises Generally, the end-of-chapter exercises are the most challenging and integrate the chapter con- cepts. The answers and worked-out solutions for all odd-numbered exercises appear at the end of the text. For exercises with more than 20 observations, the data can be found on the text’s website. These files are in Excel and Minitab formats.

Chapter Exercises 27. A sample of students attending Southeast Florida University is asked the number of social

activities in which they participated last week. The chart below was prepared from the sample data.

41 2 Activities

30

Data Set Exercises 44. Refer to the Real Estate data, which reports information on homes sold in the Goodyear,

Arizona, area during the last year. Prepare a report on the selling prices of the homes. Be sure to answer the following questions in your report. a. Develop a box plot. Estimate the first and the third quartiles. Are there any outliers? b. Develop a scatter diagram with price on the vertical axis and the size of the home on

the horizontal. Does there seem to be a relationship between these variables? Is the relationship direct or inverse?

c. Develop a scatter diagram with price on the vertical axis and distance from the center of the city on the horizontal axis. Does there seem to be a relationship between these variables? Is the relationship direct or inverse?

45. Refer to the Baseball 2009 data, which reports information on the 30 Major League Base- ball teams for the 2009 season. Refer to the variable team salary. a. Select the variable that refers to the year in which the stadium was built. (Hint: Subtract

the year in which the stadium was built from the current year to find the age of the stadium and work this variable.) Develop a box plot. Are there any outliers? Which sta- diums are outliers?

b. Select the variable team salary and draw a box plot. Are there any outliers? What are the quartiles? Write a brief summary of your analysis. How do the salaries of the New York Yankees compare with the other teams?

1. The Excel Commands for the descriptive statistics on page 69 are:

a. From the CD, retrieve the Applewood data. b. From the menu bar, select Data and then Data

Analysis. Select Descriptive Statistics and then click OK.

2. The Minitab commands for the descriptive summary on page 84 are:

Software Commands

Data Set Exercises 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 web- site. 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, but the explanations of the computer input commands for each program are placed at the end of the chapter. This allows students to focus on the sta- tistical techniques rather than on how to input data.

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Reinforce Student Learning? Answers to Self-Review The worked-out solutions to the Self-Reviews are provided at the end of each chapter.

Cases The review also includes continuing cases and several small cases that let students make decisions using tools and techniques from a variety of chapters.

Fr eq

ue nc

y

40

30

20

10

0 Cola-Plus Coca-Cola Pepsi

Beverage

Lemon-Lime

Chapter 2 Answers to Self-Review

2–1 a. Qualitative data, because the customers’ response to the taste test is the name of a beverage.

b. Frequency table. It shows the number of people who prefer each beverage.

c.

c. Class frequencies. d. The largest concentration of commissions

is $1,500 up to $1,600. The smallest commission is about $1,400 and the largest is about $1,800. The typical amount earned is $15,500.

2–3 a. 26 � 64 � 73 � 128 � 27. So seven classes are recommended.

b. The interval width should be at least (488 � 320)�7 � 24. Class intervals of 25 or 30 feet are both reasonable.

c. If we use a class interval of 25 feet and begin with a lower limit of 300 feet, eight classes would be necessary. A class interval of 30 feet beginning with 300 feet is also reasonable. This alternative requires only seven classes.

2–4 a. 45 b. .250 c. .306, found by .178 � .106 � .022

2–5 a. 20

20

BY SECTION 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 Sec- tion Review is included. Much like a review before an exam, these include a brief overview of the chapters, a glossary of key terms, 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 distri- bution as a histogram or a frequency polygon. Chapter 3 began by describing measures of loca- tion, 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, mean devi- ation, 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.

Throughout this section we stressed the importance of statistical software, such as Excel and Minitab. Many computer outputs in these chapters demonstrated how quickly and effectively a large data set can be organized into a frequency distribution, several of the measures of location or measures or variation calculated, and the information presented in graphical form.

Glossary

Chapter 1 Descriptive statistics The techniques used to describe the important characteristics of a set of data. This includes organizing the data values into a frequency distribution, computing measures of location, and computing mea-

90 degrees is 10 degrees more than a temperature of 80 degrees, and so on. Nominal measurement The “lowest” level of measure- ment. If data are classified into categories and the order of those categories is not important, it is the nominal level of

E l d ( l f l ) d

A. Century National Bank The following case will appear in subsequent review sec- tions. 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 cus- tomers. What is the balance of a typical customer?

How many other bank services do the checking ac- count customers use? Do the customers use the ATM ser- vice and, if so, how often? What about debit cards? Who uses them, and how often are they used?

To better understand the customers, Mr. Selig asked Ms. Wendy Lamberg, director of planning, to se- lect a sample of customers and prepare a report. To be- gin, she has appointed a team from her staff. You are the head of the team and responsible for preparing the report. You select a random sample of 60 customers. In addition to the balance in each account at the end of last month, you determine: (1) the number of ATM (auto-

median 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 devia- tion 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 his son Cory. The company has grown from a handful of employees to more than 500 today. Cory is concerned about several positions within the company where he has men and women doing essentially the same job but at dif- ferent pay. To investigate, he collected the information be- low. Suppose you are a student intern in the Accounting Department and have been given the task to write a report

Cases

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.

Part 2—Problems 1. The Russell 2000 index of stock prices increased by the following amounts over the last three years.

18% 4% 2%

What is the geometric mean increase for the three years?

Practice Test

There is a practice test at the end of each review section. The tests are in two parts. The first part contains several ob- jective 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 deci-

sions is called . 1. 2. Methods of organizing, summarizing, and presenting data in an informative way is called .

2. 3. The entire set of individuals or objects of interest or the measurements obtained from all individuals or objects of in-

terest is called the . 3. 4. List the two types of variables. 4.

5. The number of bedrooms in a house is an example of a . (discrete variable, continuous variable, qualitative variable—pick one) 5.

6. The jersey numbers of Major League Baseball players is an example of what level of measurement? 6.

7. The classification of students by eye color is an example of what level of measurement? 7. 8. The sum of the differences between each value and the mean is always equal to what value? 8. 9. A set of data contained 70 observations. How many classes would you suggest in order to construct a frequency

distribution? 9. 10. What percent of the values in a data set are always larger than the median? 10. 11. The square of the standard deviation is the . 11. 12. The standard deviation assumes a negative value when . (All the values are negative, when at least half the

values are negative, or never—pick one.) 12. 13. Which of the following is least affected by an outlier? (mean, median, or range—pick one) 13.

