Table Of ContentFinal PDF to printer
Statistical Techniques in
&
BUSINESS
ECONOMICS
lin39470_fm_i-xxvi.indd i 11/09/19 11:44 AM
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The McGraw-Hill/Irwin Series in Operations and Decision Sciences
SUPPLY CHAIN MANAGEMENT BUSINESS FORECASTING BUSINESS STATISTICS
Benton Keating and Wilson Bowerman, Drougas, Duckworth, Froelich,
Purchasing and Supply Chain Business Forecasting Hummel, Moninger, and Schur
Management Seventh Edition Business Statistics and Analytics in
Third Edition Practice
Bowersox, Closs, Cooper, and LINEAR STATISTICS AND REGRESSION Ninth Edition
Bowersox Kutner, Nachtsheim, and Neter Doane and Seward
Supply Chain Logistics Management Applied Linear Regression Models Applied Statistics in Business and
Fifth Edition Fourth Edition Economics
Burt, Petcavage, and Pinkerton BUSINESS SYSTEMS DYNAMICS Sixth Edition
Supply Management Doane and Seward
Sterman
Eighth Edition Essential Statistics in Business and
Business Dynamics: Systems Thinking
Johnson and Modeling for a Complex World Economics
Third Edition
Purchasing and Supply Management
Sixteenth Edition OPERATIONS MANAGEMENT Lind, Marchal, and Wathen
Simchi-Levi, Kaminsky, and Simchi-Levi Cachon and Terwiesch Basic Statistics for Business and
Designing and Managing the Supply Matching Supply with Demand: An Economics
Chain: Concepts, Strategies, Case Introduction to Operations Management Ninth Edition
Studies Second Edition Lind, Marchal, and Wathen
Third Edition Cachon and Terwiesch Statistical Techniques in Business and
Operations Management Economics
PROJECT MANAGEMENT Second Edition Eighteenth Edition
Brown and Hyer Jacobs and Chase Jaggia and Kelly
Managing Projects: A Team-Based Operations and Supply Chain Business Statistics: Communicating with
Approach Management Numbers
Larson Fifteenth Edition Third Edition
Project Management: The Managerial Jacobs and Chase Jaggia and Kelly
Process Operations and Supply Chain Essentials of Business Statistics:
SERVICE OPERATIONS MANAGEMENT Management: The Core Communicating with Numbers
Fifth Edition Second Edition
Bordoloi, Fitzsimmons and
Fitzsimmons Schroeder and Goldstein Jaggia, Kelly, Lertwachara, and Chen
Service Management: Operations, Operations Management in the Supply Business Analytics: Communicating with
Strategy, Information Technology Chain: Decisions and Cases Numbers
Ninth Edition Eighth Edition McGuckian
Stevenson Connect Master: Business Statistics
MANAGEMENT SCIENCE
Operations Management
Hillier and Hillier Fourteenth Edition
Introduction to Management Science: A Swink, Melnyk, Cooper, and Hartley
Modeling and Case Studies Approach Managing Operations across the Supply
with Spreadsheets Chain
Sixth Edition Fourth Edition
Stevenson and Ozgur
BUSINESS MATH
Introduction to Management Science
Slater and Wittry
with Spreadsheets
First Edition Math for Business and Finance:
An Algebraic Approach
BUSINESS RESEARCH METHODS Second Edition
Schindler Slater and Wittry
Business Research Methods Practical Business Math Procedures
Thirteenth Edition Thirteenth Edition
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Statistical Techniques in
&
BUSINESS
ECONOMICS
EIGHTEENTH EDITION
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 Education, 2 Penn Plaza, New York, NY 10121. Copyright © 2021 by
McGraw-Hill Education. All rights reserved. Printed in the United States of America. 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 McGraw-Hill Education, including, but not limited
to, in any network or other electronic storage or transmission, or broadcast for distance learning.
Some ancillaries, including electronic and print components, may not be available to customers outside
the United States.
This book is printed on acid-free paper.
1 2 3 4 5 6 7 8 9 LWI 24 23 22 21 20
ISBN 978-1-260-57048-9
MHID 1-260-57048-7
Cover Image: ©FreshPaint/Shutterstock
All credits appearing on page or at the end of the book are considered to be an extension of the
copyright page.
The Internet addresses listed in the text were accurate at the time of publication. The inclusion of a
website does not indicate an endorsement by the authors or McGraw-Hill Education, and McGraw-Hill
Education does not guarantee the accuracy of the information presented at these sites.
mheducation.com/highered
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DEDICATION
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, Jake, and Brady), and Mark and Sarah (Jared, Drew, and Nate).
Douglas A. Lind
To Margaret Marchal Nicholson and Andrea.
William G. Marchal
To my wonderful family: Barb, Hannah, and Isaac.
Samuel A. Wathen
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A N OTE F RO M TH E AUTH O RS
Over the years, we received many compliments on this text and understand that it’s a
favorite among students. We accept that as the highest compliment and continue to
work very hard to maintain that status.
