ELEMENTARY
STATISTICS
PICTURING THE WORLD
Fifth Edition
Ron Larson
The Pennsylvania State University
The Behrend College
Betsy Farber
Bucks County Community College
Editor-in-Chief: Deirdre Lynch
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Library of Congress Cataloging-in-Publication Data
Larson, Ron, 1941-
Elementary statistics : picturing the world / Ron Larson, Betsy Farber. -- 5th ed.
p. cm.
ISBN 978-0-321-69362-4
1. Statistics--Textbooks. I. Farber, Elizabeth. II. Title.
QA276.12.L373 2012
519.5--dc22
2010000454
Copyright © 2012, 2009, 2006, 2003 Pearson Education, Inc.
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted,
in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior
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or e-mail at http://www.pearsoned.com/legal/permissions.htm.
1 2 3 4 5 6 7 8 9 10—QGV—14 13 12 11 10
Prentice Hall ISBN 10: 0-321-69362-0
is an imprint of ISBN 13: 978-0-321-69362-4
www.pearsonhighered.com
ABOUT THE AUTHORS III
ABOUT THE AUTHORS
Ron Larson received his Ph.D. in mathematics from the University of
Colorado in 1970. At that time he accepted a position with Penn State
University, and he currently holds the rank of professor of mathematics
at the university. Larson is the lead author of more than two dozen
mathematics textbooks that range from sixth grade through calculus
levels. Many of his texts, such as the eighth edition of his calculus
text, are leaders in their markets. Larson is also one of the pioneers in
the use of multimedia and the Internet to enhance the learning of
mathematics. He has authored multimedia programs, extending from
the elementary school through calculus levels. Larson is a member of
several professional groups and is a frequent speaker at national and
regional mathematics meetings.
Ron Larson
The Pennsylvania State
University
The Behrend College
Betsy Farber Betsy Farber received her Bachelor’s degree in mathematics from Penn
State University and her Master’s degree in mathematics from the College
Bucks County of New Jersey. Since 1976, she has been teaching all levels of mathematics
Community College at Bucks County Community College in Newtown, Pennsylvania, where
she currently holds the rank of professor. She is particularly interested in
developing new ways to make statistics relevant and interesting to her
students and has been teaching statistics in many different modes—with
the TI-83 Plus, with MINITAB, and by distance learning as well as in the
traditional classroom. A member of the American Mathematical
Association of Two-Year Colleges (AMATYC), she is an author of
The Student Edition to MINITAB and A Guide to MINITAB. She served
as consulting editor for Statistics, A First Course and has written
computer tutorials for the CD-ROM correlating to the texts in the
Streeter Series in mathematics.
CONTENTS Preface X How To Study Statistics XV
Supplements XII Index of Applications XVI
Acknowledgments XIV
PART ONE DESCRIPTIVE STATISTICS
1 INTRODUCTION TO STATISTICS 1
2
CHAPTER Where You’ve Been and Where You’re Going 9
1.1 An Overview of Statistics 15
1.2 Data Classification 16
26
í Case Study: Rating Television Shows in the United States 27
1.3 Data Collection and Experimental Design 28
29
í Activity: Random Numbers 31
í Uses and Abuses 32
Chapter Summary 33
Review Exercises 34
Chapter Quiz
í Real Statistics–Real Decisions—Putting It All Together
í History of Statistics—Timeline
í Technology: Using Technology in Statistics
2 DESCRIPTIVE STATISTICS 36
CHAPTER Where You’ve Been and Where You’re Going 37
2.1 Frequency Distributions and Their Graphs 38
2.2 More Graphs and Displays 53
2.3 Measures of Central Tendency 65
79
í Activity: Mean Versus Median 80
2.4 Measures of Variation 98
99
í Activity: Standard Deviation 100
í Case Study: Earnings of Athletes 113
2.5 Measures of Position 114
í Uses and Abuses 115
Chapter Summary 119
Review Exercises 120
Chapter Quiz 121
í Real Statistics–Real Decisions—Putting It All Together 122
í Technology: Monthly Milk Production 124
í Using Technology to Determine Descriptive Statistics
Cumulative Review: Chapters 1–2
IV
CONTENTS V
PART TWO PROBABILITY AND PROBABILITY DISTRIBUTIONS
3 PROBABILITY 126
CHAPTER Where You’ve Been and Where You’re Going 127
3.1 Basic Concepts of Probability and Counting 128
í Activity: Simulating the Stock Market 144
3.2 Conditional Probability and the Multiplication Rule 145
3.3 The Addition Rule 156
í Activity: Simulating the Probability of Rolling a 3 or 4 166
í Case Study: United States Congress 167
3.4 Additional Topics in Probability and Counting 168
í Uses and Abuses 179
Chapter Summary 180
Review Exercises 181
Chapter Quiz 185
í Real Statistics–Real Decisions—Putting It All Together 186
í Technology: Simulation: Composing Mozart Variations with Dice 187
4 DISCRETE PROBABILITY DISTRIBUTIONS 188
CHAPTER Where You’ve Been and Where You’re Going 189
4.1 Probability Distributions 190
4.2 Binomial Distributions 202
216
í Activity: Binomial Distribution 217
í Case Study: Binomial Distribution of Airplane Accidents 218
4.3 More Discrete Probability Distributions 225
í Uses and Abuses 226
Chapter Summary 227
Review Exercises 231
Chapter Quiz 232
í Real Statistics–Real Decisions—Putting It All Together 233
í Technology: Using Poisson Distributions as Queuing Models
VI C O N T E N T S
5 NORMAL PROBABILITY DISTRIBUTIONS 234
CHAPTER Where You’ve Been and Where You’re Going 235
5.1 Introduction to Normal Distributions and 236
the Standard Normal Distribution 249
5.2 Normal Distributions: Finding Probabilities 257
5.3 Normal Distributions: Finding Values 265
266
í Case Study: Birth Weights in America 280
5.4 Sampling Distributions and the Central Limit Theorem 281
291
í Activity: Sampling Distributions 292
5.5 Normal Approximations to Binomial Distributions 293
297
í Uses and Abuses 298
Chapter Summary 299
Review Exercises 300
Chapter Quiz
í Real Statistics–Real Decisions—Putting It All Together
í Technology: Age Distribution in the United States
Cumulative Review: Chapters 3–5
PART THREE STATISTICAL INFERENCE
6 CONFIDENCE INTERVALS 302
CHAPTER Where You’ve Been and Where You’re Going 303
6.1 Confidence Intervals for the Mean (Large Samples) 304
317
í Case Study: Marathon Training 318
6.2 Confidence Intervals for the Mean (Small Samples) 326
327
í Activity: Confidence Intervals for a Mean 336
6.3 Confidence Intervals for Population Proportions 337
344
í Activity: Confidence Intervals for a Proportion 345
6.4 Confidence Intervals for Variance and Standard Deviation 346
349
í Uses and Abuses 350
Chapter Summary 351
Review Exercises 352
Chapter Quiz
í Real Statistics–Real Decisions—Putting It All Together
í Technology: Most Admired Polls
í Using Technology to Construct Confidence Intervals
CONTENTS VII
7 HYPOTHESIS TESTING WITH ONE SAMPLE 354
CHAPTER Where You’ve Been and Where You’re Going 355
7.1 Introduction to Hypothesis Testing 356
7.2 Hypothesis Testing for the Mean (Large Samples) 371
386
í Case Study: Human Body Temperature: What’s Normal? 387
7.3 Hypothesis Testing for the Mean (Small Samples) 397
398
í Activity: Hypothesis Tests for a Mean 403
7.4 Hypothesis Testing for Proportions 404
413
í Activity: Hypothesis Tests for a Proportion 414
7.5 Hypothesis Testing for Variance and Standard Deviation 416
417
í Uses and Abuses 421
A Summary of Hypothesis Testing 422
Chapter Summary 423
Review Exercises 424
Chapter Quiz
í Real Statistics–Real Decisions—Putting It All Together
í Technology: The Case of the Vanishing Women
í Using Technology to Perform Hypothesis Tests
8 HYPOTHESIS TESTING WITH TWO SAMPLES 426
CHAPTER Where You’ve Been and Where You’re Going 427
428
8.1 Testing the Difference Between Means
(Large Independent Samples) 441
442
í Case Study: Readability of Patient Education Materials
8.2 Testing the Difference Between Means
(Small Independent Samples)
8.3 Testing the Difference Between Means 451
(Dependent Samples)
8.4 Testing the Difference Between Proportions 461
í Uses and Abuses 469
Chapter Summary 470
Review Exercises 471
Chapter Quiz 475
í Real Statistics–Real Decisions—Putting It All Together 476
í Technology: Tails over Heads 477
í Using Technology to Perform Two-Sample Hypothesis Tests 478
Cumulative Review: Chapters 6–8 480
VIII C O N T E N T S
PART FOUR MORE STATISTICAL INFERENCE
9 CORRELATION AND REGRESSION 482
CHAPTER Where You’ve Been and Where You’re Going 483
9.1 Correlation 484
500
í Activity: Correlation by Eye 501
9.2 Linear Regression 511
512
í Activity: Regression by Eye 513
í Case Study: Correlation of Body Measurements 524
9.3 Measures of Regression and Prediction Intervals 529
9.4 Multiple Regression 530
í Uses and Abuses 531
Chapter Summary 535
Review Exercises 536
Chapter Quiz 537
í Real Statistics–Real Decisions—Putting It All Together
í Technology: Nutrients in Breakfast Cereals
10 CHI-SQUARE TESTS AND THE F-DISTRIBUTION 538
CHAPTER Where You’ve Been and Where You’re Going 539
10.1 Goodness-of-Fit Test 540
10.2 Independence 551
564
í Case Study: Fast Food Survey 565
10.3 Comparing Two Variances 574
10.4 Analysis of Variance 587
588
í Uses and Abuses 589
Chapter Summary 593
Review Exercises 594
Chapter Quiz 595
í Real Statistics–Real Decisions—Putting It All Together
í Technology: Teacher Salaries
CONTENTS IX
11 NONPARAMETRIC TESTS 596
CHAPTER Where You’ve Been and Where You’re Going 597
11.1 The Sign Test 598
11.2 The Wilcoxon Tests 609
618
í Case Study: College Ranks 619
11.3 The Kruskal-Wallis Test 625
11.4 Rank Correlation 631
11.5 The Runs Test 639
640
í Uses and Abuses 641
Chapter Summary 645
Review Exercises 646
Chapter Quiz 647
í Real Statistics–Real Decisions—Putting It All Together 648
í Technology: U.S. Income and Economic Research
Cumulative Review: Chapters 9–11
APPENDICES A1
A1
APPENDIX A ALTERNATIVE PRESENTATION OF THE STANDARD A2
NORMAL DISTRIBUTION
A7
Standard Normal Distribution Table (0-to-z) A7
Alternative Presentation of the Standard Normal Distribution A8
A11
APPENDIX B TABLES A16
TABLE 1 Random Numbers A18
TABLE 2 Binomial Distribution A19
TABLE 3 Poisson Distribution A20
TABLE 4 Standard Normal Distribution A25
TABLE 5 t-Distribution A25
TABLE 6 Chi-Square Distribution A26
TABLE 7 F-Distribution A26
TABLE 8 Critical Values for the Sign Test A27
TABLE 9 Critical Values for the Wilcoxon Signed-Rank Test
TABLE 10 Critical Values for the Spearman Rank Correlation
TABLE 11 Critical Values for the Pearson Correlation Coefficient
TABLE 12 Critical Values for the Number of Runs
APPENDIX C NORMAL PROBABILITY PLOTS AND THEIR GRAPHS A28
Answers to the Try It Yourself Exercises A30
Answers to the Odd-Numbered Exercises A50
Index
Photo Credits I1
PREFACE
Welcome to Elementary Statistics: Picturing the World, • Section 9.1, Correlation, now defines perfect pos-
Fifth Edition. You will find that this textbook is written itive linear correlation and perfect negative linear
with a balance of rigor and simplicity. It combines step- correlation.
by-step instruction, real-life examples and exercises,
carefully developed features, and technology that makes FEATURES OF THE FIFTH EDITION
statistics accessible to all.
Guiding Student Learning
We are grateful for the overwhelming acceptance of the
first four editions. It is gratifying to know that our vision Where You’ve Been and Where You’re Going
of combining theory, pedagogy, and design to exemplify Each chapter begins with a two-page visual description of a
how statistics is used to picture and describe the world real-life problem. Where You’ve Been shows students how
has helped students learn about statistics and make the chapter fits into the bigger picture of statistics by
informed decisions. connecting it to topics learned in earlier chapters. Where
You’re Going gives students an overview of the chapter,
WHAT’S NEW IN THIS EDITION exploring concepts in the context of real-world settings.
What You Should Learn Each section is organized
The goal of the Fifth Edition was a thorough update of by learning objectives, presented in everyday language in
the key features, examples, and exercises: What You Should Learn. The same objectives are then
used as subsection titles throughout the section.
Examples This edition includes more than 210 exam- Definitions and Formulas are clearly presented in
ples, approximately 50% of which are new or revised. easy-to-locate boxes. They are often followed by
Guidelines, which explain In Words and In Symbols
Exercises Approximately 50% of the more than 2100 how to apply the formula or understand the definition.
exercises are new or revised. We’ve also added 75 concep- Margin Features help reinforce understanding:
tual and critical thinking exercises throughout the text.
StatCrunch® Examples New to this edition are • Study Tips show how to read a table, use technol-
more than 50 StatCrunch Reports. These interactive ogy, or interpret a result or a graph. Round-off
reports, called out in the book with the SC icon, Rules guide the student during calculations.
provide step-by-step instructions for how to use the
online statistical software StatCrunch to solve the exam- • Insights help drive home an important interpre-
ples. Note: Accessing these reports requires a MyStatLab tation or connect different concepts.
or StatCrunch account.
• Picturing the World Each section contains a real-
StatCrunch Exercises New to this edition are more life “mini case study” called Picturing the World
than 80 exercises that instruct students to solve the exer- illustrating important concepts in the section.
cise using StatCrunch. This allows students to practice Each feature concludes with a question and can
the software skills learned in the StatCrunch Examples. be used for general class discussion or group
Note: Solving the exercises using StatCrunch requires a work. The answers to these questions are included
MyStatLab or StatCrunch account. in the Annotated Instructor’s Edition.
Extensive Feature Updates Approximately 50% Examples and Exercises
of the following key features have been replaced, making
this edition fresh and relevant to today’s students: Examples Every concept in the text is clearly illus-
trated with one or more step-by-step examples. Most
• Chapter Openers examples have an interpretation step that shows the stu-
• Case Studies dent how the solution may be interpreted within the
• Putting It All Together: Real Statistics—Real real-life context of the example and promotes critical
thinking and writing skills. Each example, which is num-
Decisions bered and titled for easy reference, is followed by a sim-
ilar exercise called Try It Yourself so students can
Revised Content The following sections have been immediately practice the skill learned. The answers to
changed: these exercises are given in the back of the book, and the
worked-out solutions are given in the Student’s Solutions
• Section 2.2, More Graphs and Displays, now Manual. The Videos on DVD show clips of an instructor
defines misleading graphs. working out each Try It Yourself exercise.
• Section 2.5, Measures of Position, now defines the
modified boxplot.
X
PREFACE XI
StatCrunch Examples New to this edition are more Chapter Quizzes Each chapter ends with a Chapter
than 50 StatCrunch Reports. These interactive reports, Quiz. The answers to all quiz questions are provided in the
called out in the book with the SC icon, provide step-by- back of the book. For additional help, see the step-by-step
step instructions for how to use the online statistical video solutions on the companion DVD-ROM.
software StatCrunch to solve the examples. Go to www.stat- Cumulative Review A Cumulative Review at the end
crunch.com, choose Explore M Groups, and search for of Chapters 2, 5, 8, and 11 concludes each part of the text.
“Larson Elementary Statistics 5/e” to access the StatCrunch Exercises in the Cumulative Review are in random order
Reports. Note: Accessing these reports requires a and may incorporate multiple ideas. Answers to all odd-
MyStatLab or StatCrunch account. numbered exercises are given in the back of the book.
