The Practice of Statistics

958 Pages·2010·51.41 MB·English

by  Daren S. Starnes, Dan Yates, David S. Moore

AP*
FOR
The
PRACTICE

STATISTICS
of
FOURTH EDITION
Director, BFW High School: Craig Bleyer
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Library of Congress Control Number: 2010934160
ISBN-13: 978-1-4292-4559-3
ISBN-10: 1-4292-4559-X
© 2012, 2008, 2003, 1999 by W. H. Freeman and Company
First printing 2010
All rights reserved
Printed in the United States of America
W. H. Freeman and Company
41 Madison Avenue
New York, NY 10010
Houndmills, Basingstoke RG21 6XS, England
www.whfreeman.com
AP*
FOR
The
PRACTICE

STATISTICS
of
FOURTH EDITION
Daren S. Starnes
The Lawrenceville School
Daniel S. Yates
Statistics Consultant
David S. Moore
Purdue University
*AP is a trademark registered and/or owned by the College Board, which was not
involved in the production of, and does not endorse, this product.
W. H. Freeman and Company
New York
CONTENTS
About the Authors vii 6 Random Variables 339
Preface ix
6.1 Discrete and Continuous Random Variables 341
Overview: What Is Statistics? xx
6.2 Transforming and Combining Random Variables 358
6.3 Binomial and Geometric Random Variables 382
1 Exploring Data 1
Chapter Review 407
Introduction:Data Analysis: Making Sense of Data 2
Chapter Review Exercises 408
1.1 Analyzing Categorical Data 8
AP Statistics Practice Test 409
1.2 Displaying Quantitative Data with Graphs 27
1.3 Describing Quantitative Data with Numbers 50
Chapter Review 75 7 Sampling Distributions 413
Chapter Review Exercises 75
7.1 What Is a Sampling Distribution 416
AP Statistics Practice Test 78
7.2 Sample Proportions 432
2 Modeling Distributions of Data 83 7.3 Sample Means 442
Chapter Review 457
2.1 Describing Location in a Distribution 85 Chapter Review Exercises 458
2.2 Normal Distributions 110 AP Statistics Practice Test 459
Chapter Review 136
Cumulative AP Practice Test 461
Chapter Review Exercises 136
AP Statistics Practice Test 138 8 Estimating with Confidence 467
8.1 Confidence Intervals: The Basics 469
3 Describing Relationships 141
8.2 Estimating a Population Proportion 484
3.1 Scatterplots and Correlation 143 8.3 Estimating a Population Mean 499
3.2 Least-Squares Regression 164 Chapter Review 522
Chapter Review 198 Chapter Review Exercises 522
Chapter Review Exercises 198 AP Statistics Practice Test 524
AP Statistics Practice Test 200
9 Testing a Claim 527
4 Designing Studies 205 9.1 Significance Tests: The Basics 529
9.2 Tests about a Population Proportion 549
4.1 Sampling and Surveys 207
9.3 Tests about a Population Mean 565
4.2 Experiments 231
Chapter Review 594
4.3 Using Studies Wisely 261
Chapter Review Exercises 594
Chapter Review 271
AP Statistics Practice Test 597
Chapter Review Exercises 271
AP Statistics Practice Test 274 10 Comparing Two Populations or Groups 601
Cumulative AP Practice Test 276 10.1 Comparing Two Proportions 604
10.2 Comparing Two Means 627
5 Probability: What Are the Chances? 281 Chapter Review 661
Chapter Review Exercises 661
5.1 Randomness, Probability, and Simulation 283
AP Statistics Practice Test 664
5.2 Probability Rules 299
Cumulative AP Practice Test 667
5.3 Conditional Probability and Independence 312
Chapter Review 334
Chapter Review Exercises 334
AP Statistics Practice Test 336
iv
11 Inference for Distributions Photo Credits PC-1
of Categorical Data 675
Notes and Data Sources N/DS-1
11.1 Chi-Square Goodness-of-Fit Tests 678
Solutions S-1
11.2 Inference for Relationships 696
Chapter Review 731
Index I-1
Chapter Review Exercises 731
AP Statistics Practice Test 733
Appendices A-1
12 More about Regression 737
Appendix A: AP Exam Tips A-1
12.1 Inference for Linear Regression 739 Appendix B: TI-Nspire Technology Corners A-3
12.2 Transforming to Achieve Linearity 765
Chapter Review 793
Formulas for AP Statistics Exam F-1
Chapter Review Exercises 793
AP Statistics Practice Test 796
Cumulative AP Practice Test 799 Tables T-1
Table A: Standard Normal Probabilities T-1
Additional topics on CD-ROM and at Table B: t Distribution Critical Values T-3
http://www.whfreeman.com/tps4e: Table C: Chi-square Distribution Critical Values T-4
Table D: Random Digits T-5
13 Analysis of Variance
Technology Corners Reference Back Endpaper
14 Multiple Linear Regression Inference Summary Back Endpaper
15 Logistic Regression
v
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ABOUT THE AUTHORS
Daren S. Starnes is Mathematics Department Chair and holds the endowed Master
Teacher chair in Mathematics at The Lawrenceville School near Princeton, New Jersey.