The objective of Statistical Techniques in Business and Economics is to provide
students majoring in management, marketing, finance, accounting, economics, and
other fields of business administration with an introductory survey of descriptive and infer-
ential statistics. To illustrate the application of statistics, we use many examples and
exercises that focus on business applications, but also relate to the current world of the
college student. A previous course in statistics is not necessary, and the mathematical
requirement is first-year algebra.
In this text, we show beginning students every step needed to be successful in a
basic statistics course. This step-by-step approach enhances performance, accelerates
preparedness, and significantly improves motivation. Understanding the concepts, see-
ing and doing plenty of examples and exercises, and comprehending the application of
statistical methods in business and economics are the focus of this book.
The first edition of this text was published in 1967. At that time, locating relevant
business data was difficult. That has changed! Today, locating data is not a problem.
The number of items you purchase at the grocery store is automatically recorded at
the checkout counter. Phone companies track the time of our calls, the length of
calls, and the identity of the person called. Credit card companies maintain informa-
tion on the number, time and date, and amount of our purchases. Medical devices
automatically monitor our heart rate, blood pressure, and temperature from remote
locations. A large amount of business information is recorded and reported almost
instantly. CNN, USA Today, and MSNBC, for example, all have websites that track
stock prices in real time.
Today, the practice of data analytics is widely applied to “big data.” The practice of
data analytics requires skills and knowledge in several areas. Computer skills are
needed to process large volumes of information. Analytical skills are needed to evalu-
ate, summarize, organize, and analyze the information. Critical thinking skills are needed
to interpret and communicate the results of processing the information.
Our text supports the development of basic data analytical skills. In this edition, we
added a new section at the end of each chapter called Data Analytics. As you work
through the text, this section provides the instructor and student with opportunities to
apply statistical knowledge and statistical software to explore several business environ-
ments. Interpretation of the analytical results is an integral part of these exercises.
A variety of statistical software is available to complement our text. Microsoft Excel
includes an add-in with many statistical analyses. Megastat is an add-in available for
Microsoft Excel. Minitab and JMP are stand-alone statistical software packages available
to download for either PC or MAC computers. In our text, Microsoft Excel, Minitab, and
Megastat are used to illustrate statistical software analyses. The text now includes refer-
ences or links to Excel tutorials in Connect. These provide users with clear demonstra-
tions using statistical software to create graphical and descriptive statistics and
statistical analyses to test hypotheses. We use screen captures within the chapters, so
the student becomes familiar with the nature of the software output.
Because of the availability of computers and software, it is no longer necessary to
dwell on calculations. We have replaced many of the calculation examples with interpre-
tative ones, to assist the student in understanding and interpreting the statistical results.
In addition, we 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 con-
cepts, along with supporting interesting and relevant examples.
vi
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WHAT’S NEW IN THE EIGHTEENTH EDITION?
We made several significant improvements to our text. First, based on reviewer sugges-
tions, Chapter 18, now titled “Forecasting with Time Series Analysis,” is completely re-
written. The chapter shows how to create forecasting models that mimic trend and
seasonal time series patterns. The chapter shows how to apply simple moving aver-
ages, simple exponential smoothing, regression, and seasonal indexing to create the
models. Forecasting error, using the mean absolute deviation, is included for every fore-
casting model. In addition, the chapter includes a discussion of autocorrelation and the
376 CHAPTER 11 Durban-Watson statistic. While there are a few similarities to past editions, all examples/
solutions and self-reviews are new; all have associated data files. All 36 exercises are
new; 28 have associated data files and require statistical software to complete the re-
At the .05 significance level, can we conclude there are more defects produced on
the day shift? sponses. Some of the data files were created by the authors; others use real data
18. The null and alternate hypotheses are:sourced from the U.S. Census Bureau website, www.census.gov. All data files are avail-
H0: μad =b 0le in Connect. We hope that this chapter satisfies the need of users to include time
H1: μsd ≠e 0ries forecasting in their courses.
The following paired observations show the number of traffic citations given for
Second, the text now uses an excellent set of Excel tutorials to demonstrate how to
speeding by Officer Dhondt and Officer Meredith of the South Carolina Highway
Patrol for the last five months. use Excel to perform the statistical analyses in the text. Rather than referrRinevg.C otnofi ram isnge Pta ogefs
written procedures, users will be able to view well-organized presentations that clearly
Number of Citations Issued
May Juned emJuoly nstAruagtuest hoSwept etmobe ruse the various statistical tools, functions, and analyses in Excel.
Officer Dhondt 30 22 The 2r5e fere1n9 ces to2 6the tutorials are indicated by a unique icon placed in the left margin
Officer Meredith 26 19 20 15 19
and aligned with the procedureTW oOr- SaAnMaPLlyE sTEisS TiSn O tFh HeY PtOeTxHtE. SIInS the eBook, these icons will 3b7e1
At the .05 significance level, is there ad diifrfeerecnctely in tlhien mkeeadn n utmob ert hof eci tattiuontso rials. Textbook users will access the tutorials through
given by the two officers? Connect.