Technology Examples Many sections contain a worked Statistics in the Real World
example that shows how technology can be used to calculate
formulas, perform tests, or display data. Screen displays from Uses and Abuses: Statistics in the Real World
MINITAB®, Excel®, and the TI-83/84 Plus graphing Each chapter features a discussion on how statistical tech-
calculator are given. Additional screen displays are presented niques should be used, while cautioning students about
at the ends of selected chapters, and detailed instructions are common abuses. The discussion includes ethics, where
given in separate technology manuals available with the book. appropriate. Exercises help students apply their knowledge.
Applet Activities Selected sections contain activities
Exercises The Fifth Edition includes more than 2100 exer- that encourage interactive investigation of concepts in the
cises, giving students practice in performing calculations, lesson with exercises that ask students to draw conclusions.
making decisions, providing explanations, and applying The accompanying applets are contained on the DVD that
results to a real-life setting. Approximately 50% of these accompanies new copies of the text.
exercises are new or revised. The exercises at the end of Chapter Case Study Each chapter has a full-page Case
each section are divided into three parts: Study featuring actual data from a real-world context and
questions that illustrate the important concepts of the chapter.
• Building Basic Skills and Vocabulary are short Putting It All Together: Real Statistics–Real
answer, true or false, and vocabulary exercises careful- Decisions This feature encourages students to think crit-
ly written to nurture student understanding. ically and make informed decisions about real-world data.
Exercises guide students from interpretation to drawing of
• Using and Interpreting Concepts are skill or word conclusions.
problems that move from basic skill development to Chapter Technology Project Each chapter has a
more challenging and interpretive problems. Technology project using MINITAB, Excel, and the TI-
83/84 Plus that gives students insight into how technology is
• Extending Concepts go beyond the material pre- used to handle large data sets or real-life questions.
sented in the section. They tend to be more challeng-
ing and are not required as prerequisites for subse- CONTINUED STRONG PEDAGOGY
quent sections. FROM THE FOURTH EDITION
For the sections that contain StatCrunch examples, there are Versatile Course Coverage The table of contents was
corresponding StatCrunch exercises that direct students to use developed to give instructors many options. For instance, the
StatCrunch to solve the exercises. Note: Using StatCrunch Extending Concepts exercises, applet activities, Real
requires a MyStatLab or StatCrunch account. Statistics–Real Decisions, and Uses and Abuses provide suf-
ficient content for the text to be used in a two-semester
Technology Answers Answers in the back of the book course. More commonly, we expect the text to be used in a
are found using tables. Answers found using technology are three-credit semester course or a four-credit semester course
also included when there are discrepancies due to rounding. that includes a lab component. In such cases, instructors will
have to pare down the text’s 46 sections.
Review and Assessment Graphical Approach As with most introductory statis-
tics texts, we begin the descriptive statistics chapter
Chapter Summary Each chapter concludes with a (Chapter 2) with a survey of different ways to display data
Chapter Summary that answers the question What did you graphically. A difference between this text and many others
learn? The objectives listed are correlated to Examples in
the section as well as to the Review Exercises.
Chapter Review Exercises A set of Review Exercises
follows each Chapter Summary. The order of the exercises
follows the chapter organization. Answers to all odd-num-
bered exercises are given in the back of the book.
XII P R E F A C E
is that we continue to incorporate the graphical display of Choice of Tables Our experience has shown that students
data throughout the text. For example, see the use of stem- find a cumulative density function (CDF) table easier to use
and-leaf plots to display data on pages 385 and 386. This than a “0-to-z” table. Using the CDF table to find the area
emphasis on graphical displays is beneficial to all students, under a normal curve is a topic of Section 5.1 on pages
especially those utilizing visual learning strategies. 239–243. Because we realize that some teachers prefer to use
Balanced Approach The text strikes a balance among the “0-to-z” table, we have provided an alternative presenta-
computation, decision making, and conceptual understand- tion of this topic using the “0-to-z” table in Appendix A.
ing. We have provided many Examples, Exercises, and Try It Page Layout Statistics is more accessible when it is care-
Yourself exercises that go beyond mere computation. fully formatted on each page with a consistent open layout.
Variety of Real-Life Applications We have chosen This text is the first college-level statistics book to be writ-
real-life applications that are representative of the majors of ten so that its features are not split from one page to the
students taking introductory statistics courses. We want sta- next. Although this process requires extra planning, the
tistics to come alive and appear relevant to students so they result is a presentation that is clean and clear.
understand the importance of and rationale for studying
statistics. We wanted the applications to be authentic—but MEETING THE STANDARDS
they also need to be accessible. See the Index of
Applications on page XVI. MAA, AMATYC, NCTM Standards This text answers
Data Sets and Source Lines The data sets in the book the call for a student-friendly text that emphasizes the uses
were chosen for interest, variety, and their ability to illus- of statistics. Our job as introductory instructors is not to
trate concepts. Most of the 240-plus data sets contain real produce statisticians but to produce informed consumers of
data with source lines. The remaining data sets contain statistical reports. For this reason, we have included exercis-
simulated data that are representative of real-life situations. es that require students to interpret results, provide written
All data sets containing 20 or more entries are available in explanations, find patterns, and make decisions.
a variety of formats; they are available electronically on the GAISE Recommendations Funded by the American
DVD and Internet. In the exercise sets, the data sets that are Statistical Association, the Guidelines for Assessment and
available electronically are indicated by the icon . Instruction in Statistics Education (GAISE) Project devel-
Flexible Technology Although most formulas in the oped six recommendations for teaching introductory statis-
book are illustrated with “hand” calculations, we assume tics in a college course. These recommendations are:
that most students have access to some form of technology • Emphasize statistical literacy and develop statistical
tool, such as MINITAB, Excel, the TI-83 Plus, or the TI-84
Plus. Because the use of technology varies widely, we have thinking.
made the text flexible. It can be used in courses with no • Use real data.
more technology than a scientific calculator—or it can be • Stress conceptual understanding rather than mere
used in courses that require sophisticated technology tools.
Whatever your use of technology, we are sure you agree knowledge of procedures.
with us that the goal of the course is not computation. • Foster active learning in the classroom.
Rather, it is to help students gain an understanding of the • Use technology for developing conceptual understand-
basic concepts and uses of statistics.
Prerequisites Algebraic manipulations are kept to a ing and analyzing data.
minimum—often we display informal versions of formulas • Use assessments to improve and evaluate student learning.
using words in place of or in addition to variables. The examples, exercises, and features in this text embrace all of
these recommendations.
SUPPLEMENTS Videos on DVD-ROM A comprehensive set of videos tied to the
textbook, containing short video clips of an instructor working
STUDENT RESOURCES every Try It Yourself exercise. New to this edition are section
lecture videos.
Student Solutions Manual Includes complete worked-out solu- (ISBN-13: 978-0-321-69374-7; ISBN-10: 0-321-69374-4)
tions to all of the Try It Yourself exercises, the odd-numbered
exercises, and all of the Chapter Quiz exercises.
(ISBN-13: 978-0-321-69373-0; ISBN-10: 0-321-69373-6)
SUPPLEMENTS XIII
A Companion DVD-ROM is bound in new copies of Elementary TECHNOLOGY SUPPLEMENTS
Statistics: Picturing the World. The DVD holds a number of
supporting materials, including: MyStatLab™ Online Course (access code required)
• Chapter Quiz Prep: video solutions to Chapter Quiz ques- MyStatLab is a series of text-specific, easily customizable online
tions in the text, with English and Spanish captions courses for Pearson Education's textbooks in statistics. For stu-
dents, MyStatLab™ provides students with a personalized interac-
• Data Sets: selected data sets from the text, available in tive learning environment that adapts to each student's learning
Excel, MINITAB (v.14), TI-83 / TI-84 and txt (tab delimited) style and gives them immediate feedback and help. Because
MyStatLab is delivered over the Internet, students can learn at
• Applets: 15 applets by Webster West their own pace and work whenever they want. MyStatLab provides
• DDXL: an Excel add-in instructors with a rich and flexible set of text-specific resources,
including course management tools, to support online, hybrid, or
Graphing Calculator Manual Tutorial instruction and worked out traditional courses. MyStatLab is available to qualified adopters
examples for the TI-83/84 Plus graphing calculator. and includes access to StatCrunch. For more information, visit
(ISBN-13: 978-0-321-69379-2; ISBN-10: 0-321-69379-5) www.mystatlab.com or contact your Pearson representative.
Excel Manual Tutorial instruction and worked-out examples for
Excel. (ISBN-13: 978-0-321-69380-8; ISBN-10: 0-321-69380-9) MathXL® for Statistics Online Course
Minitab Manual Tutorial instruction and worked-out examples for (access code required)
Minitab. (ISBN-13: 978-0-321-69377-8; ISBN-10: 0-321-69377-9)
Study Cards for the following statistical software products are MathXL® for Statistics is a powerful online homework, tutorial,
available: Minitab, Excel, SPSS, JMP, R, StatCrunch, and the TI- and assessment system that accompanies Pearson textbooks in
83/84 Plus graphing calculator. statistics. With MathXL for Statistics, instructors can:
INSTRUCTOR RESOURCES • Create, edit, and assign online homework and tests using
algorithmically generated exercises correlated at the objec-
Annotated Instructor's Edition Includes suggested activities, addi- tive level to the textbook.
tional ways to present material, common pitfalls, alternative for-
mats or approaches, and other helpful teaching tips. All answers to • Create and assign their own online exercises and import
the section and review exercises are provided with short answers TestGen tests for added flexibility.
appearing in the margin next to the exercise.
(ISBN-13: 978-0-321-69365-5; ISBN-10: 0-321-69365-5) • Maintain records of all student work, tracked in MathXL’s
Instructor Solutions Manual Includes complete solutions to all of online gradebook.
the exercises, Try It Yourself exercises, Case Studies, Technology
pages, Uses and Abuses exercises, and Real Statistics–Real With MathXL for Statistics, students can:
Decisions exercises. • Take chapter tests in MathXL and receive personalized
(ISBN-13: 978-0-321-69366-2; ISBN-10: 0-321-69366-3) study plans and/or personalized homework
TestGen® (www.pearsoned.com/testgen) Enables instructors to assignments based on their test results.
build, edit, and print, and administer tests using a computerized • Use the study plan and/or the homework to link directly to
bank of questions developed to cover all the objectives of the text. tutorial exercises for the objectives they need to study.
TestGen is algorithmically based, allowing instructors to create • Students can also access supplemental animations and
multiple but equivalent versions of the same question or test with video clips directly from selected exercises.
the click of a button. Instructors can also modify test bank ques-
tions or add new questions. The software and testbank are avail- MathXL for Statistics is available to qualified adopters. For more
able for download from Pearson Education’s online catalog information, visit our website at www.mathxl.com, or contact your
(www.pearsonhighered.com/irc). Pearson representative.
Online Test Bank A test bank derived from TestGen® available
for download at www.pearsonhighered.com/irc. StatCrunch®
PowerPoint Lecture Slides Fully editable and printable slides that
follow the textbook. Use during lecture or post to a website in an StatCrunch® is an online statistical software website that allows
online course. Most slides include notes offering suggestions for users to perform complex analyses, share data sets, and generate
how the material may effectively be presented in class. These compelling reports of their data. Developed by programmers and
slides are available within MyStatLab or at www.pearsonhigh- statisticians, StatCrunch currently has more than twelve thousand
ered.com/irc. data sets available for students to analyze, covering almost any
Active Learning Questions Prepared in PowerPoint®, these topic of interest. Interactive graphics are embedded to help users
questions are intended for use with classroom response systems. understand statistical concepts and are available for export to
Several multiple-choice questions are available for each chapter enrich reports with visual representations of data. Additional
of the book, allowing instructors to quickly assess mastery of features include:
material in class. The Active Learning Questions are available
to download from within MyStatLab or at • A full range of numerical and graphical methods that allow
www.pearsonhighered.com/irc. users to analyze and gain insights from any data set.
• Flexible upload options that allow users to work with their
.txt or Excel® files, both online and offline.
• Reporting options that help users create a wide variety of
visually appealing representations of their data.
StatCrunch is available to qualified adopters. For more informa-
tion, visit our website at www.statcrunch.com,
or contact your Pearson representative.
XIV ACKNOWLEDGMENTS
ACKNOWLEDGMENTS
We owe a debt of gratitude to the many reviewers who helped us shape and
refine Elementary Statistics: Picturing the World, Fifth Edition.
REVIEWERS OF THE CURRENT EDITION Nancy Johnson, Manatee Community College
Martin Jones, College of Charleston
Dawn Dabney, Northeast State Community College David Kay, Moorpark College
David Gilbert, Santa Barbara City College Mohammad Kazemi, University of North Carolina—Charlotte
Donna Gorton, Butler Community College Jane Keller, Metropolitan Community College
Dr. Larry Green, Lake Tahoe Community College Susan Kellicut, Seminole Community College
Lloyd Jaisingh, Morehead State Hyune-Ju Kim, Syracuse University
Austin Lovenstein, Pulaski Technical College Rita Kolb, Cantonsville Community College
Lyn A. Noble, Florida Community College at Jacksonville— Rowan Lindley, Westchester Community College
Jeffrey Linek, St. Petersburg Jr. College
South Campus Benny Lo, DeVry University, Fremont
Nishant Patel, Northwest Florida State Diane Long, College of DuPage
Jack Plaggemeyer, Little Big Horn College Rhonda Magel, North Dakota State University
Abdullah Shuaibi, Truman College Mike McGann, Ventura Community College
Vicki McMillian, Ocean County College
Cathleen Zucco-Teveloff, Rowan University Lynn Meslinsky, Erie Community College
Lyn A. Noble, Florida Community College at Jacksonville—
REVIEWERS OF THE PREVIOUS EDITIONS
South Campus
Rosalie Abraham, Florida Community College at Julie Norton, California State University—Hayward
Jacksonville Lynn Onken, San Juan College
Lindsay Packer, College of Charleston
Ahmed Adala, Metropolitan Community College Eric Preibisius, Cuyamaca Community College
Olcay Akman, College of Charleston Melonie Rasmussen, Pierce College
Polly Amstutz, University of Nebraska, Kearney Neal Rogness, Grand Valley State University
John J. Avioli, Christopher Newport University Elisabeth Schuster, Benedictine University
David P. Benzel, Montgomery College Jean Sells, Sacred Heart University
John Bernard, University of Texas—Pan American John Seppala, Valdosta State University
G. Andy Chang, Youngstown State University Carole Shapero, Oakton Community College
Keith J. Craswell, Western Washington University Aileen Solomon, Trident Technical College
Carol Curtis, Fresno City College Sandra L. Spain, Thomas Nelson Community College
Cara DeLong, Fayetteville Technical Community College Michelle Strager-McCarney, Penn State—Erie, The Behrend
Ginger Dewey, York Technical College
David DiMarco, Neumann College College
Gary Egan, Monroe Community College Deborah Swiderski, Macomb Community College
Charles Ehler, Anne Arundel Community College William J. Thistleton, SUNY—Institute of Technology, Utica
Harold W. Ellingsen, Jr., SUNY—Potsdam Agnes Tuska, California State University—Fresno
Michael Eurgubian, Santa Rosa Jr. College Clark Vangilder, DeVry University
Jill Fanter, Walters State Community College Ting-Xiu Wang, Oakton Community College
Douglas Frank, Indiana University of Pennsylvania Dex Whittinghall, Rowan University
Frieda Ganter, California State University
Sonja Hensler, St. Petersburg Jr. College
Sandeep Holay, Southeast Community College, Lincoln Campus
We also give special thanks to the people at Pearson Education who worked with us in the development of
Elementary Statistics: Picturing the World, Fifth Edition: Marianne Stepanian, Dana Jones, Chere Bemelmans, Alex
Gay, Kathleen DeChavez, Audra Walsh, Tamela Ambush, Joyce Kneuer, Courtney Marsh, Andrea Sheehan and
Rich Williams. We also thank the staff of Larson Texts, Inc., who assisted with the development and production of
the book. On a personal level, we are grateful to our spouses, Deanna Gilbert Larson and Richard Farber, for their
love, patience, and support. Also, a special thanks goes to R. Scott O’Neil.