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What Technology Connects McGraw-Hill Connect™ Business Statistics Less Managing. More Teaching. Greater Learning. McGraw-Hill Connect Business Statistics is an online assignment and assessment solution that connects students with the tools and resources they’ll need to achieve success.

McGraw-Hill Connect Business Statistics helps prepare students for their future by enabling faster learning, more efficient studying, and higher retention of knowledge.

Features. Connect Business Statistics offers a number of powerful tools and features to make manag- ing assignments easier, so faculty can spend more time teaching. With Connect Business Statistics, students can engage with their coursework anytime and anywhere, making the learning process more accessible and efficient. Connect Business Statistics offers you the features described below.

Simple Assignment Management. With Con- nect Business Statistics, creating assignments is easier than ever, so you can spend more time teaching and less time managing. The assignment management function enables you to:

• Create and deliver assignments easily with selectable end-of-chapter questions and test bank items.

• Streamline lesson planning, student pro- gress reporting, and assignment grading to make classroom management more effi- cient than ever.

• Go paperless with the eBook and on- line submission and grading of student assignments.

Integration of Excel Data Sets. A convenient feature is the inclusion of an Excel data file link in many problems using data files in their cal- culation. This allows students to easily launch into Excel, work the problem, and return to Connect to key in the answer.

Excel Integrated Data File

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Students to Business Statistics? Smart Grading. When it comes to studying, time is precious. Connect Business Statistics helps students learn more efficiently by providing feedback and practice material when they need it, where they need it. When it comes to teaching, your time also is precious. The grading function enables you to:

• Have assignments scored automatically, giving students immediate feedback on their work and side- by-side comparisons with correct answers.

• Access and review each response; manually change grades or leave comments for students to review.

• Reinforce classroom concepts with practice tests and instant quizzes.

Instructor Library. The Connect Business Statistics Instructor Library is your repository for additional resources to improve student engagement in and out of class. You can select and use any asset that enhances your lecture. The Connect Business Statistics Instructor Library includes:

• eBook

• PowerPoint presentations

• Test Bank

• Solutions Manual

• Digital Image Library

Student Study Center. The Connect Business Statistics Student Study Center is the place for students to access additional resources. The Student Study Center:

• Offers students quick access to lectures, practice materials, eBooks, and more.

• Provides instant practice material and study questions and is easily accessible on-the-go.

Guided Examples. These narrated video walkthroughs provide students with step-by-step guidelines for solving problems similar to those contained in the text. The student is given personalized instruction on how to solve a problem by applying the concepts presented in the chapter.

Student Progress Tracking. Connect Business Statistics keeps instructors informed about how each student, section, and class is performing, 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.

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What Technology Connects McGraw-Hill CONNECT™ PLUS BUSINESS STATISTICS McGraw-Hill Connect Plus Business Statistics. McGraw-Hill reinvents the textbook learning experience for the modern student with Connect Plus Business Statistics. A seamless integration of an eBook and Connect Business Statistics, Connect Plus Business Statistics provides all of the Connect Business Sta- tistics features plus the following:

• An integrated eBook, allowing for anytime, anywhere access to the textbook.

• Dynamic links between the problems or questions you assign to your students and the location in the eBook where that problem or question is covered.

• A powerful search function to pinpoint and connect key con- cepts in a snap.

In short, Connect Business Statis- tics offers you and your students powerful tools and features that optimize your time and energies, enabling you to focus on course content, teaching, and student learning. Connect Business Statis- tics also offers a wealth of content resources for both instructors and students. This state-of-the-art, thoroughly tested system supports you in preparing students for the world that awaits. For more information about Connect, go to www.mcgrawhillconnect.com or contact your local McGraw-Hill sales representative.

Tegrity Campus: Lectures 24/7 Tegrity Campus is a service that makes class time available 24/7 by automatically capturing every lec- ture 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.

McGraw-Hill Tegrity Campus 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 learn- ing moments immediately supported by your lecture.

To learn more about Tegrity, watch a two-minute Flash demo at http://tegritycampus.mhhe.com.

business statistics

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Students to Business Statistics? Assurance-of-Learning Ready Many educational institutions today are focused on the notion of assurance of learn- ing 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 outcome/objective listed in the text. You can use our test bank software, EZ Test and EZ Test Online, or Connect Business Sta- tistics to easily query for learning outcomes/objectives that directly relate to the learning 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 pre- sentation of assurance of learning data simple and easy.

AACSB Statement The McGraw-Hill Companies is a proud corporate member of AACSB International. Understand- ing the importance and value of AACSB accreditation, Statistical Techniques in Business & Eco- nomics recognizes the curricula guidelines detailed in the AACSB standards for business accredita- tion by connecting selected ques- tions in the text and the test bank to the six general knowledge and skill guidelines in the AACSB standards.

The statements contained in Statistical Techniques in Business & Economics are provided only as a guide for the users of this textbook. The AACSB leaves content coverage and assessment within the purview of individual schools, the mission of the school, and the faculty. While Statistical Techniques in Business & Economics and the teaching package make no claim of any specific AACSB qualification or eval- uation, we have labeled selected questions within Statistical Techniques in Business & Economics according to the six general knowledge and skills areas.

McGraw-Hill Customer Care Information At McGraw-Hill, we understand that getting the most from new technology can be challenging. That’s why our services don’t stop after you purchase our products. You can e-mail our Product Specialists 24 hours a day to get product-training online. Or you can search our knowledge bank of Frequently Asked Questions on our support website. For Customer Support, call 800-331-5094 or visit www.mhhe.com/support. One of our Technical Support Analysts will be able to assist you in a timely fashion.

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What Software Is Available with This Text? MegaStat® for Microsoft Excel®

MegaStat® by J. B. Orris of Butler University is a full-featured Excel add-in that is available on CD and on the MegaStat website at www.mhhe.com/megastat. It works with Excel 2003, 2007, and 2010. On the web- site, students have 10 days to successfully download and install MegaStat on their local computer. Once installed, MegaStat will remain active in Excel with no expiration date or time limitations. The software per- forms statistical analyses within an Excel workbook. It does basic functions, such as descriptive statistics, frequency distributions, and probability calculations as well as hypothesis testing, ANOVA, and regression.