Note: Use the six-step hypothesis testing procedurTe tho isrodlv,e Ctheh faolplotweinrg 8ex enrcoiswes. starts with a brief discuSsalsesipoernso no f theBe rfoeres earcAfhter process to estab-
19. The management of Discount Fulrinsithur ea, a c cohanint oefx dtis cfoourn ts fuarnmituprel isntogre sa nd data collection. ItS iad Mlsahoon ei nclude$3s20 comm$34e0nts on ethics and
in the Northeast, designed an incentive plan for salespeople. To evaluate this inno- Carol Quick 290 285
vative plan, 12 salespeople were selebctiead saet rdan dsoamm, anpdl itnhegir .w Aeefktlye irn ctohmees description of sampTloimn Jgac kmson ethod 4s2,1 a ne w475 section, “Sample
before and after the plan were recordeMd.ean as a Random Variable,” demonstrates the Aendfyf eJoncets of ran 5d10o m sa 5m10pling on the sam-
Jean Sloan 210 210
Salesperson pBelfeor e meaAnft efrollowed by the section, “Sampling DJaicsk tWrailkberu tion o 40f2 the S 5a00mple Mean.” The
Peg Mancuso 625 631
Sid Mahone s$t3a20n dard$ 3e40rror of the sampling distribution is now featured in a new section. The “sam-
Anita Loma 560 560
Carol Quick 290 285
pling error” concept continues to be a key item iJnoh nt hCueso chapte 3r6’0s disc u36s5sion.
Tom Jackson 421 475
Carl Utz 431 431
Andy Jones 510 Four 5t1h0, starting in Chapter 9, many exercisAe. Ss. K uhshanevr e be e 50n6 restr 5u25ctured with multi-
Jean Sloan it e21m0 resp 2o10nses. Reformulating these exercises wFeilrnl Lpawrtoon vide u 5s0e5 rs wi t6h19 more direction to
Jack Walker 402 500
Peg Mancuso u n62d5 ersta n63d1ing the details of a particular statistical technique. As an example, compare
Anita Loma 560 560 Was there a significant increase in the typical salesperson’s weekly income due to
John Cuso C 3h60a pter 13615, exercise 20 before, ont hteh ienn orviagtihvet ,in acenntdive a pflatne? rU, soe nth et .h05e s ilgeniffitc.ance level.
Carl Utz 431 431 a. State the null and alternate hypotheses.
A. S. Kushner 506 525 b. What is the p-value?
c. Is the null hypothesis rejected?
Fern Lawton 505 619 d. What is the conclusion indicated by the analysis?
20. The federal government recently granted funds for a special program
Was there a significant increase in the typical salesperson’s weekly income due to designed to reduce crime in high-crime areas. A study of the results of the program
the innovative incentive plan? Use the .05 significance level. Estimate the p-value, in eight high-crime areas of Miami, Florida, yielded the following results.
and interpret it.
20. The federal government recently granted funds for a special program de- Number of Crimes by Area
signed to reduce crime in high-crime areas. A study of the results of the program in
eight high-crime areas of Miami, Florida, yielded the following results. A B C D E F G H
Before 14 7 4 5 17 12 8 9
Number of Crimes by Area After 2 7 3 6 8 13 3 5
A B C D E F G H
Has there been a decrease in the number of crimes since the inauguration of the
Before 14 7 4 5 17 12 8 9 program? Use the .01 significance level.
After 2 7 3 6 8 13 3 5 a. State the null and alternate hypotheses.
b. What is the p-value?
Has there been a decrease in the number of crimes since the inauguration of the c. Is the null hypothesis rejected?
program? Use the .01 significance level. Estimate the p-value. d. What is the conclusion indicated by the analysis?
CHAPTER SUMMARY
I. In comparing two population means, we wish to know whether they could be
equal.
A. We are investigating whether the distribution of the difference between the means
could have a mean of 0.
B. The test statistic follows the standard normal distribution if the population standard
deviations are known.
1. The two populations follow normal distributions. vii
2. The samples are from independent populations.
3. The formula to compute the value of z is
z= x1−x2 (11–2)
σ21 +σ22
√n1 n2
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Confirming Pages
2
Describing Data:
FREQUENCY TABLES, FREQUENCY DISTRIBUTIONS,
AND GRAPHIC PRESENTATION
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HOW ARE CHAPTERS ORGANIZED TO ENGAGE Confirming Pages
STUDENTS AND PROMOTE LEARNING?