We have worked hard to make Elementary Statistics: Picturing the World, Fifth Edition, a clean, clear, and
enjoyable text from which to teach and learn statistics. Despite our best efforts to ensure accuracy and ease of use,
many users will undoubtedly have suggestions for improvement. We welcome your suggestions.
Ron Larson, [emailprotected] Betsy Farber, [emailprotected]
HOW TO STUDY STATISTICS XV
HOW TO STUDY STATISTICS
STUDY STRATEGIES Doing the Homework Learning statistics is like learning to
play the piano or to play basketball. You cannot develop skills just
Congratulations! You are about to begin your study of by watching someone do it; you must do it yourself. The best time
statistics. As you progress through the course, you to do your homework is right after class, when the concepts are
should discover how to use statistics in your everyday still fresh in your mind. Doing homework at this time increases
life and in your career. The prerequisites for this course your chances of retaining the information in long-term memory.
are two years of algebra, an open mind, and a willing-
ness to study.When you are studying statistics, the mate- Finding a Study Partner When you get stuck on a problem, you
rial you learn each day builds on material you learned may find that it helps to work with a partner. Even if you feel you
previously. There are no shortcuts—you must keep up are giving more help than you are getting, you will find that teach-
with your studies every day. Before you begin, read ing others is an excellent way to learn.
through the following hints that will help you succeed.
Keeping Up with the Work Don’t let yourself fall behind in
Making a Plan Make your own course plan right now! A good this course. If you are having trouble, seek help immediately—from
rule of thumb is to study at least two hours for every hour in class. your instructor, a statistics tutor, your study partner, or additional
After your first major exam, you will know if your efforts were suf- study aids such as the Chapter Quiz Prep videos on DVD-ROM
ficient. If you did not get the grade you wanted, then you should and the Try It Yourself video clips on the videos on DVD-ROM.
increase your study time, improve your study efficiency, or both. Remember: If you have trouble with one section of your statistics
text, there’s a good chance that you will have trouble with later
Preparing for Class Before every class, review your notes from sections unless you take steps to improve your understanding.
the previous class and read the portion of the text that is to be cov-
ered. Pay special attention to the definitions and rules that are Getting Stuck Every statistics student has had this experience:
highlighted. Read the examples and work through the Try It You work a problem and cannot solve it, or the answer you get
Yourself exercises that accompany each example. These steps does not agree with the one given in the text. When this happens,
take self-discipline, but they will pay off because you will bene- consider asking for help or taking a break to clear your thoughts.
fit much more from your instructor’s presentation. You might even want to sleep on it, or rework the problem, or
reread the section in the text. Avoid getting frustrated or spending
Attending Class Attend every class. Arrive on time with your too much time on a single problem.
text, materials for taking notes, and your calculator. If you must
miss a class, get the notes from another student, go to a tutor or Preparing for Tests Cramming for a statistics test seldom works.
your instructor for help, or view the appropriate Video on DVD. If you keep up with the work and follow the suggestions given here,
Try to learn the material that was covered in the class you missed you should be almost ready for the test. To prepare for the chapter
before attending the next class. test, review the Chapter Summary and work the Review Exercises
and the Cumulative Review Exercises. Then set aside some time to
Participating in Class When reading the text before class, review- take the sample Chapter Quiz. Analyze the results of your Chapter
ing your notes from a previous class, or working on your homework, Quiz to locate and correct test-taking errors.
write down any questions you have about the material. Ask your
instructor these questions during class. Doing so will help you (and Taking a Test Most instructors do not recommend studying
others in your class) understand the material better. right up to the minute the test begins. Doing so tends to make
people anxious. The best cure for test-taking anxiety is to pre-
Taking Notes Draw a vertical pare well in advance. Once the test begins, read the directions
During class, be line on your carefully and work at a reasonable pace. (You might want to
read the entire test first, then work the problems in the order in
sure to take notes note paper. which you feel most comfortable.) Don’t rush! People who hurry
tend to make careless errors. If you finish early, take a few
on definitions, Take notes After class, reread moments to clear your thoughts and then go over your work.
examples, concepts, here.
and rules. Focus on Learning from Mistakes After your test is returned to you, go
your notes and write over any errors you might have made. Doing so will help you
the instructor’s cues comments, questions, avoid repeating some systematic or conceptual errors. Don’t dis-
to identify impor- or explanations here. miss any error as just a “dumb mistake.” Take advantage of any
tant material. Then, mistakes by hunting for ways to improve your test-taking skills.
as soon after class
as possible, review your notes and add any explanations that will
help to make your notes more understandable to you.
XVI INDEX OF APPLICATIONS
INDEX OF APPLICATIONS
Biology and Life Manufacturer Groom’s age, 608 Temperature, 63, 638
Sciences claims, 246 Height, 6, 13, 486, 496, 649 Cleveland, OH, 47
earnings, 109 Denver, CO, 12
Air pollution, 31, 471 of men, 77, 86, 110, 253, 263, Mohave, AZ, 29
Air quality, 115 Product assembly, 175 277, 507, 515 Pittsburgh, PA, 604
Alligator, 125 Quality control, 7, 31, 34, 35, 129, San Diego, CA, 605
Atlantic croaker fish, 49 of women, 48, 86, 253, 263, 277,
Beagle, 48, 253 198 401 Tornadoes, 125, 197
Box turtle, 235 Sales, 2, 50, 64, 119, 158, 192, 194, UV Index, 62
Brown trout, 220 Home, 7 Water contamination, 350
Cats, 182, 259, 402, 447 195, 222, 375, 520, 521, 528, Household, 200, 300, 419, 473 Water temperatures, 622
Dogs, 142, 153, 182, 198, 200, 259, 578 Left-handed, 164 Wet or dry, Seattle, WA, 140
Salesperson, 76, 107 Marriage, 5, 29 Wildland fires, 531
402, 447 Shipping errors, 368 Most admired polls, 351
Elephants, 450, 527 Small business Moving out, 468 Economics and Finance
Endangered species, 590 owners, 214 New car, 130
Environmentally friendly websites, 208 New home prices, 119 Account balance, 75
Telemarketing, 190 Population Accounting, 199
product, 287 Wal-Mart shareholder’s equity, Allowance, 589
Fish, 13, 526 528 Alaska, 87 ATM machine, 50, 52
Fisher’s Iris data set, 58 Warehouses, 154, 177 Brazil, 96 Audit, 133, 162, 335
Florida panther, 339 Website costs, 343 cities, fastest growing, 1 Bill payment, 332, 550
Fruit flies, 110 cities, largest numerical Book spending, 49
Green turtle migration, 294–295 Combinatorics Charitable donations, 332, 499
House flies, 62, 276 increase, 1 Children’s savings accounts, 296
Kitti’s hog-nosed bat, 294, 296 Answer guessing, 154, 212 Florida, 87 Commission, 113
Koalas, 30 Area code, 176 U.S., 9, 95 Credit card, 29, 112, 213, 273, 347,
Oats, 629 Letters, 172, 175 West Ridge County, 20–22
Ostrich, 481 License plates, 131, 176, 181 Retirement age, 51 396, 432, 605
Pets, 94, 215 Password, 174, 176 Shoe size, 49, 507, 515 Credit score, 475, 641
Plants, 215 Security code, 169, 184, 185 U.S. age distribution, 163, 181, Debit card, 31
Rabbits, 220 Debt and income, 628
Salmon, 135, 147 Computers 299 Depression, 14
Sharks, 230 U.S. unemployment rate, 116 Dividends and earnings, 497, 498
Snapdragon flowers, 142 Computer, 7, 8, 201, 209, 253–255, Weight of newborns, 13, 238, 480, Dow Jones Industrial Average, 77
Soil, 175, 570 332, 368 Economic power, 8
Soybeans, 24 A6 Emergency savings, 153
Swans, 369 Computer software engineer Zip codes, 29 Executive compensation, 417
Threatened species, 590 earnings, 343 Financial advice, 213
Trees, 13, 48, 170, 270, 368, 522, Earth Science Financial debt, 605
Disk drive, 586 Financial shape, 177
527 Internet, 31, 70, 152, 183, 229, Alternative energy, 333, 349 Forecasting earnings, 5
Vertebrate groups, 590 Carbon footprint, 300 Gross domestic product, 485, 488,
Veterinarian, 447 287, 288, 369, 399, 429, 467, Clear days, May, San Francisco,
Waste, 324, 389, 394 497, 498, 506, 560 493, 502, 504, 514, 516, 518,
Water, 175, 385 Microchips, 224 CA, 210 523
Monitor, 273, 445 Climate conditions, 189 Home owner income, 7
conductivity, 391 Mozilla® Firefox®, 286 Cloudy days, June, Pittsburgh, Honeymoon financing, 213
consumption, 95 Operating system, 7 Income, 125, 496, 592, 649
hardness, 343 Printers, 96 PA, 210 Investments, 63
pH level, 391 Security, 297 Cyanide levels, 350 IRAs, 521, 522
Wheat, 591, 629 Social networking sites, 61, 197, Earthquakes, 260, 499 IRS tax filing wait times, 394
203, 304, 306–308, 310, 605 Global warming, 3, 334 Manufacturing, 63
Business Typing speed, 74 Green products, 75 Missing tax deductions, 347, 348
Videos, online, 349 Hurricane, 200, 223, 231 Money managing, 7
Advertisem*nts, 228, 400, 585 Website, visitors per day, 600 Mortgages, 324
Advertising and sales, 516 Windows® Internet Explorer®, relief efforts, 24 Mutual funds, 306, 648
Bankruptcies, 223 286 Ice thickness, 61 Paycheck errors, 224
Beverage company, 143 Lightning strikes, 231 Primary investor in household, 7
Board of directors, 169 Demographics Nitrogen dioxide, 384 Profit and loss analysis, 199
Book sales, nonfiction, 14 Old Faithful,Yellowstone Raising a child, cost, 380, 418
Bookbinding defects, 154 Age, 6, 25, 29, 31, 60, 76, 134, 157, Restaurant spending, 96, 437
Chief financial officers, survey of, 161, 496, 544, 546, 558 National Park, 44, 94, 279, Retirement income, 213
486, 489, 491, 503, 504, 514 Salaries, 4, 6, 7, 29, 31, 48, 63, 64,
212 Birth weights in America, 265 Precipitation 72, 75, 80–83, 91, 97, 117, 119,
Clothing store purchases, 212 Bride’s age, 90, 608 Baltimore, MD, 223 124, 201, 276, 296, 349, 379,
Consumer ratings, 459 Cars per household, 94 Orlando, FL, 12 383, 394, 395, 412, 431, 439,
Defective parts, 162, 176, 181, Children per household, 88 San Francisco, CA, 343 440, 471, 508, 523, 524–526,
City rent, 296 Tampa, FL, 222 535, 572, 582, 583, 586, 595,
185, 223 Drive to work, 197 Rain, 645 615, 616, 622, 623, 643
Executives, 111, 184 Ear wiggling, 153 Saffir-Simpson Hurricane Scale, Baltimore, MD, 593
Fortune 500 companies, 29, 191 Education, 593 231 Boston, MA, 92
Free samples, 402 Employee, 21, 134, 136, 141, 176, Seawater, 312
Inventory shrinkage, 57 Snowfall, 636
177, 179, 181, 184, 198, 276, January average, 14
524 –526 Mount Shasta, CA, 224
Eye color, 13, 150, 157 New York county, 275
Nome, AK, 197
Sunny and rainy days, 189, 193
Seattle, WA, 140
INDEX OF APPLICATIONS XVII
Chicago, IL, 83, 92 Musical training, 443 Game show, 138 Jelly beans, 182
Dallas, TX, 92 Nursing major, 152, 156, 164 Games of chance, 143, 199, 200 Juice drinks, 312
Jacksonville, FL, 593 Online classes, opinion, 30 Home theater system, 312, 358, Leftovers, 331
New York, NY, 92 Physics minors, 29 M&M’s, 229, 544–545
San Francisco, CA, 593 Plus/minus grading, 182 363, 572 Meat consumption, 295
Savings, 213, 548 Preschool, 439 Horse race, 176 Melons, 421
more money, 348 Public schools, 163, 535 Lottery, 139, 172, 175, 177, 179, Menu, 139, 175
Spending before traveling, 89 Quiz, 139, 199, 203 Milk
Stock, 113, 143, 181, 228, 229, 315, Recess, 124 212, 224
Reliability of testing, 155 Magazine, 8, 116, 184 consumption, 246
519, 521, 570 SAT scores, 4, 52, 92, 104, 201, Monopoly game, 146 containers, 277
McDonald’s, 535 Motion Picture Association, processing, 407
Stock market, 144 247, 252, 254, 278, 324, 421, production, 121, 532, 533
Tax preparation methods, 540, 434, 456, 481, 529, 591, 606, ratings, 12, 161 Multivitamin, 287
607 Movie ticket prices, 117 Oranges, 264
541, 543 Scholarship, 182 Movies, 25, 31, 150, 183–184, 296, Peanuts, 255
Taxes, 521, 522 Science assessment tests, 411, Pepper pungencies, 50
U.S. exports, 77 475, 572 558, 559 Pizza, 176
U.S. income and economic Secondary school teachers, 431 budget and gross, 497 Potatoes, 73, 527
Student advisory board, 172 on phone, 213 Protein, 505
research, 647 Student-athletes, 197 MP3 player, 13, 275, 368 Restaurant, 466, 557, 569
Utility bills, 105, 254, 255 Student ID numbers, 13, 137 Netbook, 185 Burger King, 573
Vacation cost, 7, 395, 418, 421, 433 Student loans, 496, A29 New Year’s Eve, 116 Long John Silver’s, 471
Student safety, 558 News, 289 McDonald’s, 573
Education Student sleep habits, 326 Nielsen Company ratings, 15, 25 serving, 420
Study habits, 30, 438, 497, 498, Oscar winners, ages, 106, 112 Wendy’s, 471
Achievement, 558, 593 506 Political blog, 49 Rye, 527
ACT, 8, 247, 253, 294, 437 Teaching experience, 301, 590 Powerball lottery, 186 Salmonella, 359
Ages of students, 68, 291, 309, Teaching methods, 449, 472 Radio stations, 118 Saturated fat intake, 51
Test grades/scores, 51, 60, 61, 63, Raffle ticket, 135, 184, 196 Sodium, 316, 417, 471, 507
313, 314, 480 69, 72, 75, 76, 107, 109, 110, Reading, 207, 333 Soft drinks, 255, 422
Alumni, annual contributions by, 116, 118, 125, 138, 238, 264, Rock concert, fan age, 66 Sports drink, 369, 407
428, 497, 498, 506, 550, 638, Satellite television, 117 Storing fish, 4
485, 489, 491, 503 649 Song lengths, 111 Sugar, 507, 531, 532
Books, 197, 312 Test scores and GNI, 629 Summer vacation, 151 Supermarket, 95, 250
Business schools, 10 Tuition, 73, 101, 102, 369 Television, 6, 10, 12, 108, 109, 118, Tea drinker, 143
Career counselors, 124 U.S. history assessment tests, 411, Vegetables, 276, 421
Class size, 395, 618 572 199, 228, 437, 439, 532, 533 Vending machine, 264
Classes, 181 Vocabulary, 496 3D TV, 282, 285 Water, 314, 383, 496
College costs, 548, 649 HDTV, 282, 284
College graduates, 288 Engineering late night, 582 Government
LCD TV, 342
jobs, 17 Aerospace engineers, 349 networks, Pittsburgh, PA, 10 Better Business Bureau, 57
College president, 31 Bolts, 341, 420 The Price Is Right, 126, 127 Congress, 167, 335
College professors, 162 Brick mortar, 50 top-ranked programs, 15
College students, 161 Building heights Video games, 31, 57, 174, 209, 368 gender profile, 14, 161
issue when voting, 7
per faculty member, 115 Atlanta, GA, 506 Food and Nutrition Department of Energy, gas