He earned his MA in Mathematics from the University of Michigan. Daren received
a GTE GIFT Grant to integrate AP Statistics and AP Environmental Science. He was
also named a Tandy Technology Scholar. Daren has led numerous one-day and week-
long AP Statistics institutes for new and experienced AP teachers, and he has been a
reader, table leader, and question leader for the AP Statistics exam since 1998. Daren is
a frequent speaker at local, state, regional, national, and international conferences. For
two years, he served as coeditor of the Technology Tips column in the NCTM journal
The Mathematics Teacher. From 2004 to 2009, Daren served on the ASA/NCTM Joint
Committee on the Curriculum in Statistics and Probability (which he chaired in 2009).
While on the committee, he edited the Guidelines for Assessment and Instruction in
Statistics Education (GAISE) pre-K–12 report and coauthored (with Roxy Peck) Mak-
ing Sense of Statistical Studies, a capstone module in statistical thinking for high school
students. Daren is also coauthor of the popular text Statistics Through Applications, First
and Second Editions.
Daniel S. Yates has taught Advanced Placement Statistics in the Electronic Classroom
(a distance-learning facility) affiliated with Henrico County Public Schools in
Richmond, Virginia. Prior to high school teaching, he was on the mathematics faculty
at Virginia Tech and Randolph-Macon College. He has a PhD in Mathematics
Education from Florida State University. He has served as President of the Greater
Richmond Council of Teachers of Mathematics and the Virginia Council of Teachers
of Mathematics. Named a Tandy Technology Scholar in 1997, Dan received a College
Board/Siemens Foundation Advanced Placement Teaching Award in 2000. Although
recently retired from classroom teaching, he stays in step with trends in teaching by
frequently conducting College Board workshops for new and experienced AP Statistics
teachers and by monitoring and participating in the AP Statistics electronic discussion
group. Dan is coauthor of Statistics Through Applications, a popular textbook for
non–AP Statistics classes.
David S. Moore is Shanti S. Gupta Distinguished Professor of Statistics at Purdue
University and 1998 President of the American Statistical Association. David is an
elected fellow of the American Statistical Association and of the Institute of
Mathematical Statistics and an elected member of the International Statistical Institute.
He has served as program director for statistics and probability at the National Science
Foundation. David has devoted his attention to the teaching of statistics. He was the
content developer for the Annenberg/Corporation for Public Broadcasting college-level
telecourseAgainst All Odds: Inside Statistics and for the series of video modules Statis-
tics: Decisions Through Data, intended to aid the teaching of statistics in schools. He is
the author of influential articles on statistics education and of several leading textbooks,
including Introduction to the Practice of Statistics (written with George P. McCabe and
Bruce Craig), The Basic Practice of Statistics, Statistics: Concepts and Controversies, The
Practice of Business Statistics, The Practice of Statistics in the Life Sciences (written with
Brigitte Baldi), and most recently Essential Statistics.
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Content Advisory Board and Supplements Team
Josh Tabor Ann Cannon
Canyon del Oro High School Cornell College
Josh is a past member of the AP Statistics Ann has been a reader, table leader, and ques-
Development Committee (2005–2009) and tion leader for the AP Statistics exam. She has
an experienced table leader and question taught the equivalent course at the college
leader at the AP Statistics Reading. He has led level for seventeen years at Cornell College
many one-week AP Summer Institutes and one-day College in Mount Vernon, Iowa. Ann has also been very active in
Board workshops around the country. Josh is the author of the the Statistics Education Section of the American Statistical
Annotated Teacher’s Edition and Teacher’s Resource Binder for Association, serving on the Executive Committee for two
The Practice of Statistics. three-year terms.
In addition to teaching AP Statistics, Josh enjoys spending In her spare time, she runs herd on her family, including
time with his wife and daughter and has combined two of his two sons, and she enjoys music, playing both the French horn
passions—statistics and sports—to write a textbook for non–AP and handbells.
classes called Statistical Reasoning in Sports.
Jason Molesky
Michael Legacy Lakeville Area Public Schools
Greenhill School Jason has served as an AP Statistics reader for
Michael is a past member of the AP Statis- the past four years. He has taught AP Statistics
tics Development Committee (2001–2005) for eight years and is currently the “Assessment
and a former table leader at the Reading. He and Accountability Coordinator” for Lakeville
currently reads the Alternate Exam. He has schools, overseeing his district’s testing program and providing
been a lead teacher at many AP Summer Institutes and stu- professional development. He also maintains the “StatsMonkey”
dent prep sessions over the past twelve years and is a frequent Web site, a clearinghouse for AP Statistics activities, notes, test
presenter at College Board conferences. Michael is the author preparation materials, and other resources.
of the 2007 College Board AP Statistics Teacher’s Guide and In his spare time, Jason enjoys spending time with his
writesthe Prep for the AP Exam Guide for The Practice of wife, their two children, and his trusty beagle.