MegaStat output is carefully formatted and ease-of-use features include Auto Expand for quick data selec- tion and Auto Label detect. Since MegaStat is easy to use, students can focus on learning statistics with- out being distracted by the software. MegaStat is always available from Excel’s main menu. Selecting a menu item pops up a dialog box. MegaStat works with all recent versions of Excel, including Excel 2007 and Excel 2010. Screencam tutorials are included that provide a walkthrough of major business statistics topics. Help files are built in, and an introductory user’s manual is also included.

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.

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What Resources Are Available for Instructors? Instructor’s Resources CD-ROM (ISBN: 0077327055) This resource allows instructors to conveniently access the Instruc- tor’s Solutions Manual, Test Bank in Word and EZ Test formats, Instructor PowerPoint slides, data files, and data sets.

Online Learning Center: www.mhhe.com/lind15e The Online Learning Center (OLC) provides the instructor with a com- plete Instructor’s Manual in Word format, the complete Test Bank in both Word files and computerized EZ Test format, Instructor Power- Point slides, text art files, an introduction to ALEKS®, an introduction to McGraw-Hill Connect Business StatisticsTM, access to Visual Statistics, 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.

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ALEKS is an assessment and learning program that provides individualized instruction in Business Statistics, Business Math, and Accounting. Available online in partnership with McGraw- Hill/lrwin, 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 stu- dent is most ready to learn. By providing topics to meet indi- vidual students’ needs, allowing students to move between explanation and practice, correcting and analyzing errors, and defining terms, ALEKS helps students to master course con- tent quickly and easily.

ALEKS also includes a new instructor module with powerful, assignment-driven features and extensive con- tent flexibility. ALEKS simplifies course management and allows instructors to spend less time with admin- istrative tasks and more time directing student learning. To learn more about ALEKS, visit www.aleks.com.

Online Learning Center: www.mhhe.com/lind15e The Online Learning Center (OLC) provides students with the following content:

• Quizzes • *Visual Statistics

• PowerPoint • Data sets/files

• *Narrated PowerPoint • Appendixes

• *Screencam tutorials • Chapter 20

• *Guided Examples

*Premium Content

Student Study Guide (ISBN: 007732711X) This supplement helps students master the course content. It highlights the important ideas in the text and pro- vides opportunities for students to review the worked-out solutions, review terms and concepts, and practice.

Basic Statistics Using Excel 2007 (ISBN: 0077327020) This workbook introduces students to Excel and shows how to apply it to introductory statistics. It presumes no prior familiarity with Excel or statistics and provides step-by-step directions in a how-to style using Excel 2007 with text examples and problems.

Business Statistics Center (BSC): www.mhhe.com/bstat/ The BSC contains links to statistical publications and resources, software downloads, learning aids, sta- tistical websites and databases, and McGraw-Hill/Irwin product websites and online courses.

What Resources Are Available for Students? CourseSmart CourseSmart is a convenient way to find and buy eTextbooks. CourseSmart has the largest selection of eTextbooks available anywhere, offering thousands of the most commonly adopted textbooks from a wide variety of higher-education publishers. Course Smart eTextbooks are available in one standard online reader with full text search, notes and highlighting, and e-mail tools for sharing notes between classmates. Visit www.CourseSmart.com for more information on ordering.

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Acknowledgments

Reviewers

Sung K. Ahn Washington State University–Pullman

Scott Bailey Troy University

Douglas Barrett University of North Alabama

Arnab Bisi Purdue University

Pamela A. Boger Ohio University–Athens

Emma Bojinova Canisius 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

Clifford B. Hawley West Virginia University

Lloyd R. Jaisingh Morehead State University

Mark Kesh University of Texas

Ken Kelley University of Notre Dame

Melody Kiang California State University–Long Beach

Morris Knapp Miami Dade College

Teresa Ling Seattle University

John D. McGinnis Pennsylvania State–Altoona

Mary Ruth J. McRae Appalachian State University

Jackie Miller 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

Robert Patterson Penn State University

Joseph Petry University of Illinois at Urbana-Champaign

Tammy Prater Alabama State University

Michael Racer University of Memphis

Darrell Radson Drexel University

Steven Ramsier Florida State University

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

Stanley D. Stephenson Texas State University–San Marcos

Debra Stiver University of Nevada

Bedassa Tadesse University of Minnesota–Duluth

Stephen Trouard Mississippi College

Elzbieta Trybus California State University–Northridge

Daniel Tschopp Daemen College

Sue Umashankar University of Arizona

Jesus M. Valencia Slippery Rock University

Joseph Van Matre University of Alabama at Birmingham

Angie Waits Gadsden State Community College

Bin Wang St. Edwards University

Kathleen Whitcomb University of South Carolina

Blake Whitten University of Iowa

Oliver Yu San Jose State University

Zhiwei Zhu University of Louisiana

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

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:

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Their suggestions and thorough reviews of the previous edition and the manuscript of this edi- tion make this a better text.

Special thanks go to a number of people. Debra K. Stiver, University of Nevada–Reno, reviewed the manuscript and page proofs, checking text and exercises for accuracy. Joan McGrory, South- west Tennessee Community College, checked the Test Bank for accuracy. Professor Kathleen Whit- comb of the University of South Carolina prepared the study guide. Dr. Samuel Wathen of Coastal Carolina University prepared the quizzes and the Test Bank. Professor René Ordonez of Southern- Oregon University prepared the PowerPoint presentation, many of the screencam tutorials, and the guided examples in Connect. Ms. Denise Heban and the authors prepared the Instructor’s Manual.

We also wish to thank the staff at McGraw-Hill. This includes Steve Schuetz, Executive Edi- tor; Wanda Zeman, Senior Development Editor; Diane Nowaczyk, Senior Project Manager; and oth- ers we do not know personally, but who have made valuable contributions.

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

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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

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Daniel Tschopp Daemen College

Bulent Uyar University of Northern Iowa

Lee J. Van Scyoc University of Wisconsin–Oshkosh

Stuart H. Warnock Tarleton State University

Mark H. Witkowski University of Texas at San Antonio

William F. Younkin University of Miami

Shuo Zhang State University of New York, Fredonia

Zhiwei Zhu University of Louisiana at Lafayette

Acknowledgments

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Changes Made in All Chapters and Major Changes to Individual Chapters:

• Changed Goals to Learning Objectives and identified the location in the chapter where the learning objective is discussed.