Continuing education, 560 Houston, TX, 115
Day care, 439 Cooling capacity, 505 Apple, 61, 264 prices, 3
Degrees, 56, 400 Flow rate, 368 Beef, 627 Federal bailout, 417
Degrees and gender, 185 Gears, 256 Caffeine, 95, 384, 494, 624 Federal funding, alternative
Doctorate degree, 627, 642, 643 Horsepower, 31 Calories, 368, 507, 508, 572
Dormitory room prices, 117 Liquid dispenser, 256, 631 Candy, 601 energy, 349
Education, study plans, 468 Machine Carbohydrates, 316, 411, 573 Federal income tax, 474
Educational attainment and calibrations, 278 Carrots, 264 Federal pension plan, 521, 522
part supplier, 140 Cereal, 247, 507, 537 Governor, Democrats, 8
work location, 553 Nails, 256 Cheese, 314 Home Security Advisory System,
Elementary school students, 183, Nut, 438 Chicken, 627
Petroleum engineering, 4 Chicken wings, 228 29
431 Plastic injection mold, 592 Coffee, 77, 95, 159, 276, 320–321, Legal system in U.S., 359
Enrollment, 201, 227, 466, Plastic sheet cutting, 314 Registered voters, 6, 35
Repairs, 176 383, 546 Securities and Exchange
626 – 627 Resistors, 293 Cookies, 213
Expenditure per student, 419 Tensile strength, 448 Corn, toxin, 173 Commission, 35
Extracurricular activities, 199, Washers, 255, 438 Dark chocolate, 413 Senate, 637
Delivery, 547 Senators, years of service, 124
358, 363, 364 Entertainment Dried fruit, 417 Tax cut, 556
Faculty hours, 394, 395 Energy bar, 417 U.S. Census
Final exam, 428 Academy Award, winning, 133 Fast food, 230, 384, 564
Final grade, 75, 76, 525, 526 Best-selling novel, 133 Fat, 505, 508 accuracy, 401
Financial aid, 561 Blu-rayTM players, 342, 644 Fat substitute, 23 participation, 347
Genders of students, 634 Broadway tickets, 14 Food away from home, money undercount, 4
GPA, 60, 74, 146, 324, 485, 494, Concert, 634 U.S. government system, 152
spent on, 419
529, 579, 586 attendance, 197 Fruit consumption, 295 Health and Medicine
Health-related fields, study plans, tickets, 73, 289 Hot chocolate, 508
Hot dogs, 206, 507 Allergy medicines, 23, 340
468 Ice cream, 264, 277, 333, 551, 552, Alzheimer’s disease, 150
Highest level, 141 Appetite suppressant, 452
Homework, 325 554–555, 572 Arthritis, 24, 469
Law school, 396, 642
Mathematics assessment test, 444
MCAT scores, 49, 73, 383
Medical school, 149
Midterm scores, 428, 525, 526
XVIII INDEX OF APPLICATIONS
Assisted reproductive Length of visit, physician’s office, Square footage, 506, 605 Conversation, most annoying
technology, 152, 232 589 Subdivision, 170 phrase, 347, 348
Tacoma Narrows Bridge, 163, 220
Asthma, 401 Lower back pain, 606 Unit size, 605 Cordless drills, 342
Bacteria vaccine, 27 Lung cancer, 368 Crawling, 514
Bariatric surgery, 375 Managed health care, 29 Law Customer service, 24
Blood, 6, 197 Maximal oxygen consumption, Die roll, 35, 72, 77, 128, 129, 132,
Booster seat, 347, 348
donations, 156, 159, 198, 214 447 California Peace Officer 136, 138, 139, 140, 143, 146,
pressure, 17, 31, 62, 150, 246, Migraines, 466 147, 150, 156–158, 162, 166,
MRI, 531, 532 Standards and Training test, 181, 183, 185, 197
357, 428, 440, 458, 460, 496, Musculoskeletal injury, 559 260 Digital camera, 342, 348
505 Nausea, 557 Case of the vanishing women, Digital photo frames, 66
type, 139, 154, 214, 296 No trouble sleeping, 214 423 Dog microchips, 638
BMI, 75, 324 Nutrients entering bloodstream, Child support, 270 DVDs, 170, 275
Body measurements, 512 Crime, 497, 498, 621–622 DVRs, 138, 313
Body temperature, 11, 13, 366, 569 Fraud, 133, 594, 597 Electricity consumption, 384
386, 455, 496 Obesity, 8, 150 Jury selection, 149, 173, 175 Electricity cost, 592
BRCA gene, 151 Organ donors, 287 Police officers, 368 Employment and educational
Breast cancer, 27 Pain relievers, 577–578 Prison sentence, length of, 641 attainment, 562–563
Calcium supplements, 473, 615, Patient education material, 441 Repeat offenders, 603 Energy cost, 584, 586
641 Personal hygiene, 23 Safe Drinking Water Act, 350 Energy efficiency, 505
Cavities, 531, 532 Physical examination, 5 Seat belts, 463 Eye survey, contacts, glasses, 73,
Cholesterol, 6, 73, 113, 252, 254, Physician assistant, 440 Software piracy, 355 165
255, 261, 314, 459, 464, 573 Physician’s intake form, 14 Speeding, 146, 395, 644 Farm values, 93, 94, 296, 504
Chronic medications, 481 Physicians, leaving medicine, 29 Theft, 645 Fire drill, 385
Colds, 603 Placebo, 557, 559, 562 identity, 133, 301, 597 Floral arrangement, 301
Cough syrup, 341, 343 Plantar heel pain, 465 Fluorescent lamps, 384
Cyanosis, 212 Plaque buildup in arteries, 458 Miscellaneous Full-body scanner, 413
Dentist, 213, 245, 332 Pregnancy study, Cebu, Furnaces, 358, 363
Diabetes, 2, 150, 462 911 calls, 199 Furniture store, 368
Diabetic, 16 Philippines, 30 Aggressive behavior, children, Garden hose, 368
Diet, 25, 31, 229, 440 Prescription drugs, 24, 616 Gas grill, 533–535
Doctor, tell truth, 347 Prostate cancer, 31 469 Gas station, 118, 227
Drinking habits, 24 Pulse rate, 51, 342, 471, 486 Air conditioners, 206 Gasoline, volume of, 191
Drug testing, 140, 290, 460, 462, Recovery time, 366 Appliances, 571 Gasoline consumption, 50
466, 557, 559, 562 Registered nurse, 119, 440, 508, Archaeology, 91 Gender of children, 181
Emergency room visits, 333 Bacteria, 510 Ghost sighting, 332
Emphysema, 146 623 Badge numbers, police officers, Global positioning system (GPS)
Exercise, 17, 24, 25, 119, 146, 485, Rotator cuff surgery, 148 navigators, 39, 41–46
556, 628 Sleep, 227, 263, 507, 523, 532, 533 31 Goals, 560
Flu, 135 Ball, numbered, 150 Grammatical errors, 456
Fluorouracil, 440 deprivation, 8, 24, 30 Bank, 343, 557, 641 Greeting cards, 227
Gastrointestinal stromal tumor, Sleep apnea, 150 Barrel of oil, 62 Grip strength, 458
466 Smoking, 19, 31, 143, 146, 230, Battery, 153, 255, 394 Grocery store waiting times, 13
Growth of a virus, 23 Birthday, 129, 154, 155, 161, 549 Guitar, string tension, 197
Headaches, 457, 643 284, 368, 383, 401, 427, 463, Births, 279 Hats, 421
Health care costs, 347, 348 464, 534, 559 Bracelets, 175 Hindenburg, 8
Health care coverage, 420 Stem cell research, 22 Breaking up, 222 Hotel rooms, 74, 115, 313, 342,
Health care rating, 300 Stress, 150 Calculators, defects, 184 412, 591
Health care reform, 124 Sudden infant death syndrome, 7 Camcorder, 63 Impression of past decade, 133
Health care visits, 369, 541 Surgery, 212 Camping chairs, 199 Lawn mowers, 369
Health club, 254, 419 corneal transplant, 231 Car dealership, 321 Life on other planets, 474
Health improvement program, procedure, 203 Car wash, 174 Light bulbs, 325, 368, 384
298 survival, 152 Carbon dioxide emission, 227, Liquid volume of cans, 115
Healthy foods, 25 Triglyceride levels, 51, 251 Living on your own survey, 73
Heart disease, 413 Ulcers, 150 413, 485, 488, 493, 502, 504, Marbles, 203
Heart medication, 369 Vitamins, 124, 335, 341, 343 516, 518, 523, 536 Memory, 8
Heart rate, 11, 75, 270, 322, 434, Weight, 72, 428 Cards, 132, 138, 139, 143, 145–147, Metacarpal bone length, 649
616 Weight loss, 18, 245, 384, 409, 452, 150, 157, 158, 162, 173, 177, Metal detector, 227
Heart rhythm abnormality, 7 457, 459, 473, 496 181, 183, 184, 202, 204 Microwave, 421
Heart transplant, 263, 279, 450 Cellular phone, 7, 29, 59, 61, 67, Middle initial, 138
Herbal medicine, 460, 642 Housing and 205, 228, 249, 269, 399, 401 Mozart, 187
HIV, 420 Construction Charitable donations, CEOs in Museum attendance, 601
Hospital, 52 Syracuse, NY, 30 Music downloads, 355
Hospital beds, 76 City house value, 296 Charity, 164 Nail polish, 333
Hospital costs, 412 Construction, 322 Chess, 368 NASA budget, 62
Hospital length of stay, 77, 325, Home insurance, 623 Chlorine levels in a pool, 407 Natural gas, 2, 648
411, 476, 583, 624 House size, 358, 363, 365, 549 Chores, 229 Nitrogen oxides emission, 536
Hospital waiting times, 325 Housing contract, 287 Clocks, 368 Nuclear power plants, 100, 102,
Influenza vaccine, 7, 19 Monthly apartment rents, 120 Cloning, 400 103
Irinotecan, 440 Prices of condominiums, 67, 569 Coffee shop, remodeling, 18 Number generator, 638
Kidney cancer survival rate, 296 Prices of homes, 68, 272, 437, 506, Coin toss, 35, 128, 129, 134, 137, Oil, 29, 64, 520, 521
Kidney transplant, 23, 223, 265, 138, 139, 146, 147, 179, 181, Opinion poll, 13
450 585, 600, 604 182, 229, 359, 477, 637 Pages, section, 228
Knee surgery, 148, 204, 611 Realty, 139 Consumption
Lead levels, 31 Residence, rent or own, 24 energy, 584, 624
Room and board, 272 fuel, 572
Sales price, new apartments, 645 Contact with parents, 607
Security system, 131, 140, 174,
368
INDEX OF APPLICATIONS XIX
Paint, 368, 644 Shark attacks, 230 Traffic signal, 274 Fishing, 207, 227, 409
cans, 277, 314 Tornado deaths, 230, 411 Traffic tickets, 227 Football, 322, 531
sprayer, 315 Travel concerns, 552, 555
Motor Vehicles and Used car cost, 394 college, 13, 142
Parachute assembly, 359 Transportation Vehicle defensive player weights, 118
Phone numbers, 10, 13 Manning, Peyton, 223
Photo printers, 276 Acceleration times, 348 crashes, 560 National Football League, 73,
Pilot’s test, 222 Age of vehicles, 522, 601 eco-friendly, 215
Power failure, 73 Air travel, 30, 32, 65–67, 124 manufacturers, 157 94, 160
Printing company departments, Airfare, 315 owned, 179, 558, 590 Super Bowl, 103, 636
Airplanes, 17, 74, 109, 118 sales, 183, 585 weight, 112, 118
30 Airport scanners, 116 yards per carry, 325
Product warning label, 23 ATV, 368 Political Science Golf, 6, 78, 92, 185, 224, 368, 450,
Puzzle, 17 Auto parts, 224, 301
Questionnaire, 7 Automobile insurance, 390, 614 111th Congress, 13, 14 589, 607, 610, 638
Queuing models, 233 Automobiles, 366 First Lady of the United States, Hockey, 125, 230, 481
Random number selection, 138, Injury, 557
battery, 301, 341, 358, 363, 581 124 Jump height, 453, 478
139 Bicycle helmet, 285 Gubernatorial Election, Virginia, Lacrosse, 174
Recycling, 332 Blood alcohol content, drivers, 30 Marathon training, 317
Refrigerator, 312, 313, 369 Brakes, 278 141 New York City marathon, 62
Salesperson, 13 Braking distance, 252, 260, 295, Officers, 176, 185, 300 Olympics, 163
Smartphones, 35 Political analyst, 35
Social Security numbers, 29 434, 436, 444, 498 Political parties, 67 100-meter times, 648
Socks, 182 Bumper, 447 President’s approval ratings, 17 Winter, 402
Space shuttle Bus, 644 Supreme Court justice, ages, 117 women’s hockey, 168
Car accident, 146, 193, 496 U.S. Presidents Running times, 52
flights, 118 Car occupancy, 163, 200, 220 Skiing, 174
fuel, 231 Carpooling, 200, 208 children, 51 Soccer, 13, 107, 315
menu, 175 Carrying capacities, 13 greatest, 327, 329 Softball, 174
speed, 191 Carry-on luggage, 74, 222 political party, 6 Sporting goods, 119
Speed of sound, 497 Compact cars, consumer testing, Voters, 135, 141, 183, 216, 331, Sports, 288, 289, 549, 584
Spinner, 137, 140 Strength shoes®, 453, 454
Spray-on water repellent, 611 78 454–455, 521, 522 Swimming, 313
Spring break, 7, 30 Crash test, 447, 539 Tennis, 325
Sprinkler system, 383 Department of Motor Vehicles Psychology Volleyball, 75
State troopers, 51 Weightlifting, 325, 434
Statistics students, 20 wait times, 392, 467 Attention-deficit hyperactivity
Sudoku, 168 Diesel engines, 230 disorder, 428 Work
Survey of shoppers, 24 Drivers, 61, 330
Survey of spectators, 6 Driver’s license exam, 182 Depression, 17, 78 Annual wage, 432, 448,
Telephone, 76, 182, 408, 445 Driving time, 271–272 Eating disorders, 74 Career placement, 642
Terrorism, 475 Engine, 256, 532, 533, 632 Experimental group, 175 CEO
Text messages, 25, 53–55, 205, 313 Flights, 155 IQ, 107, 145, 297, 303, 434, 531,
Toothbrush, 124 ages, 61
Toothpaste, 182, 225, 581 annoyances, 214 532 compensation, 30
Transmission, 312, 313 bird-aircraft collisions, 328 Mouthing behavior, 16 Committees, 174, 225
Typographical error, 223, 231 Footwell intrusion, 447 Obsessive-compulsive disorder, Driving distance, 323
UFO sighting, 133 Fuel additive, 617 Earnings, 324, 421, 444, 481, 579,
UFOs, belief in, 335 Fuel economy, 76, 118, 582, 586 559, 562
Vacation, 230, 332 ratings, 534 Passive-aggressive traits, 192, 198, 608, 613–614, 616
Vacuum cleaners, 629 Fuel efficiency, 532, 533, 534 E-mail, 327, 329
Volunteering, 645 Gas prices, 276, 279, 312 195 Employee tenure, 261, 646
Waking times, 346 Hybrid vehicle, 356, 556, 572 Psychological tests, 30, 198, 428 Employment, 14, 58
Washing cars, 295 Intersection accidents, 219–220 Reaction times, 50 Genders of recent hires, 635–636
Washing machine, 139 Mileage, 117, 356, 369, 379, 385, Self-perception, age, 607 Happiness at work, 287
Wealthy people, 37, 40, 41, 43, 44, Training dogs, 30 Hourly earnings, 62, 74, 109, 369,
396, 411, 480
46, 54, 55, 70, 100, 102–104 Motor vehicles, 14, 61, 63, 522 Sports 605, 606, 607, 645
Weigh station, 227 Motorcycles, 343 Industry workers, 142
Well-being index, 583, 586 400-meter dash, women’s, 94 Injuries, 630
Wind energy, 6, 436 fuel economy, 118, 466 40-yard dash, 454 Job offers, 624
Winning a prize, 223 helmet usage, 23, 466, 467 Baseball, 197, 212, 228, 369, 508 Job opening, 139
Yard sale, 77 New highway, 171 Job seekers, 2
Yoga, 64, 419 Oil change, 346, 358, 363, 395 batting averages, 92, 457 Leaving job, 547
Oil tankers, 223 games started, 125 Lumber cutter, 277
Mortality Parking ticket, 150 home run totals, 11 Night shift, 347
Pickup trucks, 151 Major League, 4, 29, 119, 124, Office rentals, 84
Airplane accidents, 217 Pit stop, 374 Overtime hours, 199, 295
Alcohol-related accidents, 561 Power boats, 434 251, 483, 486, 489, 493, 503, Sick days, 74, 229
Emergency response time, 49, Price of a car, 9, 390, 533 510 Time wasted, 578
Public transportation, 289 World Series, 11, 199, 200, 333, Travel time, 47, 60, 74, 312, 323,
408 Speed of vehicles, 60, 73, 105, 638
Heart disease, women, 125 Basketball, 10, 184, 300, 349, 459, 346, 434
Homicides, 547, 548 112, 249, 374 460 Union, 645, 648
Motor vehicle Sports cars, 73, 325, 347 Howard, Dwight, 230 Vacation days, 109
Taxi cab, 369 heights, 6, 65, 96, A28–A29 Work days, 379
casualties, 197, 562, 590 Tires, 110, 198, 264, 278, 301, 649 James, LeBron, 218–219 Work environment, 177, 553
crashes, 63 Towing capacities, 118 NBA draft, 178 Work time and leisure time, 505,
Traffic congestion, 334 vertical jumps, 116
weights, 96 520, 521
Bicycle race, 184 Work weeks, 289
Boston marathon, 31
Curling, 402
Daytona 500, 169
Earnings, athlete, 99
1 INTRODUCTION
TO
CHAPTER STATISTICS
1.1 An Overview of
Statistics
1.2 Data Classification
í CASE STUDY
1.3 Data Collection and
Experimental Design
í ACTIVITY
í USES AND ABUSES
í REAL STATISTICS –
REAL DECISIONS
í HISTORY OF STATISTICS –
TIMELINE
í TECHNOLOGY
In 2008, the population of New
Orleans, Louisiana grew faster than
any other large city in the United
States. Despite the increase, the
population of 311,853 was still well
below the pre-Hurricane Katrina
population of 484,674.