Statistics. In February 2010, the Siemens Corporation named
Michael the 2009–2010 AP Math/Science Teacher of the Year Heather Overstreet
for the state of Texas. Staunton River High School
In addition to his duties as pre-K–12 Math Chair, Heather has served as an AP Statistics reader
Michael teaches AP Statistics and Precalculus, indulges his for the past three years. She has taught AP
passionate interest in theater, and does the costume work for Statistics for six years and is currently working
the annual Madrigal Dinner at Greenhill School in Addison, with Virginia Advanced Study Strategies, a
Texas. program for promoting AP math, science, and English courses
in Virginia high schools.
Tim Brown In her spare time, Heather enjoys spending time with
The Lawrenceville School herhusband and chauffeuring her children to their many
Tim first piloted an AP Statistics course the activities.
year before the first exam was administered.
He has been an AP reader since 1997 and Tim Erickson
a table leader since 2004. He earned a BA Lick-Wilmerding High School
from Hampshire College and a PhD in ecology from The Tim is one of the designers of Fathom
University of North Carolina at Chapel Hill. Since 1982, he Dynamic Data software and has been its chief
has taught mathematics and statistics at The Lawrenceville curriculum developer since Fathom began
School and currently holds the Bruce McClellan Distin- in 1995. He is currently working on the Data
guished Teaching Chair. Games project and is also teaching a section of high school
In addition to his teaching and advising duties, Tim super- statistics.
vises two intramural Ultimate Disk programs at Lawrenceville. Outside the stats world, Tim is an adult-onset cellist,
Over the past twenty-eight years, he has introduced hundreds playing in a community orchestra and in a string quartet.
of students to the game.
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PREFACE
The Practice of Statistics (TPS) was the first book written spe- The Fourth Edition
cifically for the Advanced Placement (AP) Statistics course.
TPS is organized to closely follow the College Board’s AP
In planning the fourth edition of The Practice of Statistics, we
Statistics Course Description and is designed to prepare
commissioned numerous written reviews from users of the
students for the AP exam. In the fourth edition (TPS 4e), we
third edition and competitive books. As a follow-up to the writ-
have made the AP connection even stronger by:
ten feedback, we held a focus group and assembled a Content
Advisory Board to learn more about the current state of the AP
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Statistics course and the perceived strengths and weaknesses of
Outline” is covered thoroughly in the text. In addition, we
prior editions of TPS. A number of salient points emerged that
have indicated content that goes beyond the AP syllabus,
helped shape our goals for the new edition:
such as Simpson’s paradox, data ethics, and Normal approxi-
mation to the binomial.
(cid:115)(cid:0)Streamline the text. TPS 3e had 15 chapters plus a “Pre-
(cid:115)(cid:0)(cid:35)(cid:79)(cid:78)(cid:84)(cid:73)(cid:78)(cid:85)(cid:73)(cid:78)(cid:71)(cid:0)(cid:84)(cid:79)(cid:0)(cid:85)(cid:83)(cid:69)(cid:0)(cid:84)(cid:69)(cid:82)(cid:77)(cid:83)(cid:12)(cid:0)(cid:78)(cid:79)(cid:84)(cid:65)(cid:84)(cid:73)(cid:79)(cid:78)(cid:12)(cid:0)(cid:70)(cid:79)(cid:82)(cid:77)(cid:85)(cid:76)(cid:65)(cid:83)(cid:12)(cid:0)(cid:65)(cid:78)(cid:68)(cid:0)(cid:84)(cid:65)(cid:66)(cid:76)(cid:69)(cid:83)(cid:0)(cid:84)(cid:72)(cid:65)(cid:84)(cid:0) liminary Chapter.” Dividing the content into so many distinct
are consistent with those found on the AP Statistics exam. units created pacing challenges for teachers who wanted to
(cid:115)(cid:0)(cid:38)(cid:79)(cid:76)(cid:76)(cid:79)(cid:87)(cid:73)(cid:78)(cid:71)(cid:0)(cid:65)(cid:67)(cid:67)(cid:69)(cid:80)(cid:84)(cid:69)(cid:68)(cid:0)(cid:67)(cid:79)(cid:78)(cid:86)(cid:69)(cid:78)(cid:84)(cid:73)(cid:79)(cid:78)(cid:83)(cid:0)(cid:70)(cid:82)(cid:79)(cid:77)(cid:0)(cid:33)(cid:48)(cid:0)(cid:69)(cid:88)(cid:65)(cid:77)(cid:0)(cid:82)(cid:85)(cid:66)(cid:82)(cid:73)(cid:67)(cid:83)(cid:0) assess students after each chapter and still have time left for a
when presenting model solutions. comprehensive review before the AP exam. We have stream-
(cid:115)(cid:0)(cid:33)(cid:68)(cid:68)(cid:73)(cid:78)(cid:71)(cid:0)(cid:108)(cid:86)(cid:69)(cid:13)(cid:79)(cid:80)(cid:84)(cid:73)(cid:79)(cid:78)(cid:0)(cid:77)(cid:85)(cid:76)(cid:84)(cid:73)(cid:80)(cid:76)(cid:69)(cid:13)(cid:67)(cid:72)(cid:79)(cid:73)(cid:67)(cid:69)(cid:0)(cid:69)(cid:88)(cid:69)(cid:82)(cid:67)(cid:73)(cid:83)(cid:69)(cid:83)(cid:0)(cid:84)(cid:72)(cid:82)(cid:79)(cid:85)(cid:71)(cid:72)(cid:79)(cid:85)(cid:84)(cid:12)(cid:0) lined the table of contents to include 12 focused chapters.