DESCRIBING DATA: DISPLAYING AND EXPLORING DATA 95
Chapter Learning Objectives Introduction rido/123RF
Chapter 2 began our study of descriptive statistics. In order to transform raw or
Each chapter begins with a set of uMnEgRroRuILpLe LdY NdCatHa reincteon tlay cmomepalnetinedg afu slt ufodyr mof, ownlein eo irngveasntmizeen tt hpoer tdfoaliotas fionrt ao s aam fpreleq uency distri-
of clients. For the 70 participants in the study, organize these data into a frequency
learning objectives designed to pro- bduisttiroibnu. tiWone. (Speree sEexenrct isthe e4 3f raenqd uLeOn2-c3y.) distribution in graphic form as a histogram or a fre-
quency polygon. This allows us to visualize where the data tend to cluster, the largest
vide focus for the chapter and motivate
and the smallest values, and the general shape of the data.
student learning. These objectives, lo- In Chapter 3, we first computed several measures of location, sucCho nafsi rtmhien gm Peagaens,
cated in the margins next to the topic, mLeEdAiaRnN, IaNnGd mOoBdJeE. CTThIeVsEe Smeasures of location allow us to report a typical value in
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vation. Examples include the number of hours a student studied and the poCionntfsi remainrgn ePadg eosn
Chapter Opening Exercise an examinaMtoiorgnan; Sift aan lesyampled product meets quality specificTahteioren s aarned wthaey ss hioftt hoenr wthhaicnh itth ies
manufactuCreomdm; iosisro tnhs e amount of electricity used in a mEoxnctlhu sbivye a hMoemtheoodw tnoe r loacnadt eth eq umaertailen
daily high tem$p2,e03r8ature in the region for the month. Thevsaelu ecsh.a rAtsn aonthde gr rampehtsh opdr ovciadlele du sethfuel
A representative exercise opens the chapterin asinghdt ss ahso wwe 1su,7 s5he8 obwus intheMseetsh o acdnhaalyptictEesx ctrol usc eivoenhnatInnecclnuesti vo ecuar unInn cdbleuerssi vtaaepn dpMinleigeth odofd dt oaut asae.s rethael -wforomruldla
situation. DESCRIBING DATA: FR11E,,76Q2317UENCY TFMAireBsdtL iQaEnuSa,r tFilRe EQU12E,,N7023C18Y..00 DIST12R,,70IB3398U..50TION0S.2, A5Nn D+ G 0RA.7P5H ItCo PlRoEcSaEteN TtAhTeI OpNo sition1 9of
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and shows a relevant business applica- 27 1• ,5T29ionesta Ford Lincoln sells Ford and Lin7co5l%n coafr st ahned dtrautcak sv.alues are less than
tion that helps students answer the 27 3• ,0O82lean Automotive Inc. has the Nissan thfrean cvhailsuee a os fw tehlle a sth tihrde Gqeunaertrialel .M Wotohresn
question, “How can I apply this 222889Mon d121••a ,,,y962 bSK590126rhaaennTfeduf isMee slooddft aMoCyrho set oovfrrfsWoe TlIreensiotd c,t nnh.C eeseases dCtdllaishall aFryByco us,r liadecnk rLT,d, iDhGn GuocMrMdosClgdCn eat r,ttty urhhau cneeckdk s ssr,JF e.aHersmieydupuapl ntyllsied n a efii rs,a oSa smlna awdtr u egKtrlhedli aeaa, .sy t htBweMo Wd im fafenedrteh Vnoocdlveso .iins
concept?” 29 23 1,342 33 27 28 small. 3F9o r examp2le6, in the Applewood
30 32 Every m2o8n th, Ms. Ball 3co3l leActus tdoa tGa3 r5for oump edaactha 3o 2tfh tehere f oaurre d e1a8le0r svheiphsi -
and enters them into an Excel spreadsheet. Last month the Applewood
cles. T he2 9q uartiles 2c5o mputed u3s6in g both me3t1h ods are 3s2h own to 2th7e above. Based on
Auto Group sold 180 vehicles at the four dealerships. A copy of the first
the va ria3b5l e profit, 3425f e wo fo bthseer v1a38ti5o0 n sv aalpupeesa r(s2 t35o7% t h) ea lreeft . lTeh3se6s vtahraianb lbeso3 tc0ho llveacltueed sin colfu dthee: first
quartile, and 135 of the 180 values (75%) are less than both values of the third quartile.
When using Exce l,• b eA gcea—retfhuel atog eu onfd tehres btaunyder tahte t hme etitmheo do fu thsee dp utorc hcaaslceu.late quartiles.
• Profit—the amount earned by the dealership on the sale of each
The Excel function, Quartvieleh.iecxlec., will result in the same answer as the Exclusive Method
(formula 4–1). The E x•c eLlo cfuantioctnio—nth, eQ dueaalretrisleh.ipin wc,h ewreil lt hree vseuhltic lien wtahse p uInrcchluasseivde. Method
answers. • Vehicle type—SUV, sedan, compact, hybrid, or truck.
Self-Reviews • Previous—the number of vehicles previously purchased at any of the
four Applewood dealerships by the consumer.