ĪĪ WHERE YOU’VE BEEN
You are already familiar with many of the the United States. If you were in charge of such
practices of statistics, such as taking surveys, a census, how would you do it? How would you
collecting data, and describing populations. What ensure that your results are accurate? These and
you may not know is that collecting accurate many more concerns are the responsibility of the
statistical data is often difficult and costly. United States Census Bureau, which conducts
Consider, for instance, the monumental task of the census every decade.
counting and describing the entire population of
W H E R E Y O U ’ R E G O I N G ĪĪ
In Chapter 1, you will be introduced to the basic their gender, age, race, and ethnicity. Previously,
concepts and goals of statistics. For instance, a long form, which covered additional topics, was
statistics were used to construct the following sent to about 17% of the population. But for the
graphs, which show the fastest growing U.S. cities first time since 1940, the long form is being
(population over 100,000) in 2008 by percent replaced by the American Community Survey,
increase in population, U.S. cities with the largest which will survey about 3 million households a
numerical increases in population, and the year throughout the decade. These 3 million
regions where the cities are located. households will form a sample. In this course,
you will learn how the data collected from a
For the 2010 Census, the Census Bureau sent sample are used to infer characteristics about the
short forms to every household. Short forms ask entire population.
all members of every household such things as
Location of the 25 Fastest
Fastest Growing U.S. Cities Growing U.S. Cities
(Population over 100,000)
Increase (percent) West
10 32%
8
6 South
4 68%
2
LA McKGiilnCbnaereryty,,, TNACZX
TX
NReowunOdrlReoacnsk,,
U.S. Cities with Largest Location of the 25 U.S. Cities with
Numerical Increases Largest Numerical Increases
Increase (number) 60,000 West Northeast
LSaosnNePHAAwhonntougYsoeetolnnroiieksnox,,,,, TNTCAXYZXA50,00044% 4%
40,000
30,000 Midwest
20,000 8%
10,000
South
44%
1
2 C H A P T E R 1 INTRODUCTION TO STATISTICS
1.1 An Overview of Statistics
WHAT YOU SHOULD LEARN A Definition of Statistics Ī Data Sets Ī Branches of Statistics
Ī The definition of statistics Ī A DEFINITION OF STATISTICS
Ī How to distinguish between a As you begin this course, you may wonder: What is statistics? Why should I study
population and a sample and statistics? How can studying statistics help me in my profession? Almost every day
between a parameter and a you are exposed to statistics. For instance, consider the following.
statistic
• “The number of Americans with diabetes will nearly double in the next
Ī How to distinguish between 25 years.” (Source: Diabetes Care)
descriptive statistics and
inferential statistics • “The NRF expects holiday sales to decline 1% versus a 3.4% drop in holiday
sales the previous year.” (Source: National Retail Federation)
• “EIA projects total U.S. natural gas consumption will decline by 2.6 percent
in 2009 and increase by 0.5 percent in 2010.” (Source: Energy Information
Administration)
The three statements you just read are based on the collection of data.
DEFINITION
Data consist of information coming from observations, counts, measurements,
or responses.
Sometimes data are presented graphically. If you have ever read
USA TODAY, you have certainly seen one of that newspaper’s most popular
features, USA TODAY Snapshots. Graphics such as this present information in a
way that is easy to understand.
The use of statistics dates back to census taking in ancient Babylonia, Egypt,
and later in the Roman Empire, when data were collected about matters
concerning the state, such as births and deaths. In fact, the word statistics is derived
from the Latin word status, meaning “state.” So, what is statistics?
DEFINITION
Statistics is the science of collecting, organizing, analyzing, and interpreting
data in order to make decisions.
SECTION 1.1 AN OVERVIEW OF STATISTICS 3
INSIGHT Ī DATA SETS
A census consists of data There are two types of data sets you will use when studying statistics. These data
from an entire population. sets are called populations and samples.
But, unless a population
is small, it is usually DEFINITION
impractical to obtain A population is the collection of all outcomes, responses, measurements, or
all the population counts that are of interest.
data. In most studies, A sample is a subset, or part, of a population.
information must be
obtained from a sample.
A sample should be representative of a population so that sample data
can be used to form conclusions about that population. Sample data must be
collected using an appropriate method, such as random sampling. (You will learn
more about random sampling in Section 1.3.) If they are not collected using an
appropriate method, the data are of no value.
EXAMPLE 1
Identifying Data Sets
In a recent survey, 1500 adults in the United States were asked if they thought
there was solid evidence of global warming. Eight hundred fifty-five of the
adults said yes. Identify the population and the sample. Describe the sample
data set. (Adapted from Pew Research Center)
Solution
The population consists of the responses of all adults in the United States, and
the sample consists of the responses of the 1500 adults in the United States in
the survey. The sample is a subset of the responses of all adults in the United
States. The sample data set consists of 855 yes’s and 645 no’s.
Responses of all adults in the
United States (population)
Responses of adults
in survey (sample)
Try It Yourself 1
The U.S. Department of Energy conducts weekly surveys of approximately
900 gasoline stations to determine the average price per gallon of regular
gasoline. On January 11, 2010, the average price was $2.75 per gallon. Identify
the population and the sample. Describe the sample data set. (Source: Energy
Information Administration)
a. Identify the population and the sample. Answer: Page A30
b. What does the sample data set consist of?
Whether a data set is a population or a sample usually depends on the context
of the real-life situation. For instance, in Example 1, the population was the set of
responses of all adults in the United States. Depending on the purpose of the
survey, the population could have been the set of responses of all adults who live
in California or who have cellular phones or who read a particular magazine.
4 C H A P T E R 1 INTRODUCTION TO STATISTICS
Two important terms that are used throughout this course are parameter and
statistic.
Population undercountSTUDY TIP DEFINITION
(in millions)
The terms parameter and statistic A parameter is a numerical description of a population characteristic.
are easy to remember if you use
the mnemonic device of A statistic is a numerical description of a sample characteristic.
matching the first
letters in population It is important to note that a sample statistic can differ from sample to
parameter and the sample whereas a population parameter is constant for a population.
first letters in sample
statistic. EXAMPLE 2
PICTURING THE Distinguishing Between a Parameter and a Statistic
WORLD Decide whether the numerical value describes a population parameter or a
sample statistic. Explain your reasoning.
How accurate is the U.S. census?
According to a post-census 1. A recent survey of 200 college career centers reported that the average
evaluation conducted by the starting salary for petroleum engineering majors is $83,121. (Source: National
Census Bureau, the 1990 census Association of Colleges and Employers)
undercounted the U.S. popula-
tion by an estimated 4.0 million 2. The 2182 students who accepted admission offers to Northwestern
people. The 1990 census was University in 2009 have an average SAT score of 1442. (Source: Northwestern
the first census since at least University)
1940 to be less accurate than
its predecessor. Notice that the 3. In a random check of a sample of retail stores, the Food and Drug
undercount for the 2000 census Administration found that 34% of the stores were not storing fish at the
was - 1.3 million people. This proper temperature.
means that the 2000 census
overcounted the U.S. population Solution
by 1.3 million people.
1. Because the average of $83,121 is based on a subset of the population, it is
U.S. Census Undercount a sample statistic.
8 7.5 2. Because the SAT score of 1442 is based on all the students who accepted
6.5 admission offers in 2009, it is a population parameter.
6 5.7 5.7 3. Because the percent of 34% is based on a subset of the population, it is a
4 4.0 sample statistic.
2.8 Try It Yourself 2
2 In 2009, Major League Baseball teams spent a total of $2,655,395,194 on
players’ salaries. Does this numerical value describe a population parameter or
0 a sample statistic? (Source: USA Today)
−2 − 1.3 a. Decide whether the numerical value is from a population or a sample.
1940 1960 1980 2000 b. Specify whether the numerical value is a parameter or a statistic.
Year
Answer: Page A30
What are some difficulties in
collecting population data? In this course, you will see how the use of statistics can help you make
informed decisions that affect your life. Consider the census that the U.S.
government takes every decade. When taking the census, the Census Bureau
attempts to contact everyone living in the United States. Although it is impossible
to count everyone, it is important that the census be as accurate as it can be,
because public officials make many decisions based on the census information.
Data collected in the 2010 census will determine how to assign congressional
seats and how to distribute public funds.
SECTION 1.1 AN OVERVIEW OF STATISTICS 5
Ī BRANCHES OF STATISTICS
The study of statistics has two major branches: descriptive statistics and
inferential statistics.
DEFINITION
Descriptive statistics is the branch of statistics that involves the organization,
summarization, and display of data.
Inferential statistics is the branch of statistics that involves using a sample to
draw conclusions about a population. A basic tool in the study of inferential
statistics is probability.
EXAMPLE 3
Descriptive and Inferential Statistics
Decide which part of the study represents the descriptive branch of statistics.
What conclusions might be drawn from the study using inferential statistics?
1. A large sample of men, aged 48, was SSttiillll AAlliivvee aatt 6655 70%
studied for 18 years. For unmarried 90%
men, approximately 70% were alive at Unmarried Men
age 65. For married men, 90% were Married Men
alive at age 65. (Source: The Journal of
Family Issues)
2. In a sample of Wall Street analysts, the percentage who incorrectly forecasted
high-tech earnings in a recent year was 44%. (Source: Bloomberg News)
Solution
1. Descriptive statistics involves statements such as “For unmarried men,
approximately 70% were alive at age 65” and “For married men, 90% were
alive at 65.” A possible inference drawn from the study is that being
married is associated with a longer life for men.
2. The part of this study that represents the descriptive branch of statistics
involves the statement “the percentage [of Wall Street analysts] who
incorrectly forecasted high-tech earnings in a recent year was 44%.” A
possible inference drawn from the study is that the stock market is difficult
to forecast, even for professionals.
Try It Yourself 3
A survey conducted among 1017 men and women by Opinion Research
Corporation International found that 76% of women and 60% of men had a
physical examination within the previous year. (Source: Men’s Health)
a. Identify the descriptive aspect of the survey. Answer: Page A30
b. What inferences could be drawn from this survey?
Throughout this course you will see applications of both branches. A major
theme in this course will be how to use sample statistics to make inferences about
unknown population parameters.
6 C H A P T E R 1 INTRODUCTION TO STATISTICS
1.1 EXERCISES
{ BUILDING BASIC SKILLS AND VOCABULARY
1. How is a sample related to a population?
2. Why is a sample used more often than a population?
3. What is the difference between a parameter and a statistic?
4. What are the two main branches of statistics?
True or False? In Exercises 5–10, determine whether the statement is true or
false. If it is false, rewrite it as a true statement.
5. A statistic is a measure that describes a population characteristic.
6. A sample is a subset of a population.
7. It is impossible for the Census Bureau to obtain all the census data about the
population of the United States.
8. Inferential statistics involves using a population to draw a conclusion about
a corresponding sample.
9. A population is the collection of some outcomes, responses, measurements,
or counts that are of interest.
10. A sample statistic will not change from sample to sample.
Classifying a Data Set In Exercises 11–20, determine whether the data set is
a population or a sample. Explain your reasoning.
11. The height of each player on a school’s basketball team
12. The amount of energy collected from every wind turbine on a wind farm
13. A survey of 500 spectators from a stadium with 42,000 spectators
14. The annual salary of each pharmacist at a pharmacy
15. The cholesterol levels of 20 patients in a hospital with 100 patients
16. The number of televisions in each U.S. household
17. The final score of each golfer in a tournament
18. The age of every third person entering a clothing store
19. The political party of every U.S. president
20. The soil contamination levels at 10 locations near a landfill
Graphical Analysis In Exercises 21–24, use the Venn diagram to identify the
population and the sample.
21. Parties of registered voters in 22. Number of students who
Warren County donate at a blood drive
Parties of Warren Number of
County voters who students who
donate that
respond to have type O+
online survey
blood
SECTION 1.1 AN OVERVIEW OF STATISTICS 7
23. Ages of adults in the United 24. Incomes of home
States who own cellular phones owners in Texas
Ages of adults Incomes of home
in the U.S. who owners in Texas
own Samsung with mortgages
cellular phones
{ USING AND INTERPRETING CONCEPTS
Identifying Populations and Samples In Exercises 25–34, identify the
population and the sample.
25. A survey of 1000 U.S. adults found that 59% think buying a home is the best
investment a family can make. (Source: Rasmussen Reports)
26. A study of 33,043 infants in Italy was conducted to find a link between a
heart rhythm abnormality and sudden infant death syndrome. (Source: New
England Journal of Medicine)
27. A survey of 1442 U.S. adults found that 36% received an influenza vaccine
for the current flu season. (Source: Zogby International)
28. A survey of 1600 people found that 76% plan on using the Microsoft
Windows 7 ™ operating system at their businesses. (Source: Information
Technology Intelligence Corporation and Sunbelt Software)
29. A survey of 800 registered voters found that 50% think economic stimulus is
the most important issue to consider when voting for Congress. (Source:
Diageo/Hotline Poll)
30. A survey of 496 students at a college found that 10% planned on traveling
out of the country during spring break.
31. A survey of 546 U.S. women found that more than 56% are the primary
investors in their households. (Adapted from Roper Starch Worldwide for Intuit)
32. A survey of 791 vacationers from the United States found that they planned
on spending at least $2000 for their next vacation.
33. A magazine mails questionnaires to each company in Fortune magazine’s
top 100 best companies to work for and receives responses from 85 of them.
34. At the end of the day, a quality control inspector selects 20 light bulbs from
the day’s production and tests them.
Distinguishing Between a Parameter and a Statistic In Exercises
35–42, determine whether the numerical value is a parameter or a statistic. Explain
your reasoning.
35. The average annual salary for 35 of a company’s 1200 accountants is $68,000.
36. In a survey of a sample of high school students, 43% said that their mothers
had taught them the most about managing money. (Source: Harris Poll for
Girls Incorporated)
8 C H A P T E R 1 INTRODUCTION TO STATISTICS
37. Sixty-two of the 97 passengers aboard the Hindenburg airship survived its
explosion.
38. In January 2010, 52% of the governors of the 50 states in the United States
were Democrats.
39. In a survey of 300 computer users, 8% said their computers had
malfunctions that needed to be repaired by service technicians.
40. In a recent year, the interest category for 12% of all new magazines was
sports. (Source: Oxbridge Communications)
41. In a recent survey of 2000 people, 44% said China is the world’s leading
economic power. (Source: Pew Research Center)
42. In a recent year, the average math scores for all graduates on the ACT
was 21.0. (Source: ACT, Inc.)