as well as an AP Statistics Practice Test at the end of each (cid:115)(cid:0)Make the link to AP Statistics more explicit. Even
chapter and four Cumulative AP Practice Tests. thoughTPS has been the primary text used for AP Statistics
(cid:115)(cid:0)(cid:41)(cid:78)(cid:67)(cid:76)(cid:85)(cid:68)(cid:73)(cid:78)(cid:71)(cid:0)(cid:33)(cid:48)(cid:0)(cid:37)(cid:88)(cid:65)(cid:77)(cid:0)(cid:52)(cid:73)(cid:80)(cid:83)(cid:0)(cid:73)(cid:78)(cid:0)(cid:84)(cid:72)(cid:69)(cid:0)(cid:77)(cid:65)(cid:82)(cid:71)(cid:73)(cid:78)(cid:0)(cid:87)(cid:72)(cid:69)(cid:82)(cid:69)(cid:0)(cid:65)(cid:80)(cid:80)(cid:82)(cid:79)(cid:80)(cid:82)(cid:73)(cid:65)(cid:84)(cid:69)(cid:14) since the first edition was published, some reviewers suggest-
ed that we were being a bit too subtle about this fact. As you
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will see, from the front cover to the last page of the book, we
team who are intimately familiar with the AP Statistics
have rededicated ourselves to our primary mission: preparing
course and exam.
students for success in the course and on the AP exam.
TPS 4e is a book for high school students, written by high school (cid:115)(cid:0)Enhance the design. Today’s students are accustomed to
teachers. We deliberately chose contexts in the examples and operating in a visually stimulating environment. A textbook
exercises to appeal to a teenage audience. Our writing style is with an engaging look and feel is more likely to get used
straightforward enough to make ideas clear to students at varied regularly. We have attempted to create visual appeal without
reading levels (including English-language learners) without making the pages too busy or distracting.
sacrificing statistical accuracy. Students can learn by reading (cid:115)(cid:0)Focus on readability. Explanations that are too technical
the narrative, but they will develop deeper understanding by or formal discourage students from reading. Narrative that’s
doing Activities and Data Explorations, answering Check Your excessively casual can lead to sloppy statistics. Finding a
Understanding questions, and working lots of exercises. The comfortable middle ground, where students hear a consistent
text takes advantage of the simulation, graphing, and computa- voice and tone throughout, was a major priority for the new
tion capabilities of the TI-83/84, TI-89, and TI-Nspire statistical edition. Readability tests and reviewer comments suggest that
software and online applets to promote active learning. the fourth edition has improved accessibility without sacrific-
TPS 4e is aligned with the National Council of Teachers ing accuracy.
of Mathematics (NCTM) content standard “Data Analysis
and Probability,” with the American Statistical Association Daren Starnes has undertaken a substantial revision of the
(ASA)Guidelines for Assessment and Instruction in Statistics entire book with these goals in mind. A summary of the
Education (GAISE), and with joint recommendations of the important changes to content and features follows.
ASA and the Mathematical Association of America concern-
ing first courses in statistics:
Content
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To streamline the text:
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formulas (cid:115)(cid:0)TPS 3e Chapter P was replaced with a brief overview of
(cid:115)(cid:0)(cid:38)(cid:79)(cid:83)(cid:84)(cid:69)(cid:82)(cid:0)(cid:65)(cid:67)(cid:84)(cid:73)(cid:86)(cid:69)(cid:0)(cid:76)(cid:69)(cid:65)(cid:82)(cid:78)(cid:73)(cid:78)(cid:71) statistical thinking. Material from Chapter P was relocated as
ix