The entire data set is available in Connect and in Appendix A.4 at the end
Self-Reviews are interspersed SELF-REVIEW 4–2 of the text.
throughout each chaptlien3r94 7a0_nch0d4_ 094-129.indd 95 Source: Microsoft Excel 08/22/19 07:53 PM
follow Example/Solution sec- LO2-1 The QualitCy Coonntsrotl rduepcarttminengt oFf Prleainqsvuillee nPecanyu tT Caombplaenys is responsible for checking
Summarize qualitatthivee weight of the 8-ounce jar of peanut butter. The weights of a sample of nine jars pro-
tions. They help students mon- variables with freqduuecnecyd lastR heocaulrl farorem: Chapter 1 that techniques used to describe a set of data are called descrip-
itor their progress and provide and relative frequency tive statistics. Descriptive statistics organize data to show the general pattern of the
tables. data, t7o. 6id9 entif7y. 7w2 here7 .v8a0l ues7 .t8e6n d to7 .c9o0 ncen7t.r9a4t e, an7.d9 7to ex8p.o06s e ex8tr.0e9me or unusual
immediate reinforcement for data values. The first technique we discuss is a frequency table.
that particular technique. (a) What is the median weight?
(b) DetermFinReE QthUeE wNeCiYg hTtAs BcLoErr eAs pgroonudpiinngg toof qthuea lfitirastitv aen dda ttah iirndt oq muaurttuilaellsy. exclusive and
Answers are in Appendix D. collectively exhaustive classes showing the number of observations in each class.
viii
lin39470_ch04_094-1l2in93.9in4d7d0_ ch10021_ 018-050.indd 19 0086//2282//1199 0 077:0:59 3P MPM
lin39470_fm_i-xxvi.indd viii 11/09/19 11:44 AM
Confirming Pages
Confirming Pages
142 CHAPTER 5
A SURVEY OF PROBABILITY CONCEPTS 145
SELF-REVIEW 5–3
A sample of employees of Worldwide Enterprises is to be surveyed about a new health
care plan. The employees are classified as follows:
15. Suppose the probability you will get an A in this class is .25 and the probability you
will get a B is .50. What is the probability your gradCel awsislli fbicea taiobno ve a C? Event Number of Employees
16. Two coins are tossed. If A is the event “two heads” and B is the event “two tails,”
are A and B mutually exclusive? Are they complemSeunptes?rvisors A 120
17. The probabilities of the events A and B are .20 and M.3a0in, treensapnecec tively. The probaBb ility 50
that both A and B occur is .15. What is the probabilitPyr oodf uecittihoen r A or B occurring?C 1,460
18. Let P(X) = .55 and P(Y) = Final PDF to printer 302
What is the probability of either X or Y occurring? 68
19. Suppose the two events A and B
their joint occurrence? (a) What is the probability that the first person selected is:
20. A student is taking two courses, histo(ir)y anedit hmeart hin. Tmhaei nptreonbaanbciliety o trh ea ssteucdreentat rwyi?ll
pass the history course is .60, an d the(i ip) robnaobti liinty mofa pnaasgseinmg ethnet? math course is .70.
The probability of passing both is( b.5) 0. DWrhaawt ias tVhee npnro dbiaabgilriatym o fi lpluasstsriantgin agt lyeoasutr o annes?wers to part (a).
21. The aquarium at Sea Critters D(ce)p otA creo ntthaein es v1e4n0ts fiinsh p. aEritg (hat)y( i)o cf otmhepslee mfisehn taarrey or mutually exclusive or both?
green swordtails (44 female and 36 male) and 60 are orange swordtails (36 female
and 24 males). A fish is randomlyT chapetu rGede fronme threa alq uRaruiulme: of Addition
a. What is the probability the selected fish is a green swordtail?
b. What is the probability the seTlehcete od ufitscho ims mesa leo?f an experiment may not be mutually exclusive. For example, the Florida
c. What is the probability the seTleocuterids tf isCho ims am misasleio gnr eseenle scwtoerdd taai ls? a mple of 200 tourists who visited the state during the
d. What is the probability the seyleecater.d T fhiseh sisu erviteheyr rae vmeaalele odr ath garte C1eon2n 0sfwi troomrudinrtiagsi tlP?s a wgeesnt to Disney World and 100 went to Busch
22. A National Park Service survey Gofa vrdiseitonrss. tWo hthaet Riso ctkhye M poruonbtaaibni lriteyg itohna rte av epaelerds on selected visited either Disney World or
that 50% visit Yellowstone, 40% visit the Tetons, and 35% visit both.
Busch Gardens? If the special rule of addition is used, the probability of selecting a tourist
a. What is the probability a vacationer will visit at least one of these parks?
who went to Disney World is .60, found by 120/200. Similarly, the probability of a tourist
b. What is the probability .35 called?
going to Busch Gardens is .50. The sum of these probabilities is 1.10. We know, however,
c. Are the events mutually exclusive? Explain.
Statistics in Action that this probability cannot be greater than 1. The explanation is that many tourists visited
A SURVEY OF PROBABILITY CONCEbPoTtSh attractions and are being counted twi1c4e!3 A check of the survey responses revealed
STATISTICS IN ACTION
LO5-4 Rules of Multiplicatiothant 6t0o o uCt oaf 2lc00u slaamtpeled P dirdo, inb faacbt, viilsiitt byoth attractions.