43. Which part of the survey described in Exercise 31 represents the descriptive
branch of statistics? Make an inference based on the results of the survey.
44. Which part of the survey described in Exercise 32 represents the descriptive
branch of statistics? Make an inference based on the results of the survey.
{ EXTENDING CONCEPTS
45. Identifying Data Sets in Articles Find a newspaper or magazine article that
describes a survey.
(a) Identify the sample used in the survey.
(b) What is the sample’s population?
(c) Make an inference based on the results of the survey.
46. Sleep Deprivation In a recent study, volunteers who had 8 hours of sleep
were three times more likely to answer questions correctly on a math test
than were sleep-deprived participants. (Source: CBS News)
(a) Identify the sample used in the study.
(b) What is the sample’s population?
(c) Which part of the study represents the descriptive branch of statistics?
(d) Make an inference based on the results of the study.
47. Living in Florida A study shows that senior citizens who live in Florida
have better memories than senior citizens who do not live in Florida.
(a) Make an inference based on the results of this study.
(b) What is wrong with this type of reasoning?
48. Increase in Obesity Rates A study shows that the obesity rate among boys
ages 2 to 19 has increased over the past several years. (Source: Washington Post)
(a) Make an inference based on the results of this study.
(b) What is wrong with this type of reasoning?
49. Writing Write an essay about the importance of statistics for one of the
following.
• A study on the effectiveness of a new drug
• An analysis of a manufacturing process
• Making conclusions about voter opinions using surveys
SECTION 1.2 DATA CLASSIFICATION 9
1.2 Data Classification
WHAT YOU SHOULD LEARN Types of Data Ī Levels of Measurement
Ī How to distinguish between Ī TYPES OF DATA
qualitative data and
quantitative data When doing a study, it is important to know the kind of data involved. The nature
of the data you are working with will determine which statistical procedures can
Ī How to classify data with be used. In this section, you will learn how to classify data by type and by level of
respect to the four levels measurement. Data sets can consist of two types of data: qualitative data and
of measurement: nominal, quantitative data.
ordinal, interval, and ratio
DEFINITION
Qualitative data consist of attributes, labels, or nonnumerical entries.
Quantitative data consist of numerical measurements or counts.
EXAMPLE 1
Classifying Data by Type
The suggested retail prices of several Ford vehicles are shown in the table.
Which data are qualitative data and which are quantitative data? Explain your
reasoning. (Source: Ford Motor Company)
Model Suggested retail price
Focus Sedan $15,995
Fusion $19,270
Mustang $20,995
Edge $26,920
Flex $28,495
Escape Hybrid $32,260
Expedition $35,085
F-450 $44,145
City Population Solution
Baltimore, MD 636,919 The information shown in the table can be separated into two data sets.
Jacksonville, FL 807,815 One data set contains the names of vehicle models, and the other contains the
Memphis, TN 669,651 suggested retail prices of vehicle models. The names are nonnumerical entries,
Pasadena, CA 143,080 so these are qualitative data. The suggested retail prices are numerical entries,
San Antonio, TX 1,351,305 so these are quantitative data.
Seattle, WA 598,541
Try It Yourself 1
The populations of several U.S. cities are shown in the table. Which data are
qualitative data and which are quantitative data? (Source: U.S. Census Bureau)
a. Identify the two data sets.
b. Decide whether each data set consists of numerical or nonnumerical entries.
c. Specify the qualitative data and the quantitative data. Answer: Page A30
10 C H A P T E R 1 INTRODUCTION TO STATISTICS
Ī LEVELS OF MEASUREMENT
Another characteristic of data is its level of measurement. The level of
measurement determines which statistical calculations are meaningful. The four
levels of measurement, in order from lowest to highest, are nominal, ordinal,
interval, and ratio.
DEFINITION
Data at the nominal level of measurement are qualitative only. Data at this
level are categorized using names, labels, or qualities. No mathematical
computations can be made at this level.
Data at the ordinal level of measurement are qualitative or quantitative. Data
at this level can be arranged in order, or ranked, but differences between data
entries are not meaningful.
When numbers are at the nominal level of measurement, they simply
represent a label. Examples of numbers used as labels include Social Security
numbers and numbers on sports jerseys. For instance, it would not make sense
to add the numbers on the players’ jerseys for the Chicago Bears.
PICTURING THE EXAMPLE 2
WORLD
Classifying Data by Level
In 2009, Forbes Magazine chose Two data sets are shown. Which data set consists of data at the nominal level?
the 75 best business schools in Which data set consists of data at the ordinal level? Explain your reasoning.
the United States. Forbes based
their rankings on the return on (Source: The Nielsen Company)
investment achieved by the
graduates from the class of 2004. Top Five TV Programs Network Affiliates
Graduates of the top five M.B.A. (from 5/4/09 to 5/10/09) in Pittsburgh, PA
programs typically earn more
than $200,000 within five years. 1. American Idol–Wednesday WTAE (ABC)
(Source: Forbes) 2. American Idol–Tuesday WPXI (NBC)
3. Dancing with the Stars KDKA (CBS)
Forbes Top Five U.S. 4. NCIS WPGH (FOX)
Business Schools 5. The Mentalist
1. Stanford Solution
2. Dartmouth
3. Harvard The first data set lists the ranks of five TV programs. The data set consists of
4. Chicago the ranks 1, 2, 3, 4, and 5. Because the ranks can be listed in order, these data
5. Pennsylvania are at the ordinal level. Note that the difference between a rank of 1 and 5 has
no mathematical meaning. The second data set consists of the call letters of
In this list, what is the level of each network affiliate in Pittsburgh. The call letters are simply the names of
measurement? network affiliates, so these data are at the nominal level.
Try It Yourself 2
Consider the following data sets. For each data set, decide whether the data are
at the nominal level or at the ordinal level.
1. The final standings for the Pacific Division of the National Basketball
Association
2. A collection of phone numbers
a. Identify what each data set represents.
b. Specify the level of measurement and justify your answer.
Answer: Page A30
SECTION 1.2 DATA CLASSIFICATION 11
The two highest levels of measurement consist of quantitative data only.
DEFINITION
Data at the interval level of measurement can be ordered, and meaningful
differences between data entries can be calculated. At the interval level, a
zero entry simply represents a position on a scale; the entry is not an inherent
zero.
Data at the ratio level of measurement are similar to data at the interval level,
with the added property that a zero entry is an inherent zero. A ratio of two
data values can be formed so that one data value can be meaningfully
expressed as a multiple of another.
New York Yankees’ An inherent zero is a zero that implies “none.” For instance, the amount
World Series Victories (Years) of money you have in a savings account could be zero dollars. In this case,
the zero represents no money; it is an inherent zero. On the other hand, a
1923, 1927, 1928, 1932, 1936, temperature of 0°C does not represent a condition in which no heat is present.
1937, 1938, 1939, 1941, 1943, The 0°C temperature is simply a position on the Celsius scale; it is not an
1947, 1949, 1950, 1951, 1952, inherent zero.
1953, 1956, 1958, 1961, 1962,
1977, 1978, 1996, 1998, 1999, To distinguish between data at the interval level and at the ratio level,
2000, 2009 determine whether the expression “twice as much” has any meaning in the
context of the data. For instance, $2 is twice as much as $1, so these data are at
the ratio level. On the other hand, 2°C is not twice as warm as 1°C, so these data
are at the interval level.
2009 American League EXAMPLE 3
Home Run Totals (by Team)
Classifying Data by Level
Baltimore 160 Two data sets are shown at the left. Which data set consists of data at the
Boston 212 interval level? Which data set consists of data at the ratio level? Explain your
Chicago 184 reasoning. (Source: Major League Baseball)
Cleveland 161
Detroit 183 Solution
Kansas City 144 Both of these data sets contain quantitative data. Consider the dates of the
Los Angeles 173 Yankees’ World Series victories. It makes sense to find differences between
Minnesota 172 specific dates. For instance, the time between the Yankees’ first and last World
New York 244 Series victories is
Oakland 135
Seattle 160 2009 - 1923 = 86 years.
Tampa Bay 199
Texas 224 But it does not make sense to say that one year is a multiple of another. So,
Toronto 209 these data are at the interval level. However, using the home run totals, you
can find differences and write ratios. From the data, you can see that Texas hit
63 more home runs than Cleveland hit and that New York hit about 1.5 times
as many home runs as Seattle hit. So, these data are at the ratio level.
Try It Yourself 3
Decide whether the data are at the interval level or at the ratio level.
1. The body temperatures (in degrees Fahrenheit) of an athlete during an
exercise session
2. The heart rates (in beats per minute) of an athlete during an exercise session
a. Identify what each data set represents.
b. Specify the level of measurement and justify your answer.
Answer: Page A30
12 C H A P T E R 1 INTRODUCTION TO STATISTICS
The following tables summarize which operations are meaningful at each
of the four levels of measurement. When identifying a data set’s level of
measurement, use the highest level that applies.
Level of Put data in Arrange Subtract Determine if one
measurement categories data in data data value is a
order values
Nominal Yes multiple of another
Ordinal Yes No No
Interval Yes No
Ratio Yes Yes No
No
Yes Yes
No
Yes Yes
Yes
Summary of Four Levels of Measurement
Example of a Data Set Meaningful Calculations
Put in a category.
Nominal Level Types of Shows Televised by a Network
(Qualitative data) For instance, a show televised by
Comedy Documentaries the network could be put into
Drama Cooking one of the eight categories shown.
Reality Shows Soap Operas
Sports Talk Shows Put in a category and put in order.
For instance, a PG rating has
Ordinal Level Motion Picture Association of America Ratings a stronger restriction than a
(Qualitative or Description G rating.
quantitative data)
G General Audiences Put in a category, put in order, and
find differences between values.
PG Parental Guidance Suggested
For instance, 57.2 - 47.6 = 9.6°F.
PG-13 Parents Strongly Cautioned So, May is 9.6° warmer than April.
R Restricted
NC-17 No One Under 17 Admitted
Interval Level Average Monthly Temperatures (in degrees
(Quantitative data) Fahrenheit) for Denver, CO
Jan 29.2 Jul 73.4
Feb 33.2 Aug 71.7
Mar 39.6 Sep 62.4
Apr 47.6 Oct 51.0
May 57.2 Nov 37.5
Jun 67.6 Dec 30.3
(Source: National Climatic Data Center)
Ratio Level Average Monthly Precipitation (in inches) Put in a category, put in order, find
(Quantitative data) for Orlando, FL differences between values, and find
ratios of values.
Jan 2.4 Jul 7.2
Feb 2.4 Aug 6.3 Fisotrwiincsetaanscme,u37c..74h = 2. So, there
Mar 3.5 Sep 5.8 in May. rain in June as
Apr 2.4 Oct 2.7
May 3.7 Nov 2.3
Jun 7.4 Dec 2.3
(Source: National Climatic Data Center)
SECTION 1.2 DATA CLASSIFICATION 13
1.2 EXERCISES
{ BUILDING BASIC SKILLS AND VOCABULARY
1. Name each level of measurement for which data can be qualitative.
2. Name each level of measurement for which data can be quantitative.
True or False? In Exercises 3–6, determine whether the statement is true or
false. If it is false, rewrite it as a true statement.
3. Data at the ordinal level are quantitative only.
4. For data at the interval level, you cannot calculate meaningful differences
between data entries.
5. More types of calculations can be performed with data at the nominal level
than with data at the interval level.
6. Data at the ratio level cannot be put in order.
{ USING AND INTERPRETING CONCEPTS
Classifying Data by Type In Exercises 7–18, determine whether the data are
qualitative or quantitative. Explain your reasoning.
7. telephone numbers in a directory 8. heights of hot air balloons
9. body temperatures of patients 10. eye colors of models
11. lengths of songs on MP3 player 12. carrying capacities of pickups
13. player numbers for a soccer team 14. student ID numbers
15. weights of infants at a hospital 16. species of trees in a forest
17. responses on an opinion poll 18. wait times at a grocery store
Classifying Data by Level In Exercises 19–24, determine whether the data
are qualitative or quantitative, and identify the data set’s level of measurement.
Explain your reasoning.
19. Football The top five teams in the final college football poll released in
January 2010 are listed. (Source: Associated Press)
1. Alabama 2. Texas 3. Florida 4. Boise State 5. Ohio State
20. Politics The three political parties in the 111th Congress are listed below.
Republican Democrat Independent
21. Top Salespeople The regions representing the top salespeople in a
corporation for the past six years are given.
Southeast Northwest Northeast
Southeast Southwest Southwest
22. Fish Lengths The lengths (in inches) of a sample of striped bass caught in
Maryland waters are listed. (Adapted from National Marine Fisheries Service,
Fisheries Statistics and Economics Division)
16 17.25 19 18.75 21 20.3 19.8 24 21.82
14 C H A P T E R 1 INTRODUCTION TO STATISTICS
23. Best Seller List The top five hardcover nonfiction books on The New York
Times Best Seller List on January 19, 2010 are shown. (Source: The New York
Times)
1. Committed 2. Have a Little Faith 3. The Checklist Manifesto
4. Going Rogue 5. Stones Into Schools
24. Ticket Prices The average ticket prices for 10 Broadway shows in 2009 are
listed. (Adapted from The Broadway League)
$149 $128 $124 $91 $96 $106 $112 $95 $86 $74
Graphical Analysis In Exercises 25–28, identify the level of measurement of
the data listed on the horizontal axis in the graph.
25. Over the Next Few Years, How 26. Average January Snowfall
Likely Is It That the United States for 15 Cities
Will Enter a 1930s-Like Depression?
40 5
Percent35
Very30 4
likely
Somewhat25 3
likely20
Not very15
likely10 2
Not at all
likely
Not sure
Number of cities
51
Response 1 3 5 7 9 11
(Source: Rasmussen Reports) Snowfall (in inches)
27. Gender Profile of the (Source: National Climatic Data Center)
111th Congress 28. Motor Vehicle Accidents
500 by Year
400
300 12.0
200 11.5
100 11.0
Number 10.5
Number (in millions) 10.0
9.5
Women Men 2003 2004 2005 2006 2007
Gender Year
(Source: Congressional Research Service) (Source: National Safety Council)
29. The following items appear on a physician’s intake form. Identify the level of
measurement of the data.
a. Temperature b. Allergies
c. Weight d. Pain level (scale of 0 to 10)
30. The following items appear on an employment application. Identify the level
of measurement of the data.
a. Highest grade level completed b. Gender
c. Year of college graduation d. Number of years at last job
{ EXTENDING CONCEPTS
31. Writing What is an inherent zero? Describe three examples of data sets
that have inherent zeros and three that do not.
32. Writing Describe two examples of data sets for each of the four levels of
measurement. Justify your answer.
CASE STUDY 15
Rating Television Shows in the CASE STUDY
United States
The Nielsen Company has been rating television programs TV programs viewed by all households
for more than 60 years. Nielsen uses several sampling in the United States (114.5 million households)
procedures, but its main one is to track the viewing
patterns of 20,000 households. These contain more than TV programs viewed
45,000 people and are chosen to form a cross section of by Nielsen sample
the overall population. The households represent various (20,000 households)
locations, ethnic groups, and income brackets. The data
gathered from the Nielsen sample of 20,000 households
are used to draw inferences about the population of all
households in the United States.
Top-Ranked Programs in Overall Viewing for the Week of 11/23/09–11/29/09
Rank Program Name Network Day, Time Rating Share Audience
Rank Last Week
1 2 Dancing with the Stars ABC Mon., 8:00 P.M. 12.9 19 20,411,000
2 1 NCIS CBS Tues., 8:00 P.M. 12.3 20 20,348,000
3 4 Dancing with the Stars Results ABC Tues., 9:00 P.M. 12.0 20 19,294,000
4 3 NBC Sunday Night Football NBC Sun., 8:15 P.M. 11.5 18 19,210,000
5 8 NCIS: Los Angeles CBS Tues., 9:00 P.M. 10.4 16 17,221,000
6 5 60 Minutes CBS Sun., 7:00 P.M. 9.0 14 14,377,000
7 15 The Big Bang Theory CBS Mon., 9:30 P.M. 8.4 13 14,129,000
8 16 Sunday Night NFL Pre-Kick NBC Sun., 8:00 P.M. 8.4 13 13,927,000
9 12 Two and a Half Men CBS Mon., 9:00 P.M. 8.3 12 13,877,000
10 11 Criminal Minds CBS Wed., 9:00 P.M. 8.2 14 13,605,000
{ EXERCISES Copyrighted information of The Nielsen Company, licensed for use herein.
