Statistics through applications

579 Pages·2011·30.578 MB·English

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

STATISTICS THROUGH
APPLICATIONS
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STATISTICS THROUGH
APPLICATIONS
SECOND EDITION
DAREN S. STARNES
THE LAWRENCEVILLE SCHOOL
DANIEL S. YATES
STATISTICS CONSULTANT
DAVID S. MOORE
PURDUE UNIVERSITY
W. H. FREEMAN AND COMPANY / NEW YORK
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Library of Congress Control Number: 2009936387
ISBN-13: 9-781-4292-1974-7
ISBN-10: 1-4292-1974-2
© 2011, 2005 by W. H. Freeman and Company
All rights reserved
Printed in the United States of America
First Printing
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W. H. Freeman and Company
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CONTENTS
About the Authors vii CHAPTER 4 DESCRIBING
Preface ix RELATIONSHIPS 141
4.1 Scatterplots and
CHAPTER 1 STATISTICS: THE ART Correlation 142
AND SCIENCE OF DATA 1 4.2 Regression and Prediction 168
1.1 Where Do Data Come From? 2 Chapter 4 Review 194
1.2 Drawing Conclusions from Chapter 4 Review Exercises 195
Data 18
Chapter 1 Review 28
Chapter 1 Review Exercises 29 Part B Producing Data 199
CHAPTER 5 SAMPLING AND
SURVEYS 201
Part A Analyzing Data 33
5.1 Samples, Good and
CHAPTER 2 DESCRIBING
Bad 202
DISTRIBUTIONS OF DATA 35
5.2 What Do Samples
2.1 Displaying Distributions Tell Us? 219
with Graphs 36 5.3 Sample Surveys in the
2.2 Describing Distributions Real World 236
with Numbers 59 Chapter 5 Review 252
2.3 Use and Misuse of Statistics 82 Chapter 5 Review Exercises 253
Chapter 2 Review 94
Chapter 2 Review Exercises 96
CHAPTER 6 DESIGNING
EXPERIMENTS 257
CHAPTER 3 MODELING
6.1 Experiments, Good
DISTRIBUTIONS OF DATA 101
and Bad 258
3.1 Measuring Location in a 6.2 Experiments in the
Distribution 102 Real World 273
3.2 Normal Distributions 116 6.3 Data Ethics 292
Chapter 3 Review 136 Chapter 6 Review 305
Chapter 3 Review Exercises 137 Chapter 6 Review Exercises 306
vi Contents
Chapter 9 Review 464
Part C Chance 309
Chapter 9 Review Exercises 466
CHAPTER 7 PROBABILITY: WHAT
ARE THE CHANCES? 311 CHAPTER 10 INFERENCE IN
PRACTICE 469
7.1 Randomness, Probability,
and Simulation 312 10.1 Chi-Square Tests: Goodness of Fit
7.2 Probability Rules 329 and Two-Way Tables 470
7.3 Conditional Probability 10.2 Inference about a Population
and Independence 348 Mean 493
Chapter 7 Review 364 Chapter 10 Review 516
Chapter 7 Review Exercises 365 Chapter 10 Review Exercises 517
Notes and Data Sources N-1
CHAPTER 8 PROBABILITY Solutions to Odd-Numbered Exercises S-1
MODELS 369 Index I-1
8.1 Probability Distributions 370 Tables T-1
8.2 Counting and Probability 387 Table A Standard Normal
8.3 Binomial Distributions 399 Probabilities T-1
Chapter 8 Review 413 Table B Random Digits T-2
Chapter 8 Review Exercises 414 Table C t Distribution Critical Values T-3
Table D Critical Values of z* T-4
Table E Chi-Square Critical Values T-4
Part D Inference 417
Additional Topics on CD-ROM and at
www.whfreeman.com/sta2e
CHAPTER 9 INTRODUCTION
S.1 Measuring
TO INFERENCE 419
S.2 The Consumer Price Index and
9.1 What Is a Confi dence
Government Statistics
Interval? 420
9.2 What Is a Signifi cance Test? 438
9.3 Use and Abuse of Statistical
Inference 453
ABOUT THE AUTHORS
DAREN S. STARNES 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. In 1997, he received a GTE GIFT Grant to integrate AP
Statistics and AP Environmental Science. He was named a Tandy Technology Scholar
in 1999. Daren has led numerous one-day and weeklong 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. In 2001–2002, he served as coeditor of the Technology Tips
column in the NCTM journal The Mathematics Teacher. Since 2004, Daren has 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) Making Sense of Statistical Studies, a capstone module in
statistical thinking for high school students. Daren is also coauthor of the popular text
The Practice of Statistics, second and third editions.
DANIEL S. YATES has taught AP Statistics in the Electronic Classroom (a distance
learning facility affi liated with Henrico County Public Schools in Richmond, Virginia).
Before he was a high school teacher, Dan 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 is a 2000 recipient of the College
Board/Siemens Foundation Advanced Placement Teaching Award. 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 The Practice of Statistics, fi rst, second, and third editions.
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 telecourse Against