• Added section numbering to each main heading.

• Identified exercises where the data file is included on the text website.

• Revised the Major League Baseball data set to reflect the latest complete season, 2009.

• Revised the Real Estate data to ensure the outcomes are more realistic to the current economy.

• Added a new data set regarding school buses in a pub- lic school system.

• Updated screens for Excel 2007, Minitab, and MegaStat.

• Revised the core example in Chapters 1–4 to reflect the current economic conditions as it relates to automobile dealers. This example is also discussed in Chapter 13 and 17.

• Added a new section in Chapter 7 describing the expo- nential distribution.

• Added a new section in Chapter 13 describing a test to determine whether the slope of the regression line dif- fers from zero.

• Added updates and clarifications throughout.

Chapter 1 What Is Statistics? • New photo and chapter opening exercise on the “Nook”

sold by Barnes and Nobel.

• Census updates on U.S. population, sales of Boeing air- craft, and Forbes data in “Statistics in Action” feature.

• New chapter exercises 17 (data on 2010 vehicle sales) and 19 (ExxonMobil sales prior to Gulf oil spill).

Chapter 2 Describing Data: Frequency Tables, Frequency Distributions, and Graphic Presentation

• New data on Ohio State Lottery expenses for 2009 with new Excel 2007 screenshot.

• New exercises 45 (brides picking their wedding site) and 46 (revenue in the state of Georgia).

Chapter 3 Describing Data: Numerical Measures

• New data on averages in the introduction: average num- ber of TV sets per home, average spending on a wed- ding, and the average price of a theater ticket.

• A new description of the calculation and interpretation of the population mean using the distance between exits on I-75 through Kentucky.

• A new description of the median using the time manag- ing Facebook accounts.

• Updated example/solution on the population in Las Vegas.

• Update “Statistics in Action” on the highest batting aver- age in Major League Baseball for 2009. It was Joe Mauer of the Minnesota Twins, with an average of .365.

• New chapter exercises 22 (real estate commissions), 67 (laundry habits), 77 (public universities in Ohio), 72 (blood sugar numbers), and 82 (Kentucky Derby payoffs). Exer- cises 30 to 34 were revised to include the most recent data.

Chapter 4 Describing Data: Displaying and Exploring Data

• New exercise 22 with 2010 salary data for the New York Yankees.

• New chapter exercise 36 (American Society of Peri- Anesthesia nurses component membership).

Chapter 5 A Survey of Probability Concepts • New exercise 58 (number of hits in a Major League

Baseball game), 59 (winning a tournament), and 60 (win- ning Jeopardy).

Chapter 6 Discrete Probability Distributions • No changes.

Chapter 7 Continuous Probability Distributions • New Self-Review 7–4 and 7–5 involving coffee

temperature.

• New exercise 26 (SAT Reasoning Test).

• New exercise 29 (Hurdle Rate for economic investment).

• New section and corresponding problems on the expo- nential probability distribution.

• Several glossary updates and clarifications.

Chapter 8 Sampling Methods and the Central Limit Theorem

• No changes.

Chapter 9 Estimation and Confidence Intervals • A new Statistics in Action describing EPA fuel economy.

• New separate section on point estimates.

• Integration and application of the central limit theorem.

Enhancements to Statistical Techniques in Business & Economics, 15e

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xx

• A revised discussion of determining the confidence interval for the population mean.

• Expanded section on calculating sample size.

• New exercise 12 (milk consumption), 33 (cost of apart- ments in Milwaukee), 47 (drug testing in the fashion industry), and 48 (survey of small-business owners regarding healthcare).

• The discussion of the finite correction factor has been relocated in the chapter.

Chapter 10 One-Sample Tests of Hypothesis • New exercises 17 (daily water consumption), 19 (number

of text messages by teenagers), 35 (household size in the United States), 49 (Super Bowl coin flip results), 54 (failure of gaming industry slot machines), 57 (study of the percentage of Americans that do not eat breakfast), and 60 (daily water usage).

Chapter 11 Two-Sample Tests of Hypothesis • New exercises 15 (2010 New York Yankee salaries), 37

(Consumer Confidence Survey), and 39 (pets as listeners).

Chapter 12 Analysis of Variance • Revised the names of airlines in the one-way ANOVA

example.

• New exercise 30 (flight times between Los Angeles and San Francisco).

Chapter 13 Correlation and Linear Regression • Rewrote the introduction section to the chapter.

• Added a new section using the Applewood Auto Group data from chapters 1 to 4.

• Added a section on testing the slope of a regression line.

• Added discussion of the regression ANOVA table with Excel examples.

• Rewrote and relocated the section on the coefficient of determination.

• Updated exercise 60 (movie box office amounts).

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.

• Added a separate section on qualitative variables in regression analysis.

• Moved the “Stepwise Regression” section to improve the sequence of topics.

• Added a summary problem at the end of the chapter to review the major concepts.

Chapter 15 Index Numbers • Updated census and economic data.

Chapter 16 Time Series and Forecasting • Updated economic data.

Chapter 17 Nonparametric Methods: Goodness-of-Fit Tests

• Reworked the Example/Solution on the chi-square goodness-of-fit test with equal cell frequencies (favorite meals of adults).

• Added a section and corresponding examples describing the goodness-of-fit test for testing whether sample data are from a normal population.

• Added a section and corresponding examples using graphical methods for testing whether sample data are from a normal population.

Chapter 18 Nonparametric Methods: Analysis of Ranked Data

• Revised the Example/Solution for the Kruskal-Wallis test (waiting times in the emergency room).

• Revised the Example/Solution for the Spearman coeffi- cient of rank correlation (comparison of recruiter and plant scores for trainees).

Chapter 19 Statistical Process Control and Quality Management

• Updated the section on the Malcolm Baldrige National Quality Award.

• Reworked and updated the section on Six Sigma.