Statistics in Action articles aCraelc uslactea tptreobraebdili ttiehsr ough- If you wish to get some To answer our question, “What is the probability a selected person visited either
out the text, usually about utwsinog tphee rru lcehs aofp ter. TheIyn this s aetctetinotnio, nw aet tdheis nceuxsts g aththe- rules fDoirs cnoemy pWutoinrlgd thoer lBikueslichho oGda trhdaet ntws?o” e(1ve) natds db oththe probability that a tourist visited Disney
provide unique, interestingm aulptipplilciactaiotni.ons and hish-appen,e orinr gt hyeouir ajottienntd p, aronbnoaubnilcitey . ForW eoxarlmd palen,d 1 t6h%e opfr othbea 2b0ili1ty8 htaex orer tsuhrnes v wiseitreed p Breu-sch Gardens, and (2) subtract the proba-
pared btyh aHt &yoRu B bleolciekv ea nthda t7 Pa5t( D%is onfe yth) =os b.6ei0 lirteyt uorfn vs isshiPtoi(Bnwugse cbdho )a =t hr e..5 fT0uhnuds. :What is the likelihood
torical insights in the field of statistics. a person’s tax form was prepared by H&R Block and the person received a refund?
Venn dialegarsat mtwso i lplueostprlaet per ethseisn ta s the intersectioPn(D oifs tnweoy eovre Bnutss. cTho) f=in dP (tDheis lnikeeyli)h +o oPd( Bouf sch) − P(both Disney and Busch)
were born on the same
two evednatste h—athpapte isn, itnhge, swame eu se the rules of multiplication. There ar=e t.w60o r+u l.e5s0 o −f m .3u0lti -= .80
plication: the special rule and the general rule.
day of the year but not When two events both occur, the probability is called a joint probability. The prob-
Specinaecle Rssaurillye th eo sfa mMe uyelatr.i plicaabtiiloityn (.30) that a tourist visits both attractions is an example of a joint probability.
If there are 30 people in
The spetchiea rl oroumle, tohfe mpruobltaipbliilcitay toiof n requires that two events A and B are independent.
Two evean dtsu palricea tine dise .p7e06n.d Ief tnhte irfe t he occurrence of one event does not alter the probabil-
Definitions ity of thea roec 6c0u prreeonpclee ino ft hthe ero ootmh,e Pr (eDvisennety. and Busch) = .30
the probability is .994 that
at least two people share the
Definitions of new terms or terms unique to INDEPsEamNeD bEirNthCdaEy . TWhiteh aosc fceuwr rence of one event has no effect on the probability of
tJhOe IoNcTacs uP 2rRr3eO pneBcoeAp lBoe fIt LhaIenT coYht ahAnec rpe erso vbeanbt.ility that measures the likelihood two or more
the study of statistics are set apart from the
eventasr we iellv ehna,p tphaetn i sc .o5n0c, uthraret ntly.
text and highlighted for easy reference and at least two people share
One way to think about independence is to assume that events A and B occur at differ-
review. They also appear in the Glossary at ent timetsh. eF soarm eex abmirtphldea, yw. Hheinnt: event B occurs after event A occurs, does A have any effect
the end of the book. on thSeo li Tktoeh leciho mgooepdnue tetrh atahl ti sreu, vflieen dno ttf h Bae dodccituiorns?, wIf hthiceh a inss uwseerd is t on oc, othmepnu tAe atnhde Bp raorbea ibnidliteyp eonf dtwenot
eevveenntsts. Tpthoroa ibtll auabsrietlri atnyt oeet v inemrdyueotpuneea nlwlyda eesn xccelu, ssivuep,p ios:se two coins are tossed. The outcome of a coin
toss (heabdo ronr o tna ial) disi fufenraefnfte dcateyd a nbdy the outcome of any other pRorisotisr lacvo Ginlin tsokys/Ssh (uhtteerastdo cokr tail).
For utsweo t hine dceompepnledmeenntt eruvlee.n ts A and B, the probability that A and B will both occur is
Formulas fouGnEdN bEyTRr ymA tLuh liRtsi pUinly LyiEon ugOr tFchl aAes Dst.wDoIT pIOroNb abilitiePs(A.T Thoheri sBf o)i sl=l ot hPwe(Ai ns)g p+ eV cPei(aBnln) r− ud liPea( gAor faa mmndu s lBthi)po Clwiocnsaf ttirwi[om5on–in 4eag]nv Pedan gtess that are not mutually exclusive. The two
events overlap to illustrate the joint event that some people have visited both attractions.
is written symbolically as:
Formulas that are used for the first time are For the expression P(A or B), the word or suggests that A may oCcocnufri rmori nBg Pmaagyes
boxed and numbered for reference. In addi- oSccPuErC. TIAhLis RaUlsLoE in OclFu dMeUs LtThIeP pLIoCsAsiTbIiOlitNy that A andP B(A m aanyd o Bc)c =ur .P T(Ah)iPs (uBs) e of or is[ 5so–m5]e-
times called an inclusive. You could also write P(A or B or both) to emphasize that the
tion, a formula card is bound into the back of
union of the events includes the intersection of A and B.
the text that lists all the key formulas. If weD cEoSmCpRaIBreIN Gth eD AgTeAn: eNrUalM aEnRdIC sApLe MciaElA rSuUleRsE So f addition, the important difference 61
is determining if the events are mutually exclusive. If the events are mutually exclusive,
then thDeE jSoCinRt IBpIrNoGba DbAilTitAy : PN(UA MaEnRdI CBA) Lis M 0E AaSnUd RwEeS could use the special rule of additio7n9.