1. Rating Points Each rating point represents 5. Interval Level of Measurement Which
1,145,000 households, or 1% of the households in column in the table contains data at the interval
the United States. Does a program with a rating level? How can these data be ordered?
of 8.4 have twice the number of households as
a program with a rating of 4.2? Explain your 6. Ratio Level of Measurement Which columns
reasoning. contain data at the ratio level?
2. Sampling Percent What percentage of the 7. Rankings The column listed as “Share” gives
total number of U.S. households is used in the the percentage of televisions in use at a given
Nielsen sample? time. The 11th ranked program for this week is
CSI: Miami with a rating of 8.4 and share of 14.
3. Nominal Level of Measurement Which Using this information, how does Nielsen rank
columns in the table contain data at the nominal the programs? Why do you think they do it this
level? way? Explain your reasoning.
4. Ordinal Level of Measurement Which 8. Inferences What decisions (inferences) can be
columns in the table contain data at the ordinal made on the basis of the Nielsen ratings?
level? Describe two ways that the data can be
ordered.
16 C H A P T E R 1 INTRODUCTION TO STATISTICS
1.3 Data Collection and Experimental Design
WHAT YOU SHOULD LEARN Design of a Statistical Study Ī Data Collection Ī Experimental Design
Ī Sampling Techniques
Ī How to design a statistical
study Ī DESIGN OF A STATISTICAL STUDY
Ī How to collect data by The goal of every statistical study is to collect data and then use the data to make
doing an observational study, a decision. Any decision you make using the results of a statistical study is only
performing an experiment, as good as the process used to obtain the data. If the process is flawed, then the
using a simulation, or using resulting decision is questionable.
a survey
Although you may never have to develop a statistical study, it is likely that
Ī How to design an experiment you will have to interpret the results of one. And before you interpret the results
Ī How to create a sample using of a study, you should determine whether the results are valid, as well as reliable.
In other words, you should be familiar with how to design a statistical study.
random sampling, simple
random sampling, stratified GUIDELINES
sampling, cluster sampling,
and systematic sampling Designing a Statistical Study
and how to identify a
biased sample 1. Identify the variable(s) of interest (the focus) and the population
of the study.
INSIGHT
2. Develop a detailed plan for collecting data. If you use a sample, make
In an observational study, sure the sample is representative of the population.
a researcher does not
influence the responses. 3. Collect the data.
In an experiment, a
researcher deliberately 4. Describe the data, using descriptive statistics techniques.
applies a treatment
before observing 5. Interpret the data and make decisions about the population using
the responses. inferential statistics.
6. Identify any possible errors.
Ī DATA COLLECTION
There are several ways you can collect data. Often, the focus of the study dictates
the best way to collect data. The following is a brief summary of four methods of
data collection.
• Do an observational study In an observational study, a researcher observes
and measures characteristics of interest of part of a population but does
not change existing conditions. For instance, an observational study was
performed in which researchers observed and recorded the mouthing
behavior on nonfood objects of children up to three years old. (Source:
Pediatrics Magazine)
• Perform an experiment In performing an experiment, a treatment is applied
to part of a population and responses are observed. Another part of the
population may be used as a control group, in which no treatment is applied.
In many cases, subjects (sometimes called experimental units) in the control
group are given a placebo, which is a harmless, unmedicated treatment, that
is made to look like the real treatment. The responses of the treatment group
and control group can then be compared and studied. In most cases, it is a
good idea to use the same number of subjects for each treatment. For
instance, an experiment was performed in which diabetics took cinnamon
extract daily while a control group took none. After 40 days, the diabetics
who took the cinnamon reduced their risk of heart disease while the control
group experienced no change. (Source: Diabetes Care)
SECTION 1.3 DATA COLLECTION AND EXPERIMENTAL DESIGN 17
PICTURING THE • Use a simulation A simulation is the use of a mathematical or physical
WORLD model to reproduce the conditions of a situation or process. Collecting data
often involves the use of computers. Simulations allow you to study situations
The Gallup Organization conducts that are impractical or even dangerous to create in real life, and often they
many polls (or surveys) regarding save time and money. For instance, automobile manufacturers use simulations
the president, Congress, and with dummies to study the effects of crashes on humans. Throughout this
political and nonpolitical issues. course, you will have the opportunity to use applets that simulate statistical
A commonly cited Gallup poll processes on a computer.
is the public approval rating of
the president. For instance, the • Use a survey A survey is an investigation of one or more characteristics
approval ratings for President of a population. Most often, surveys are carried out on people by asking
Barack Obama throughout 2009 them questions. The most common types of surveys are done by interview,
are shown in the following mail, or telephone. In designing a survey, it is important to word the questions
graph. (The rating is from the so that they do not lead to biased results, which are not representative
poll conducted at the end of of a population. For instance, a survey is conducted on a sample of female
each month.) physicians to determine whether the primary reason for their career choice
is financial stability. In designing the survey, it would be acceptable to
President’s Approval make a list of reasons and ask each individual in the sample to select her
Ratings, 2009 first choice.
70 67 65 EXAMPLE 1
60 56 55
50 Deciding on Methods of Data Collection
Consider the following statistical studies. Which method of data collection
40 would you use to collect data for each study? Explain your reasoning.
30 1. A study of the effect of changing flight patterns on the number of airplane
accidents
20
2. A study of the effect of eating oatmeal on lowering blood pressure
10
3. A study of how fourth grade students solve a puzzle
Jan Apr Jul Oct
4. A study of U.S. residents’ approval rating of the U.S. president
Month
Percent approving Solution
Discuss some ways that
Gallup could select a biased 1. Because it is impractical to create this situation, use a simulation.
sample to conduct a poll. How
could Gallup select a sample 2. In this study, you want to measure the effect a treatment (eating oatmeal)
that is unbiased? has on patients. So, you would want to perform an experiment.
3. Because you want to observe and measure certain characteristics of part of
a population, you could do an observational study.
4. You could use a survey that asks, “Do you approve of the way the president
is handling his job?”
Try It Yourself 1
Consider the following statistical studies. Which method of data collection
would you use to collect data for each study?
1. A study of the effect of exercise on relieving depression
2. A study of the success of graduates of a large university in finding a job
within one year of graduation
a. Identify the focus of the study. Answer: Page A30
b. Identify the population of the study.
c. Choose an appropriate method of data collection.
18 C H A P T E R 1 INTRODUCTION TO STATISTICS
Ī EXPERIMENTAL DESIGN
In order to produce meaningful unbiased results, experiments should be carefully
designed and executed. It is important to know what steps should be taken to
make the results of an experiment valid. Three key elements of a well-designed
experiment are control, randomization, and replication.
Because experimental results can be ruined by a variety of factors, being able
to control these influential factors is important. One such factor is a confounding
variable.
DEFINITION
A confounding variable occurs when an experimenter cannot tell the
difference between the effects of different factors on a variable.
INSIGHT For instance, to attract more customers, a coffee shop owner experiments by
remodeling her shop using bright colors. At the same time, a shopping mall
The Hawthorne effect nearby has its grand opening. If business at the coffee shop increases, it cannot be
occurs in an experiment determined whether it is because of the new colors or the new shopping mall. The
when subjects change effects of the colors and the shopping mall have been confounded.
their behavior simply
because they know Another factor that can affect experimental results is the placebo effect. The
they are participating placebo effect occurs when a subject reacts favorably to a placebo when in fact
in an experiment. the subject has been given no medicated treatment at all. To help control or
minimize the placebo effect, a technique called blinding can be used.
DEFINITION
Blinding is a technique where the subjects do not know whether they are
receiving a treatment or a placebo. In a double-blind experiment, neither
the experimenter nor the subjects know if the subjects are receiving a
treatment or a placebo. The experimenter is informed after all the data
have been collected. This type of experimental design is preferred by
researchers.
Another technique that can be used to obtain unbiased results is
randomization.
DEFINITION
Randomization is a process of randomly assigning subjects to different
treatment groups.
All 30-39 Control In a completely randomized design, subjects are assigned to different
subjects years old Treatment treatment groups through random selection. In some experiments, it may be
necessary for the experimenter to use blocks, which are groups of subjects with
40-49 Control similar characteristics. A commonly used experimental design is a randomized
years old Treatment block design. To use a randomized block design, you should divide subjects with
Over 50 similar characteristics into blocks, and then, within each block, randomly assign
years old Control
Treatment subjects to treatment groups. For instance, an experimenter who is testing the
Randomized Block Design effects of a new weight loss drink may first divide the subjects into age categories
such as 30–39 years old, 40–49 years old, and over 50 years old, and then, within
each age group, randomly assign subjects to either the treatment group or the
control group as shown.
SECTION 1.3 DATA COLLECTION AND EXPERIMENTAL DESIGN 19
INSIGHT Another type of experimental design is a matched-pairs design, where
subjects are paired up according to a similarity. One subject in the pair is
The validity of an randomly selected to receive one treatment while the other subject receives a
experiment refers to the different treatment. For instance, two subjects may be paired up because of their
accuracy and reliability age, geographical location, or a particular physical characteristic.
of the experimental
results. The results of Sample size, which is the number of subjects, is another important part of
a valid experiment experimental design. To improve the validity of experimental results, replication
are more likely to is required.
be accepted in the
scientific community. DEFINITION
Replication is the repetition of an experiment under the same or similar
conditions.
For instance, suppose an experiment is designed to test a vaccine against a
strain of influenza. In the experiment, 10,000 people are given the vaccine and
another 10,000 people are given a placebo. Because of the sample size, the
effectiveness of the vaccine would most likely be observed. But, if the subjects in
the experiment are not selected so that the two groups are similar (according to
age and gender), the results are of less value.
EXAMPLE 2
Analyzing an Experimental Design
A company wants to test the effectiveness of a new gum developed to help
people quit smoking. Identify a potential problem with the given experimental
design and suggest a way to improve it.
1. The company identifies ten adults who are heavy smokers. Five of the
subjects are given the new gum and the other five subjects are given a
placebo. After two months, the subjects are evaluated and it is found that
the five subjects using the new gum have quit smoking.
2. The company identifies one thousand adults who are heavy smokers. The
subjects are divided into blocks according to gender. Females are given the
new gum and males are given the placebo. After two months, a significant
number of the female subjects have quit smoking.
Solution
1. The sample size being used is not large enough to validate the results of the
experiment. The experiment must be replicated to improve the validity.
2. The groups are not similar. The new gum may have a greater effect on
women than on men, or vice versa. The subjects can be divided into blocks
according to gender, but then, within each block, they must be randomly
assigned to be in the treatment group or in the control group.
Try It Yourself 2
Using the information in Example 2, suppose the company identifies
240 adults who are heavy smokers. The subjects are randomly assigned to be
in a treatment group or in a control group. Each subject is also given a DVD
featuring the dangers of smoking. After four months, most of the subjects
in the treatment group have quit smoking.
a. Identify a potential problem with the experimental design.
b. How could the design be improved? Answer: Page A30
20 C H A P T E R 1 INTRODUCTION TO STATISTICS
INSIGHT Ī SAMPLING TECHNIQUES
A biased sample is one that is not A census is a count or measure of an entire population. Taking a census provides
representative of the population complete information, but it is often costly and difficult to perform. A sampling
from which it is drawn. is a count or measure of part of a population, and is more commonly used in
For instance, a sample statistical studies. To collect unbiased data, a researcher must ensure that the
consisting of only sample is representative of the population. Appropriate sampling techniques
18- to 22-year-old must be used to ensure that inferences about the population are valid. Remember
college students would that when a study is done with faulty data, the results are questionable. Even with
not be representative the best methods of sampling, a sampling error may occur. A sampling error is the
of the entire 18- to difference between the results of a sample and those of the population. When you
22-year-old population learn about inferential statistics, you will learn techniques of controlling sampling
in the country. errors.
To explore this topic further, A random sample is one in which every member of the population has an
see Activity 1.3 on page 26. equal chance of being selected. A simple random sample is a sample in which
every possible sample of the same size has the same chance of being selected.
One way to collect a simple random sample is to assign a different number to
each member of the population and then use a random number table like the one
in Appendix B. Responses, counts, or measures for members of the population
whose numbers correspond to those generated using the table would be in the
sample. Calculators and computer software programs are also used to generate
random numbers (see page 34).
92630 78240 19267 95457 53497 23894 37708 79862
79445 78735 71549 44843 26104 67318 00701 34986
59654 71966 27386 50004 05358 94031 29281 18544
31524 49587 76612 39789 13537 48086 59483 60680
06348 76938 90379 51392 55887 71015 09209 79157
Portion of Table 1 found in Appendix B
STUDY TIP Consider a study of the number of people who live in West Ridge County. To use
a simple random sample to count the number of people who live in West Ridge
Here are instructions for using the County households, you could assign a different number to each household, use
random integer generator on a a technology tool or table of random numbers to generate a sample of numbers,
TI-83/84 Plus for Example 3. and then count the number of people living in each selected household.
MATH EXAMPLE 3 SC Report 1
Choose the PRB menu.
Using a Simple Random Sample
5: randInt(
1, 731, 8) There are 731 students currently enrolled in a statistics course at your school.
ENTER You wish to form a sample of eight students to answer some survey questions.
Select the students who will belong to the simple random sample.
Continuing to press
ENTER will generate Solution
more random samples
of 8 integers. Assign numbers 1 to 731 to the students in the course. In the table of random
numbers, choose a starting place at random and read the digits in groups of
three (because 731 is a three-digit number). For instance, if you started in the
third row of the table at the beginning of the second column, you would group
the numbers as follows:
719 ƒ 66 2 ƒ 738 ƒ 6 50 ƒ 004 ƒ 053 ƒ 58 9 ƒ 403 ƒ 1 29 ƒ 281 ƒ 185 ƒ 44
Ignoring numbers greater than 731, the first eight numbers are 719, 662, 650, 4, 53,
589, 403, and 129. The students assigned these numbers will make up the sample.
To find the sample using a TI-83/84 Plus, follow the instructions in the margin.
SECTION 1.3 DATA COLLECTION AND EXPERIMENTAL DESIGN 21
Try It Yourself 3
A company employs 79 people. Choose a simple random sample of five to survey.
a. In the table in Appendix B, randomly choose a starting place.
b. Read the digits in groups of two.
c. Write the five random numbers. Answer: Page A30
When you choose members of a sample, you should decide whether it is
acceptable to have the same population member selected more than once. If it
is acceptable, then the sampling process is said to be with replacement. If it is not
acceptable, then the sampling process is said to be without replacement.
There are several other commonly used sampling techniques. Each has
advantages and disadvantages.
• Stratified Sample When it is important for the sample to have members
from each segment of the population, you should use a stratified sample.
Depending on the focus of the study, members of the population are divided
into two or more subsets, called strata, that share a similar characteristic such
as age, gender, ethnicity, or even political preference. A sample is then
randomly selected from each of the strata. Using a stratified sample ensures
that each segment of the population is represented. For instance, to collect a
stratified sample of the number of people who live in West Ridge County
households, you could divide the households into socioeconomic levels, and
then randomly select households from each level.
Group 1: Group 2: Group 3:
Low income Middle income High income
Stratified Sampling
INSIGHT • Cluster Sample When the population falls into naturally occurring
subgroups, each having similar characteristics, a cluster sample may be the
For stratified sampling, each most appropriate. To select a cluster sample, divide the population into
of the strata contains members groups, called clusters, and select all of the members in one or more (but not
with a certain characteristic (for all) of the clusters. Examples of clusters could be different sections of the
instance, a particular age group). same course or different branches of a bank. For instance, to collect a cluster
In contrast, clusters consist of sample of the number of people who live in West Ridge County households,
geographic groupings, and each divide the households into groups according to zip codes, then select all the
cluster should contain members households in one or more, but not all, zip codes and count the number of
with all of the characteristics people living in each household. In using a cluster sample, care must be taken
(for instance, all age to ensure that all clusters have similar characteristics. For instance, if one of
groups). With stratified the zip code clusters has a greater proportion of high-income people, the data
samples, some of the might not be representative of the population.
members of each group
are used. In a cluster Zip Code Zones in West Ridge County
sampling, all of the
members of one or Zone 1 Zone 2
more groups are used. Zone 3
Zone 4
Cluster Sampling
22 C H A P T E R 1 INTRODUCTION TO STATISTICS
• Systematic Sample A systematic sample is a sample in which each member
of the population is assigned a number. The members of the population are
ordered in some way, a starting number is randomly selected, and then
sample members are selected at regular intervals from the starting number.