Enhancements to Statistical Techniques in Business & Economics, 15e

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Brief Contents

1 What Is Statistics? 1 2 Describing Data: Frequency Tables, Frequency Distributions, and Graphic

Presentation 21

3 Describing Data: Numerical Measures 57 4 Describing Data: Displaying and Exploring Data 102 5 A Survey of Probability Concepts 144 6 Discrete Probability Distributions 186 7 Continuous Probability Distributions 222 8 Sampling Methods and the Central Limit Theorem 265 9 Estimation and Confidence Intervals 297

10 One-Sample Tests of Hypothesis 333 11 Two-Sample Tests of Hypothesis 371 12 Analysis of Variance 410 13 Correlation and Linear Regression 461 14 Multiple Regression Analysis 512 15 Index Numbers 573 16 Time Series and Forecasting 604 17 Nonparametric Methods: Goodness-of-Fit Tests 648 18 Nonparametric Methods: Analysis of Ranked Data 680 19 Statistical Process Control and Quality Management 720 20 An Introduction to Decision Theory On the website:

www.mhhe.com/lind15e

Appendixes: Data Sets, Tables, Answers 753

Photo Credits 829

Index 831

Review Section

Review Section

Review Section

Review Section

Review Section

Review Section

Review Section

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xxii

Contents

A Note from the Authors iv

Chapter

1 What Is Statistics? 1 1.1 Introduction 2

1.2 Why Study Statistics? 2

1.3 What Is Meant by Statistics? 4

1.4 Types of Statistics 6

Descriptive Statistics 6 Inferential Statistics 6

1.5 Types of Variables 8

1.6 Levels of Measurement 9

Nominal-Level Data 10 Ordinal-Level Data 11 Interval-Level Data 11 Ratio-Level Data 12

Exercises 14

1.7 Ethics and Statistics 14

1.8 Computer Applications 14

Chapter Summary 16

Chapter Exercises 16

Data Set Exercises 19

Answers to Self-Review 20

Chapter

2 Describing Data: Frequency Tables, Frequency Distributions, and Graphic Presentation 21 2.1 Introduction 22

2.2 Constructing a Frequency Table 23

Relative Class Frequencies 23 Graphic Presentation of Qualitative Data 24

Exercises 28

2.3 Constructing Frequency Distributions: Quantitative Data 29

2.4 A Software Example 34

2.5 Relative Frequency Distribution 34

Exercises 35

2.6 Graphic Presentation of a Frequency Distribution 36

Histogram 36 Frequency Polygon 38

Exercises 41

Cumulative Frequency Distributions 42

Exercises 44

Chapter Summary 46

Chapter Exercises 46

Data Set Exercises 53

Software Commands 54

Answers to Self-Review 55

Chapter

3 Describing Data: Numerical Measures 57 3.1 Introduction 58

3.2 The Population Mean 58

3.3 The Sample Mean 60

3.4 Properties of the Arithmetic Mean 61

Exercises 62

3.5 The Weighted Mean 63

Exercises 64

3.6 The Median 64

3.7 The Mode 65

Exercises 67

3.8 Software Solution 69

3.9 The Relative Positions of the Mean, Median, and Mode 69

Exercises 71

3.10 The Geometric Mean 72

Exercises 73

3.11 Why Study Dispersion? 74

3.12 Measures of Dispersion 75

Range 75 Mean Deviation 76

Exercises 79

Variance and Standard Deviation 79

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Contents xxiii

Exercises 82

3.13 Software Solution 84

Exercises 84

3.14 Interpretation and Uses of the Standard Deviation 85

Chebyshev’s Theorem 85 The Empirical Rule 86

Exercises 87

3.15 The Mean and Standard Deviation of Grouped Data 88

The Arithmetic Mean 88 Standard Deviation 89

Exercises 91

3.16 Ethics and Reporting Results 92

Chapter Summary 92

Pronunciation Key 94

Chapter Exercises 94

Data Set Exercises 99

Software Commands 100

Answers to Self-Review 100

Chapter

4 Describing Data: Displaying and Exploring Data 102 4.1 Introduction 103

4.2 Dot Plots 103

4.3 Stem-and-Leaf Displays 105

Exercises 109

4.4 Measures of Position 111

Quartiles, Deciles, and Percentiles 111

Exercises 115

Box Plots 116

Exercises 118

4.5 Skewness 119

Exercises 123

4.6 Describing the Relationship between Two Variables 124

Exercises 127

Chapter Summary 129

Pronunciation Key 129

Chapter Exercises 130

Data Set Exercises 135

Software Commands 135

Answers to Self-Review 136

A Review of Chapters 1–4 137

Glossary 137

Problems 139

Cases 141

Practice Test 142

Chapter

5 A Survey of Probability Concepts 144 5.1 Introduction 145

5.2 What Is a Probability? 146

5.3 Approaches to Assigning Probabilities 148

Classical Probability 148 Empirical Probability 149 Subjective Probability 150

Exercises 152

5.4 Some Rules for Computing Probabilities 153

Rules of Addition 153

Exercises 158

Rules of Multiplication 159

5.5 Contingency Tables 162

5.6 Tree Diagrams 164

Exercises 166

5.7 Bayes’ Theorem 167

Exercises 170

5.8 Principles of Counting 171

The Multiplication Formula 171 The Permutation Formula 172 The Combination Formula 174

Exercises 176

Chapter Summary 176

Pronunciation Key 177

Chapter Exercises 178

Data Set Exercises 182

Software Commands 183

Answers to Self-Review 184

Chapter

6 Discrete Probability Distributions 186 6.1 Introduction 187

6.2 What Is a Probability Distribution? 187

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xxiv Contents

6.3 Random Variables 189

Discrete Random Variable 190 Continuous Random Variable 190

6.4 The Mean, Variance, and Standard Deviation of a Discrete Probability Distribution 191

Mean 191 Variance and Standard Deviation 191

Exercises 193

6.5 Binomial Probability Distribution 195

How Is a Binomial Probability Computed? 196 Binomial Probability Tables 198

Exercises 201

Cumulative Binomial Probability Distributions 202

Exercises 203

6.6 Hypergeometric Probability Distribution 204

Exercises 207

6.7 Poisson Probability Distribution 207

Exercises 212

Chapter Summary 212

Chapter Exercises 213

Data Set Exercises 218

Software Commands 219

Answers to Self-Review 221

Chapter

7 Continuous Probability Distributions 222 7.1 Introduction 223

7.2 The Family of Uniform Probability Distributions 223

Exercises 226

7.3 The Family of Normal Probability Distributions 227

7.4 The Standard Normal Probability Distribution 229

Applications of the Standard Normal Distribution 231 The Empirical Rule 231

Exercises 233

Finding Areas under the Normal Curve 233

Exercises 236

Exercises 239

Exercises 241

7.5 The Normal Approximation to the Binomial 242

Continuity Correction Factor 242 How to Apply the Correction Factor 244

Exercises 245

7.6 The Family of Exponential Distributions 246

Exercises 250

Chapter Summary 251

Chapter Exercises 252

Data Set Exercises 256

Software Commands 256

Answers to Self-Review 257

A Review of Chapters 5–7 258

Glossary 259

Problems 260

Cases 261

Practice Test 263

Chapter

8 Sampling Methods and the Central Limit Theorem 265 8.1 Introduction 266

8.2 Sampling Methods 266

Reasons to Sample 266 Simple Random Sampling 267 Systematic Random Sampling 270 Stratified Random Sampling 270 Cluster Sampling 271