Software Solution
Exercises Otherwise, we must account for the joint probability and use the general rule of addition.
lin39470_ch05_130-172.indd 142 10/08/19 06:43 PM
We can use a statistical software package to find many measures of location.
EXERCISES
Exercises are included alinf39t4e70r_c h05_130-172.indd 145 EXAMPLE 10/08/19 06:43 PM
sections within the chapter and What isF othrE eEXx peArrocMibseaPsb 4iLli7tEy– 5th2a, dt oa tchaer fdo lclohwoisnegn: at random from a standard deck of cards
a. Compute the sample variance.
at the end of the chapter. Sec- will be eitT habeb.r l eDa e2kt–ein4rgm o ionnre p atah gheee s aa2rm6t? pslheo swtasn dthaerd p droefviita otino nt.he sales of 180 vehicles at Applewood
tion exercises cover the mate- 47.A uCtoon Gsirdoeur pth. eDseet evramluiense a t hseam mpelea:n 7 a, n2d, 6 t,h 2e, manedd 3ia. n selling price.
rial studied in the section. Many SOLU4489T.. ITOheN f oDllaovwei’nsg A fuivteo mvaaltuice sD aoroer ,a r esafemrrpelde : t1o1 i,n 6 E, x1e0r,c 6is,e a 3nd7 ,7 in.stalls automatic garage
exercises have data files avail- We may bSedO oinoLcrlU ionpeTedIn Oteor sNa. dBda stehde opnr oab saabmilpitlye ,o ffo allo kwiningg aanred tthhee t ipmroesb,a inb imlityin uotfe as , hreeqaurti.r eBdu tto
able to import into statistical tahlsiso cwrei5tah0t e.tT hshien ea sh tmapelr aleo T1rabth0snle. e, d Smsomoao. e,mr Ii fdfop iwwplaeeene n ,o dsefa iormnse :ditp gh2 lhay8mt t, a ,o 3cdtdo2hdam,e l2t phk4aaei,mnn 4gipoe6 rsuo,o n4fbi nt4ahs ,b e t4hoial0efirt t ,y psa5 ore4iosfr, fo ai3cts o8pka,uia nr3nceg2et e , r( tdeianhn pdewdour iers4ttht e2ra yd.tr ,he rei ne4 f k eitinhrnr egea sd df oaetlonlco dkiwn ing
software. They are indicated ouEtxpeurct i(shei g3h8li,g whates ds uinrv tehyee ds carse eton tshheoirt )r.e Stueren tohne iEnxvceestlm Teuntot rliaaslt inye tahre. Tlehfet mreasurgltisn to
of 52 cards) to the probability of a heart (there are 13 in a deck of 52 cards) and report
leaarren 1h0o.6w, 1to2 .6cr, e1a4t.e8 , t1h8e. 2fo, 1llo2w.0i,n 1g4 .s8t,a 1ti2s.t2ic, aaln sdu 1m5m.6a.ry. There are 180 vehicles in
with the FILE icon. Answers to that 175 o1u.t ht oef s5tu2 Td chyae, rs dHoso umusseitnoegnt ,t ahT eecx aralecsq,u uMlairoteotemrl weOnowtu,n lwedr e bA hesa stvoeecd iicaootiuousnn atcenoddn dtphureco tkneiedn gato os euf rrhvreoeary.r rtse gtwaridcien.g
the odd-numbered exercises Tutorial #W20e need tow seuebktdraacyt m1 octaerld r afrteosm i nth teh e1 7ar esoa. tLhiest keidn gb eolof hwe ias rtths eis r coooumn rtaetde ofonrl yb ounsicnee.s Ts-hculass, s
in Conntehctere are 16gu ceasrtds sf othr aa ts aarmep eleit hoef r1 h0e maorttse losr. kings. So the probability is 16/52 = .3077.
are in Appendix C.