(For instance, every 3rd, 5th, or 100th member is selected.) For instance, to
collect a systematic sample of the number of people who live in West Ridge
County households, you could assign a different number to each household,
randomly choose a starting number, select every 100th household, and count
the number of people living in each. An advantage of systematic sampling is
that it is easy to use. In the case of any regularly occurring pattern in the data,
however, this type of sampling should be avoided.
Systematic Sampling
A type of sample that often leads to biased studies (so it is not recommended)
is a convenience sample. A convenience sample consists only of available members
of the population.
EXAMPLE 4
Identifying Sampling Techniques
You are doing a study to determine the opinions of students at your school
regarding stem cell research. Identify the sampling technique you are using if
you select the samples listed. Discuss potential sources of bias (if any). Explain.
1. You divide the student population with respect to majors and randomly
select and question some students in each major.
2. You assign each student a number and generate random numbers. You then
question each student whose number is randomly selected.
3. You select students who are in your biology class.
Solution
1. Because students are divided into strata (majors) and a sample is selected
from each major, this is a stratified sample.
2. Each sample of the same size has an equal chance of being selected and
each student has an equal chance of being selected, so this is a simple
random sample.
3. Because the sample is taken from students that are readily available, this is
a convenience sample. The sample may be biased because biology students
may be more familiar with stem cell research than other students and may
have stronger opinions.
Try It Yourself 4
You want to determine the opinions of students regarding stem cell research.
Identify the sampling technique you are using if you select the samples listed.
1. You select a class at random and question each student in the class.
2. You assign each student a number and, after choosing a starting number,
question every 25th student.
a. Determine how the sample is selected and identify the corresponding
sampling technique.
b. Discuss potential sources of bias (if any). Explain. Answer: Page A30
SECTION 1.3 DATA COLLECTION AND EXPERIMENTAL DESIGN 23
1.3 EXERCISES
{ BUILDING BASIC SKILLS AND VOCABULARY
1. What is the difference between an observational study and an experiment?
2. What is the difference between a census and a sampling?
3. What is the difference between a random sample and a simple random
sample?
4. What is replication in an experiment, and why is it important?
True or False? In Exercises 5–10, determine whether the statement is true or
false. If it is false, rewrite it as a true statement.
5. In a randomized block design, subjects with similar characteristics are
divided into blocks, and then, within each block, randomly assigned to
treatment groups.
6. A double-blind experiment is used to increase the placebo effect.
7. Using a systematic sample guarantees that members of each group within a
population will be sampled.
8. A census is a count of part of a population.
9. The method for selecting a stratified sample is to order a population in some
way and then select members of the population at regular intervals.
10. To select a cluster sample, divide a population into groups and then select all
of the members in at least one (but not all) of the groups.
Deciding on the Method of Data Collection In Exercises 11–16, explain
which method of data collection you would use to collect data for the study.
11. A study of the health of 168 kidney transplant patients at a hospital
12. A study of motorcycle helmet usage in a city without a helmet law
13. A study of the effect on the human digestive system of potato chips made
with a fat substitute
14. A study of the effect of a product’s warning label to determine whether
consumers will still buy the product
15. A study of how fast a virus would spread in a metropolitan area
16. A study of how often people wash their hands in public restrooms
{ USING AND INTERPRETING CONCEPTS
17. Allergy Drug A pharmaceutical company wants to test the effectiveness of
a new allergy drug. The company identifies 250 females 30–35 years old who
suffer from severe allergies. The subjects are randomly assigned into two
groups. One group is given the new allergy drug and the other is given a
placebo that looks exactly like the new allergy drug. After six months, the
subjects’ symptoms are studied and compared.
(a) Identify the experimental units and treatments used in this experiment.
(b) Identify a potential problem with the experimental design being used
and suggest a way to improve it.
(c) How could this experiment be designed to be double-blind?
24 C H A P T E R 1 INTRODUCTION TO STATISTICS
18. Sneakers Nike developed a new type of sneaker designed to help delay the
onset of arthritis in the knee. Eighty people with early signs of arthritis
volunteered for a study. One-half of the volunteers wore the experimental
sneakers and the other half wore regular Nike sneakers that looked exactly
like the experimental sneakers. The individuals wore the sneakers every day.
At the conclusion of the study, their symptoms were evaluated and MRI tests
were performed on their knees. (Source: Washington Post)
(a) Identify the experimental units and treatments used in this experiment.
(b) Identify a potential problem with the experimental design being used
and suggest a way to improve it.
(c) The experiment is described as a placebo-controlled, double-blind study.
Explain what this means.
(d) Of the 80 volunteers, suppose 40 are men and 40 are women. How could
blocking be used in designing this experiment?
Identifying Sampling Techniques In Exercises 19–26, identify the sampling
technique used, and discuss potential sources of bias (if any). Explain.
19. Using random digit dialing, researchers call 1400 people and ask what
obstacles (such as childcare) keep them from exercising.
20. Chosen at random, 500 rural and 500 urban persons age 65 or older are asked
about their health and their experience with prescription drugs.
21. Questioning students as they leave a university library, a researcher asks
358 students about their drinking habits.
22. After a hurricane, a disaster area is divided into 200 equal grids. Thirty of the
grids are selected, and every occupied household in the grid is interviewed to
help focus relief efforts on what residents require the most.
23. Chosen at random, 580 customers at a car dealership are contacted and
asked their opinions of the service they received.
24. Every tenth person entering a mall is asked to name his or her favorite store.
25. Soybeans are planted on a 48-acre field. The field is divided into one-acre
subplots. A sample is taken from each subplot to estimate the harvest.
26. From calls made with randomly generated telephone numbers, 1012
respondents are asked if they rent or own their residences.
27. Random Number Table Use the seventh row of Table 1 in Appendix B to
generate 12 random numbers between 1 and 99.
28. Random Number Table Use the twelfth row of Table 1 in Appendix B to
generate 10 random numbers between 1 and 920.
29. Sleep Deprivation A researcher wants to study the effects of sleep
deprivation on motor skills. Eighteen people volunteer for the experiment:
Jake, Maria, Mike, Lucy, Ron, Adam, Bridget, Carlos, Steve, Susan, Vanessa,
Rick, Dan, Kate, Pete, Judy, Mary, and Connie. Use a random number
generator to choose nine subjects for the treatment group. The other nine
subjects will go into the control group. List the subjects in each group. Tell
which method you would use to generate the random numbers.
30. Random Number Generation Volunteers for an experiment are numbered
from 1 to 70. The volunteers are to be randomly assigned to two different
treatment groups. Use a random number generator different from the one you
used in Exercise 29 to choose 35 subjects for the treatment group. The other 35
subjects will go into the control group. List the subjects, according to number,
in each group. Tell which method you used to generate the random numbers.
SECTION 1.3 DATA COLLECTION AND EXPERIMENTAL DESIGN 25
Choosing Between a Census and a Sampling In Exercises 31 and 32,
determine whether you would take a census or use a sampling. If you would
use a sampling, decide what sampling technique you would use. Explain your
reasoning.
31. The average age of the 115 residents of a retirement community
32. The most popular type of movie among 100,000 online movie rental subscribers
Recognizing a Biased Question In Exercises 33–36, determine whether the
survey question is biased. If the question is biased, suggest a better wording.
33. Why does eating whole-grain foods improve your health?
34. Why does text messaging while driving increase the risk of a crash?
35. How much do you exercise during an average week?
36. Why do you think the media have a negative effect on teen girls’ dieting
habits?
37. Writing A sample of television program ratings by The Nielsen Company
is described on page 15. Discuss the strata used in the sample. Why is it
important to have a stratified sample for these ratings?
SC 38. Use StatCrunch to generate the following random numbers.
a. 8 numbers between 1 and 50
b. 15 numbers between 1 and 150
c. 16 numbers between 1 and 325
d. 20 numbers between 1 and 1000
{ EXTENDING CONCEPTS
39. Observational studies are sometimes referred to as natural experiments.
Explain, in your own words, what this means.
40. Open and Closed Questions Two types of survey questions are open
questions and closed questions. An open question allows for any kind of
response; a closed question allows for only a fixed response. An open
question, and a closed question with its possible choices, are given below. List
an advantage and a disadvantage of each question.
Open Question What can be done to get students to eat healthier foods?
Closed Question How would you get students to eat healthier foods?
1. Mandatory nutrition course
2. Offer only healthy foods in the cafeteria and remove unhealthy foods
3. Offer more healthy foods in the cafeteria and raise the prices on
unhealthy foods
41. Who Picked These People? Some polling agencies ask people to call
a telephone number and give their response to a question. (a) List an
advantage and a disadvantage of a survey conducted in this manner.
(b) What sampling technique is used in such a survey?
42. Give an example of an experiment where confounding may occur.
43. Why is it important to use blinding in an experiment?
44. How are the placebo effect and the Hawthorne effect similar? How are they
different?
45. How is a randomized block design in experiments similar to a stratified sample?
26 C H A P T E R 1 INTRODUCTION TO STATISTICS
ACTIVITY 1.3 Random Numbers
The random numbers applet is designed to allow you to generate random
numbers from a range of values. You can specify integer values for the minimum
value, maximum value, and the number of samples in the appropriate fields. You
should not use decimal points when filling in the fields.When SAMPLE is clicked,
the applet generates random values, which are displayed as a list in the text field.
Minimum value:
Maximum value:
Number of samples:
Sample
{ Explore
Step 1 Specify a minimum value.
Step 2 Specify a maximum value.
Step 3 Specify the number of samples.
Step 4 Click SAMPLE to generate a list of random values.
{ Draw Conclusions
1. Specify the minimum, maximum, and number of samples to be 1, 20, and 8,
respectively, as shown. Run the applet. Continue generating lists until you
obtain one that shows that the random sample is taken with replacement.
Write down this list. How do you know that the list is a random sample taken
with replacement?
Minimum value: 1
Maximum value: 20
Number of samples: 8
Sample
2. Use the applet to repeat Example 3 on page 20. What values did you use for
the minimum, maximum, and number of samples? Which method do you
prefer? Explain.
USES AND ABUSES 27
USES AND ABUSES
Uses Statistics in the Real World
Experiments with Favorable Results An experiment that began
in March 2003 studied 321 women with advanced breast cancer. All of the
women had been previously treated with other drugs, but the cancer had stopped
responding to the medications. The women were then given the opportunity to
take a new drug combined with a particular chemotherapy drug.
The subjects were divided into two groups, one that took the new drug
combined with a chemotherapy drug, and one that took only the chemotherapy
drug. After three years, results showed that the new drug in combination with
the chemotherapy drug delayed the progression of cancer in the subjects. The
results were so significant that the study was stopped, and the new drug was
offered to all women in the study. The Food and Drug Administration has
since approved use of the new drug in conjunction with a chemotherapy drug.
Abuses
Experiments with Unfavorable Results From 1988 to 1991, one hundred
eighty thousand teenagers in Norway were used as subjects to test a new vaccine
against the deadly bacteria meningococcus b. A brochure describing the possi-
ble effects of the vaccine stated, “it is unlikely to expect serious complications,”
while information provided to the Norwegian Parliament stated, “serious side
effects can not be excluded.” The vaccine trial had some disastrous results: More
than 500 side effects were reported, with some considered serious, and several
of the subjects developed serious neurological diseases. The results showed that
the vaccine was providing immunity in only 57% of the cases. This result was
not sufficient for the vaccine to be added to Norway’s vaccination program.
Compensations have since been paid to the vaccine victims.
Ethics
Experiments help us further understand the world that surrounds us. But, in
some cases, they can do more harm than good. In the Norwegian experiments,
several ethical questions arise. Was the Norwegian experiment unethical if the
best interests of the subjects were neglected? When should the experiment
have been stopped? Should it have been conducted at all? If serious side
effects are not reported and are withheld from subjects, there is no ethical
question here, it is just wrong.
On the other hand, the breast cancer researchers would not want to deny
the new drug to a group of patients with a life-threatening disease. But again,
questions arise. How long must a researcher continue an experiment that
shows better-than-expected results? How soon can a researcher conclude a
drug is safe for the subjects involved?
{ EXERCISES
1. Unfavorable Results Find an example of a real-life experiment that had
unfavorable results. What could have been done to avoid the outcome of
the experiment?
2. Stopping an Experiment In your opinion, what are some problems that
may arise if clinical trials of a new experimental drug or vaccine are
stopped early and then the drug or vaccine is distributed to other subjects
or patients?
28 C H A P T E R 1 INTRODUCTION TO STATISTICS REVIEW
EXAMPLE(S) EXERCISES
1 CHAPTER SUMMARY
1 1–4
What did you learn? 2 5–8
3 9, 10
Section 1.1
í How to distinguish between a population and a sample 1 11–16
2, 3 17–20
í How to distinguish between a parameter and a statistic
1 21–24
í How to distinguish between descriptive statistics and inferential statistics 2 25, 26
3, 4 27–34
Section 1.2 4 35–38
í How to distinguish between qualitative data and quantitative data
í How to classify data with respect to the four levels of measurement:
nominal, ordinal, interval, and ratio
Section 1.3
í How data are collected: by doing an observational study, performing an
experiment, using a simulation, or using a survey
í How to design an experiment
í How to create a sample using random sampling, simple random sampling,
stratified sampling, cluster sampling, and systematic sampling
í How to identify a biased sample
REVIEW EXERCISES 29
1 REVIEW EXERCISES
{ SECTION 1.1
In Exercises 1–4, identify the population and the sample.
1. A survey of 1000 U.S. adults found that 83% think credit cards tempt people
to buy things they cannot afford. (Source: Rasmussen Reports)
2. Thirty-eight nurses working in the San Francisco area were surveyed
concerning their opinions of managed health care.
3. A survey of 39 credit cards found that the average annual percentage rate
(APR) is 12.83%. (Source: Consumer Action)
4. A survey of 1205 physicians found that about 60% had considered leaving
the practice of medicine because they were discouraged over the state of U.S.
health care. (Source: The Physician Executive Journal of Medical Management)
In Exercises 5–8, determine whether the numerical value describes a parameter or
a statistic.
5. The 2009 team payroll of the Philadelphia Phillies was $113,004,046. (Source:
USA Today)
6. In a survey of 752 adults in the United States, 42% think there should be a
law that prohibits people from talking on cell phones in public places.
(Source: University of Michigan)
7. In a recent study of math majors at a university, 10 students were minoring in
physics.
8. Fifty percent of a sample of 1508 U.S. adults say they oppose drilling for oil
and gas in the Arctic National Wildlife Refuge. (Source: Pew Research Center)
9. Which part of the study described in Exercise 3 represents the descriptive
branch of statistics? Make an inference based on the results of the study.
10. Which part of the survey described in Exercise 4 represents the descriptive
branch of statistics? Make an inference based on the results of the survey.
{ SECTION 1.2
In Exercises 11–16, determine which data are qualitative data and which are
quantitative data. Explain your reasoning.
11. The monthly salaries of the employees at an accounting firm
12. The Social Security numbers of the employees at an accounting firm
13. The ages of a sample of 350 employees of a software company
14. The zip codes of a sample of 350 customers at a sporting goods store
15. The 2010 revenues of the companies on the Fortune 500 list
16. The marital statuses of all professional golfers
In Exercises 17–20, identify the data set’s level of measurement. Explain your
reasoning.
17. The daily high temperatures (in degrees Fahrenheit) for Mohave, Arizona for
a week in June are listed. (Source: Arizona Meteorological Network)
93 91 86 94 103 104 103
18. The levels of the Homeland Security Advisory System are listed.
Severe High Elevated Guarded Low