Exercises 272

8.3 Sampling “Error” 274

8.4 Sampling Distribution of the Sample Mean 275

Exercises 278

8.5 The Central Limit Theorem 279

Exercises 285

8.6 Using the Sampling Distribution of the Sample Mean 286

Exercises 289

Chapter Summary 289

Pronunciation Key 290

Chapter Exercises 290

Data Set Exercises 295

Software Commands 295

Answers to Self-Review 296

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Contents xxv

Chapter

9 Estimation and Confidence Intervals 297 9.1 Introduction 298

9.2 Point Estimate for a Population Mean 298

9.3 Confidence Intervals for a Population Mean 299

Population Standard Deviation Known � 300 A Computer Simulation 304

Exercises 305

Population Standard Deviation � Unknown 306

Exercises 312

9.4 A Confidence Interval for a Proportion 313

Exercises 316

9.5 Choosing an Appropriate Sample Size 316

Sample Size to Estimate a Population Mean 317 Sample Size to Estimate a Population Proportion 318

Exercises 320

9.6 Finite-Population Correction Factor 320

Exercises 322

Chapter Summary 323

Chapter Exercises 323

Data Set Exercises 327

Software Commands 328

Answers to Self-Review 329

A Review of Chapters 8 and 9 329

Glossary 330

Problems 331

Case 332

Practice Test 332

Chapter

10 One-Sample Tests of Hypothesis 333 10.1 Introduction 334

10.2 What Is a Hypothesis? 334

10.3 What Is Hypothesis Testing? 335

10.4 Five-Step Procedure for Testing a Hypothesis 335

Step 1: State the Null Hypothesis (H0 ) and the Alternate Hypothesis (H1) 336 Step 2: Select a Level of Significance 337 Step 3: Select the Test Statistic 338 Step 4: Formulate the Decision Rule 338 Step 5: Make a Decision 339

10.5 One-Tailed and Two-Tailed Tests of Significance 340

10.6 Testing for a Population Mean: Known Population Standard Deviation 341

A Two-Tailed Test 341 A One-Tailed Test 345

10.7 p-Value in Hypothesis Testing 345

Exercises 347

10.8 Testing for a Population Mean: Population Standard Deviation Unknown 348

Exercises 352

A Software Solution 353

Exercises 355

10.9 Tests Concerning Proportions 356

Exercises 359

10.10 Type II Error 359

Exercises 362

Chapter Summary 362

Pronunciation Key 363

Chapter Exercises 364

Data Set Exercises 368

Software Commands 369

Answers to Self-Review 369

Chapter

11 Two-Sample Tests of Hypothesis 371 11.1 Introduction 372

11.2 Two-Sample Tests of Hypothesis: Independent Samples 372

Exercises 377

11.3 Two-Sample Tests about Proportions 378

Exercises 381

11.4 Comparing Population Means with Unknown Population Standard Deviations 382

Equal Population Standard Deviations 383

Exercises 386

Unequal Population Standard Deviations 388

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Exercises 391

11.5 Two-Sample Tests of Hypothesis: Dependent Samples 392

11.6 Comparing Dependent and Independent Samples 395

Exercises 398

Chapter Summary 399

Pronunciation Key 400

Chapter Exercises 400

Data Set Exercises 406

Software Commands 407

Answers to Self-Review 408

Chapter

12 Analysis of Variance 410 12.1 Introduction 411

12.2 The F Distribution 411

12.3 Comparing Two Population Variances 412

Exercises 415

12.4 ANOVA Assumptions 416

12.5 The ANOVA Test 418

Exercises 425

12.6 Inferences about Pairs of Treatment Means 426

Exercises 429

12.7 Two-Way Analysis of Variance 430

Exercises 434

12.8 Two-Way ANOVA with Interaction 435

Interaction Plots 436 Hypothesis Test for Interaction 437

Exercises 440

Chapter Summary 442

Pronunciation Key 443

Chapter Exercises 443

Data Set Exercises 451

Software Commands 452

Answers to Self-Review 454

A Review of Chapters 10–12 455

Glossary 455

Problems 456

Cases 459

Practice Test 459

Chapter

13 Correlation and Linear Regression 461 13.1 Introduction 462

13.2 What Is Correlation Analysis? 463

13.3 The Correlation Coefficient 465

Exercises 470

13.4 Testing the Significance of the Correlation Coefficient 472

Exercises 475

13.5 Regression Analysis 476

Least Squares Principle 476 Drawing the Regression Line 479

Exercises 481

13.6 Testing the Significance of the Slope 483

Exercises 486

13.7 Evaluating a Regression Equation’s Ability to Predict 486

The Standard Error of Estimate 486 The Coefficient of Determination 487

Exercises 488

Relationships among the Correlation Coefficient, the Coefficient of Determination, and the Standard Error of Estimate 488

Exercises 490

13.8 Interval Estimates of Prediction 490

Assumptions Underlying Linear Regression 490 Constructing Confidence and Prediction Intervals 492

Exercises 494

13.9 Transforming Data 495

Exercises 497

Chapter Summary 498

Pronunciation Key 499

Chapter Exercises 500

Data Set Exercises 509

Software Commands 510

Answers to Self-Review 511

Chapter

14 Multiple Regression Analysis 512 14.1 Introduction 513

14.2 Multiple Regression Analysis 513

xxvi Contents

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Contents xxvii

Exercises 517

14.3 Evaluating a Multiple Regression Equation 519

The ANOVA Table 519 Multiple Standard Error of Estimate 520 Coefficient of Multiple Determination 521 Adjusted Coefficient of Determination 522