All Odds: Inside Statistics and for the series of video modules Statistics: Decisions
Through Data, intended to aid the teaching of statistics in schools. He is the author of
infl uential 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.
vii
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PREFACE
Statistics Through Applications, second edition (STA 2e), is investigate, discuss, and make use of statistical ideas and
designed to support a fi rst course in statistics that empha- methods. Examples and exercises have been carefully
sizes statistical thinking. The focus of this text is on statistical selected to pique students’ interest and curiosity. Although
ideas and reasoning and on their relevance to such fi elds as the text has a fairly relaxed style and demands only an
medicine, education, environmental science, business, algebra background, its emphasis on ideas and reasoning
psychology, sports, politics, and entertainment. asks more of the student than many texts that emphasize
In its publication Principles and Standards for procedures over concepts.
School Mathematics, the National Council of Teachers Students learn to think about data by working with data.
of Mathematics (NCTM) identifi es “Data Analysis and Consequently, we have included many elementary graphical
Probability” as one of fi ve content standards. Here is the and numerical techniques in STA 2e. We have not, however,
precise statement of this NCTM standard: allowed techniques to dominate concepts. Our intention is to
invite discussion and even argument about statistical ideas
Instructional programs from prekindergarten rather than to focus exclusively on computation (though
through grade 12 should enable all students to— some computation remains essential). The coverage in
STA 2e is considerably broader than that of some traditional
• formulate questions that can be addressed with
statistics texts, as the table of contents reveals.
data and collect, organize, and display relevant
data to answer them;
• select and use appropriate statistical methods to THE STRUCTURE OF STA 2e
analyze data; STA 2e contains 10 chapters organized in four parts:
• develop and evaluate inferences and predictions analyzing data, producing data, chance, and inference. Each
that are based on data; chapter consists of two or three sections, each devoted to a
single coherent set of ideas. Sections are further divided into
• understand and apply basic concepts of probability.1
small subsections of material that can be fully addressed in
More recently, the American Statistical Association (ASA) a standard 45- or 50-minute high school period. Exercises
published its Guidelines for Assessment and Instruction appear at the end of each subsection, section, and chapter.
in Statistics Education (GAISE) Pre-K–12 Report to Summaries at the end of each section and chapter help
elaborate on the NCTM Data Analysis and Probability students distill what they have learned.
standard. The joint curriculum committee of the ASA
and the Mathematical Association of America (MAA)
THE SECOND EDITION
recommends that any fi rst course in statistics “emphasize
In revising Statistics Through Applications, we have
the elements of statistical thinking” and feature “more
attempted to build on the elements that made the fi rst
data and concepts, fewer recipes and derivations.”2STA 2e
edition successful:
incorporates the recommendations made by the NCTM,
ASA, and MAA by taking a conceptual and verbal approach • Clear explanations of statistical ideas and
rather than a methods-oriented one. terminology are presented.
Statistics Through Applications is ideally suited for • Hands-on Activities that allow students to explore
a non-AP-level introduction to statistics for high school statistical concepts begin each section.
students. It may be used effectively in either a one- or a
• Abundant examples from a variety of fi elds
two-semester course.
illustrate important statistical ideas.
• Varied exercises (with descriptive titles) refl ect the
THE NATURE OF STA 2e
usefulness of statistics in many different subject areas.
Statistics Through Applications is written to be read by
• Numerous cartoons enliven the pages.
students. It is somewhat informal, with thought-provoking
stories (“nuggets”) in the margins and cartoons and photo- • More than 30 short marginal nuggets offer
graphs interspersed throughout. Activities, Applications, interesting and often amusing anecdotes about
and Data Explorations give students an opportunity to statistics and its impact.
ix