Isbn 0 205 34405 4

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