Exercises 523

14.4 Inferences in Multiple Linear Regression 523

Global Test: Testing the Multiple Regression Model 524 Evaluating Individual Regression Coefficients 526

Exercises 530

14.5 Evaluating the Assumptions of Multiple Regression 531

Linear Relationship 532 Variation in Residuals Same for Large and Small Values 533 Distribution of Residuals 534 Multicollinearity 534 Independent Observations 537

14.6 Qualitative Independent Variables 537

14.7 Regression Models with Interaction 540

14.8 Stepwise Regression 542

Exercises 544

14.9 Review of Multiple Regression 546

Chapter Summary 551

Pronunciation Key 553

Chapter Exercises 553

Data Set Exercises 565

Software Commands 566

Answers to Self-Review 567

A Review of Chapters 13 and 14 567

Glossary 568

Problems 569

Cases 570

Practice Test 571

Chapter

15 Index Numbers 573 15.1 Introduction 574

15.2 Simple Index Numbers 574

15.3 Why Convert Data to Indexes? 577

15.4 Construction of Index Numbers 577

Exercises 578

15.5 Unweighted Indexes 579

Simple Average of the Price Indexes 579 Simple Aggregate Index 580

15.6 Weighted Indexes 581

Laspeyres Price Index 581 Paasche Price Index 582 Fisher’s Ideal Index 584

Exercises 584

15.7 Value Index 585

Exercises 586

15.8 Special-Purpose Indexes 587

Consumer Price Index 588 Producer Price Index 589 Dow Jones Industrial Average (DJIA) 589 S&P 500 Index 590

Exercises 591

15.9 Consumer Price Index 592

Special Uses of the Consumer Price Index 592

15.10 Shifting the Base 595

Exercises 597

Chapter Summary 598

Chapter Exercises 599

Software Commands 602

Answers to Self-Review 603

Chapter

16 Time Series and Forecasting 604 16.1 Introduction 605

16.2 Components of a Time Series 605

Secular Trend 605 Cyclical Variation 606 Seasonal Variation 607 Irregular Variation 608

16.3 A Moving Average 608

16.4 Weighted Moving Average 611

Exercises 614

16.5 Linear Trend 615

16.6 Least Squares Method 616

Exercises 618

16.7 Nonlinear Trends 618

Exercises 620

16.8 Seasonal Variation 621

Determining a Seasonal Index 621

Ŷ

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Exercises 626

16.9 Deseasonalizing Data 627

Using Deseasonalized Data to Forecast 628

Exercises 630

16.10 The Durbin-Watson Statistic 631

Exercises 636

Chapter Summary 636

Chapter Exercises 636

Data Set Exercise 643

Software Commands 643

Answers to Self-Review 644

A Review of Chapters 15 and 16 645

Glossary 646

Problems 646

Practice Test 647

Chapter

17 Nonparametric Methods: Goodness-of-Fit Tests 648 17.1 Introduction 649

17.2 Goodness-of-Fit Test: Equal Expected Frequencies 649

Exercises 654

17.3 Goodness-of-Fit Test: Unequal Expected Frequencies 655

17.4 Limitations of Chi-Square 657

Exercises 659

17.5 Testing the Hypothesis That a Distribution of Data Is from a Normal Population 659

17.6 Graphical and Statistical Approaches to Confirm Normality 662

Exercises 665

17.7 Contingency Table Analysis 667

Exercises 671

Chapter Summary 672

Pronunciation Key 672

Chapter Exercises 672

Data Set Exercises 677

Software Commands 678

Answers to Self-Review 679

Chapter

18 Nonparametric Methods: Analysis of Ranked Data 680 18.1 Introduction 681

18.2 The Sign Test 681

Exercises 685

Using the Normal Approximation to the Binomial 686

Exercises 688

Testing a Hypothesis about a Median 688

Exercises 689

18.3 Wilcoxon Signed-Rank Test for Dependent Samples 690

Exercises 693

18.4 Wilcoxon Rank-Sum Test for Independent Samples 695

Exercises 698

18.5 Kruskal-Wallis Test: Analysis of Variance by Ranks 698

Exercises 702

18.6 Rank-Order Correlation 704

Testing the Significance of rs 706

Exercises 707

Chapter Summary 709

Pronunciation Key 710

Chapter Exercises 710

Data Set Exercises 713

Software Commands 713

Answers to Self-Review 714

A Review of Chapters 17 and 18 716

Glossary 716

Problems 717

Cases 718

Practice Test 718

Chapter

19 Statistical Process Control and Quality Management 720 19.1 Introduction 721

19.2 A Brief History of Quality Control 721

Six Sigma 724

19.3 Causes of Variation 724

xxviii Contents

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Contents xxix

19.4 Diagnostic Charts 725

Pareto Charts 725 Fishbone Diagrams 727

Exercises 728

19.5 Purpose and Types of Quality Control Charts 729

Control Charts for Variables 729 Range Charts 733

19.6 In-Control and Out-of-Control Situations 734

Exercises 736

19.7 Attribute Control Charts 737

Percent Defective Charts 737 c-Bar Charts 740

Exercises 741

19.8 Acceptance Sampling 742

Exercises 746

Chapter Summary 746

Pronunciation Key 747

Chapter Exercises 747

Software Commands 751

Answers to Self-Review 752

On the website: www.mhhe.com/lind15e Chapter

20 An Introduction to Decision Theory 20.1 Introduction

20.2 Elements of a Decision

20.3 A Case Involving Decision Making under Conditions of Uncertainty

Payoff Table Expected Payoff

Exercises

Opportunity Loss

Exercises

Expected Opportunity Loss

Exercises

20.4 Maximin, Maximax, and Minimax Regret Strategies

20.5 Value of Perfect Information

20.6 Sensitivity Analysis

Exercises

20.7 Decision Trees

Chapter Summary

Chapter Exercises

Answers to Self-Review

Appendixes 753

Appendix A: Data Sets 754

Appendix B: Tables 764

Appendix C: Answers to Odd-Numbered Chapter Exercises and Review Exercises and Solutions to Practice Tests 782

Photo Credits 829

Index 831

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Goals When you have completed this chapter, you will be able to:

1 Organize data into a fre- quency distribution.

2 Portray a frequency distribu- tion in a histogram, frequency polygon, and cumulative fre- quency polygon.

3 Present data using such graphical techniques as line charts, bar charts, and pie charts.FPO

1 Learning Objectives When you have completed this chapter, you will be able to:

LO1 List ways that statistics is used.