$101 $97 $103 $110 $78 $87 $101 $80 $106 $88
Card Probability Explanation
52K. ing A consumePr(A w) at ch d =o g 4 o/5r2g anization i4s kcinognsc ienr an ededc ka bofo 5u2t ccarreddsit card debt. A
Computer Output Hespauartri dve ayn o af v1e0r aygoeuP no(Bgf) j auds tu lot sv= ew 1r i3t$h/51 c20r 0e dpite rc amrdo1 nd3teh hb eata gortasfi nmins oat r tdehe etchikra obnf a 5$l2a2 nc,0care0ds0s. sLhisotewde db ethloewy
Kinagr eo ft hHeea artms ountsP e(Aa cahnd y Bo)u =n g 1a/5d2u lt paid 1la ksitn gm oofn hteha.rts in a deck of 52 cards
The text includes many software examples, using Ex- $110 $126 $103 $93 $99 $113 $87 $101 $109 $100
cel, MegaStat®, and Minitab. The software results are
illustrated in the chapters. InstructioLOn3s-5 for the softwareIN TERPRETATION AND USES
examples are referenced in oExnpllaiinn ean d taupptloy rials inO F THE STANDARD DEVIATION
Chebyshev’s theorem
Connect. and the Empirical Rule. The standard deviation is commonly used as a measure to compare the spread in two
or more sets of observations. For example, the standard deviation of the biweekly
amounts invested in the Dupree Paint Company profit-sharing plan is computed to be
lin39470_ch05_130-172.indd 143 $7.51. Suppose these employees are located in Georgia. If the standard d1e0/v08ia/1t9i o 0n6: 4f3o PrM a
groupS ooufr cee:m Mipcrloosoyfte Eexcse lin Texas is $10.47, and the means are about the same, it indicates
that the amounts invested by the Georgia employees are not dispersed as much as
those in TTehxea sm (ebaenc apursoefi t$ i7s .5$11 ,8<4 $31.107.4 a7n).d S tihnec em tehdei aanm iosu $n1ts,8 in8v2e.5s0te. dT hbeys teh etw Goe voargluiae s
emplaoryee leess sa trhea nc l$u4st0e raepda rtm, soore e itchloesr evlayl uaeb ios uret atshoen ambelea.n W, eth cea nm aelsaon sfeoer ftrhoem Gtheeo Ergxicixae l
STATISTICS IN ACTION emploouyetpeust itsh aat m thoerree r weleiarbel e1 8m0e vaeshuircele tsh asno ltdh ea nmde tahne ifro tro tthale p Treoxfiat sw garso $u3p3.1,770.00. We
will describe the meaning of standard error, standard deviation, and other measures
Most colleges report the Cherebpoyrstehd eonv ’thse Touhtpeuot lraetemr in this chapter and in later chapters.
“average class size.” This
information can be mislead- We have stressed that a small standard deviation for a set of values indicates that these
ingE beXcauEse RaveCrageI cSlassE S values are located close to the mean. Conversely, a large standard deviation reveals that
size can be found in several the observations are widely scattered about the mean. The Russian mathematician P. L.
ways. If we find the number Cheb1y3s.h eWv h(1at8 w2o1u–ld1 y8o9u4 r)e dpeovrte alos ptheed m ao tdhael ovarelume ftohra at saellto owf so busse trvoa dtioentes rimf thineere t hwee rme ian itmotualm o f:
of students in each class at proportio na . o1f 0th oeb vsaelruveasti othnast a lnied wnoith tiwno a v saplueecsif iweedr en uthmeb searm oef ?s tandard deviations of the
lin39470_fm_i-xxvi.indd ix a particular university, the mean. F orb .e x6a ombpsleer, vaacticoonrsd ianngd ttoh eCyh webeyres haell vt’hse t hsaemoree?m , at least three 1o1u/0t 9o/f1 9e v 1e1r:y4 4f oAuMr,
result is the mean number or 75%, ocf .t h6e o vbasleurevsa tmiounsst alined b tehetw veaelune tsh we emree a1n, 2p, l3u,s 3 t,w 4o, asntadn 4d?a rd deviations and the
of students per class. If we meanF omri nEuxes rtcwisoe ss t1a4nd–a1r6d, ddeetveiarmtioinnes .t hTeh i(sa )r emlaetaionn, s(bh)i pm aepdpialine, sa rnedg (acr)d mleosdse o.f the shape of
compile a list of the class the distribution. Further, at least eight of nine values, or 88.9%, will lie between plus three
sizes for each student and stand1a4rd. Tdheev iafotilolonws inagn di sm tihneu sn uthmrebee rs toafn odial rcdh adnegveiast iofonrs thoef thlaes tm 7e adna.y sA ta lte tahset 2J4iff yo fL 2ub5e
find the mean class size, we values, or l o9c6a%te, dw aillt ltihee b ceotwrneeer no fp Elulms aSntrde emti nanuds fPiveen nsstaynlvdaanrida dAevevinautieo.ns of the mean.
might find the mean to be Chebyshev’s theorem st4a1t es : 15 39 54 31 15 33
quite different. One school
found the mean number of CHEBYSHEV’S THEOREM For any set of observations (sample or population), the
students in each of its 747 proportion of the values that lie within k standard deviations of the mean is at least
classes to be 40. But when 1 – 1/k2, where k is any value greater than 1.
(continued)
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lin39470_ch03_051-093.indd 79 06/28/19 08:17 PM