LO2 Know the differences between descriptive and inferential statistics.

LO3 Understand the differ- ences between a sample and a population.

LO4 Explain the difference between qualitative and quan- titative variables.

LO5 Compare the differences between discrete and continu- ous variables.

LO6 Recognize the levels of measurement in data.

What Is Statistics?

Barnes & Noble stores recently began selling the Nook. With this

device, you can download over 1,500 books electronically and read

the book on a small monitor instead of purchasing the book. Assume

you have the number of Nooks sold each day for the last month at the

Barnes & Noble store at the Market Commons Mall in Riverside,

California. Describe a condition in which this information could be

considered a sample. Illustrate a second situation in which the same

data would be regarded as a population. (See Exercise 11 and LO3.)

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2 Chapter 1

1.1 Introduction More than 100 years ago, H. G. Wells, an English author and historian, suggested that one day quantitative reasoning will be as necessary for effective citizenship as the ability to read. He made no mention of business because the Industrial Revo- lution was just beginning. Mr. Wells could not have been more correct. While “busi-

ness experience,” some “thoughtful guesswork,” and “intuition” are key attributes of successful managers, today’s business problems tend to be too complex for this type of decision making alone.

One of the tools used to make decisions is statistics. Statistics is used not only by businesspeople; we all also apply statistical concepts in our lives. For example, to start the day you turn on the shower and let it run for a few moments. Then you put your hand in the shower to sample the temperature and decide to add more hot water or more cold water, or determine that the temperature is just right and then enter the shower. As a second example, suppose you are at Costco Wholesale and wish to buy a frozen pizza. One of the pizza makers has a stand, and they offer a small wedge of their pizza. After sampling the pizza, you

decide whether to purchase the pizza or not. In both the shower and pizza examples, you make a decision and select a course of action based on a sample.

Businesses face similar situations. The Kellogg Company must ensure that the mean amount of Raisin Bran in the 25.5-gram box meets label specifications. To do so, it sets a “target” weight somewhat higher than the amount specified on the label. Each box is then weighed after it is filled. The weighing machine reports a distribu- tion of the content weights for each hour as well as the number “kicked-out” for being under the label specification during the hour. The Quality Inspection Depart- ment also randomly selects samples from the production line and checks the qual- ity of the product and the weight of the contents of the box. If the mean product weight differs significantly from the target weight or the percent of kick-outs is too large, the process is adjusted.

As a student of business or economics, you will need basic knowledge and skills to organize, analyze, and transform data and to present the information. In this text, we will show you basic statistical techniques and methods that will develop your ability to make good personal and business decisions.

1.2 Why Study Statistics? If you look through your university catalog, you will find that statistics is required for many college programs. Why is this so? What are the differences in the sta- tistics courses taught in the Engineering College, the Psychology or Sociology Departments in the Liberal Arts College, and the College of Business? The biggest difference is the examples used. The course content is basically the same. In the College of Business we are interested in such things as profits, hours worked, and wages. Psychologists are interested in test scores, and engineers are interested in how many units are manufactured on a particular machine. However, all three are interested in what is a typical value and how much variation there is in the data. There may also be a difference in the level of mathematics required. An engi- neering statistics course usually requires calculus. Statistics courses in colleges of business and education usually teach the course at a more applied level. You should be able to handle the mathematics in this text if you have completed high school algebra.

So why is statistics required in so many majors? The first reason is that numer- ical information is everywhere. Look in the newspapers (USA Today), news maga- zines (Time, Newsweek, U.S. News and World Report), business magazines (Busi- nessWeek, Forbes), or general interest magazines (People), women’s magazines

Examples of why we study statistics

LO1 List ways that statistics is used.

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What Is Statistics? 3

(Ladies Home Journal or Elle), or sports magazines (Sports Illustrated, ESPN The Magazine), and you will be bombarded with numerical information.

Here are some examples:

• The average increase in weekly earnings, in 1982–84 dollars, from January 2009 to January 2010 was $8.32.

• In January 2010 the average amount of credit card debt per household was $7,394. This is a decrease from $7,801 in July 2009. A 2010 Federal Reserve survey found that 75 percent of U.S. households have at least one credit card.

• The following table summarizes the number of commercial aircraft manufactured by Boeing, Inc. between 2006 and 2009.

USA TODAY Snapshot

By Jae Yang and Paul Trap, USA TODAY Source: SnagAJob.com Reprinted with permission (April 29, 2010) USA TODAY.

Sales of Boeing Aircraft

Type of Aircraft

Year 737 747 767 777 787 Total

2006 733 72 8 77 160 1,050 2007 850 25 36 143 369 1,423 2008 488 4 29 54 94 669 2009 197 5 7 30 24 263

• Go to the following website: www.youtube.com/watch?v=pMcfrLYDm2U. It provides interesting numerical information about countries, business, geogra- phy, and politics.

• USA Today (www.usatoday.com) prints “Snapshots” that are the result of sur- veys conducted by various research organizations, foundations, and the federal government. The following chart summarizes what recruiters look for in hiring seasonal employees.

A second reason for taking a statistics course is that statistical techniques are used to make decisions that affect our daily lives. That is, they affect our personal welfare. Here are a few examples:

• Insurance companies use statistical analysis to set rates for home, automobile, life, and health insurance. Tables are available showing estimates that a 20-year- old female has 60.25 years of life remaining, an 87-year-old woman 4.56 years remaining, and a 50-year-old man 27.85 years remaining. Life insurance premi- ums are established based on these estimates of life expectancy. These tables are available at www.ssa.gov/OACT/STATS/table4cb.html. [This site is sensitive to capital letters.]

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• The Environmental Protection Agency is interested in the water quality of Lake Erie as well as other lakes. They periodically take water samples to establish the level of contamination and maintain the level of quality.

• Medical researchers study the cure rates for diseases using different drugs and different forms of treatment. For example, what is the effect of treating a cer- tain type of knee injury surgically or with physical therapy? If you take an aspirin each day, does that reduce your risk of a heart attack?