DAV Public School Week 5 Statistics Problems

ftoc.qxd
10/15/09
12:38 PM
Page xviii
This online teaching and learning environment
integrates the entire digital textbook with the
most effective instructor and student resources
to fit every learning style.
With WileyPLUS:
? Students achieve concept
mastery in a rich,
structured environment
that?s available 24/7
? Instructors personalize and manage
their course more effectively with
assessment, assignments, grade
tracking, and more
? manage time better
? study smarter
? save money
From multiple study paths, to self-assessment, to a wealth of interactive
visual and audio resources, WileyPLUS gives you everything you need to
personalize the teaching and learning experience.
? F i n d o u t h ow t o M a k e I t Yo u r s ?
www.wileyplus.com
all the help, resources, and personal support
you and your students need!
2-Minute Tutorials and all
of the resources you & your
students need to get started
www.wileyplus.com/firstday
Pre-loaded, ready-to-use
assignments and presentations
www.wiley.com/college/quickstart
Student support from an
Collaborate with your colleagues,
experienced student user
find a mentor, attend virtual and live
Ask your local representative
events, and view resources
for details!
www.WhereFacultyConnect.com
Technical Support 24/7
FAQs, online chat,
and phone support
www.wileyplus.com/support
Your WileyPLUS
Account Manager
Training and implementation support
www.wileyplus.com/accountmanager
Make It Yours!
ffirs.qxd
10/15/09
12:24 PM
Page iii
Statistics
Principles and Methods
SIXTH EDITION
Richard A. Johnson
University of Wisconsin at Madison
Gouri K. Bhattacharyya
John Wiley & Sons, Inc.
ffirs.qxd
10/15/09
12:24 PM
Page iv
Vice President & Executive Publisher
Project Editor
Senior Development Editor
Production Manager
Senior Production Editor
Marketing Manager
Creative Director
Design Director
Production Management Services
Photo Editor
Editorial Assistant
Media Editor
Cover Photo Credit
Cover Designer
Laurie Rosatone
Ellen Keohane
Anne Scanlan-Rohrer
Dorothy Sinclair
Valerie A. Vargas
Sarah Davis
Harry Nolan
Jeof Vita
mb editorial services
Sheena Goldstein
Beth Pearson
Melissa Edwards
Gallo Images-Hein von
Horsten/Getty Images, Inc.
Celia Wiley
This book was set in 10/12 Berling by Laserwords Private Limited, India and printed and bound by
RR Donnelley-Crawsfordville. The cover was printed by RR Donnelley-Crawsfordville.
Copyright ? 2010, 2006 John Wiley & Sons, 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, scanning or otherwise, except as permitted
under Sections 107 or 108 of the 1976 United States Copyright Act, without either the prior
written permission of the Publisher, or authorization through payment of the appropriate per-copy
fee to the Copyright Clearance Center, Inc. 222 Rosewood Drive, Danvers, MA 01923, website
www.copyright.com. Requests to the Publisher for permission should be addressed to the
Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030-5774,
(201)748-6011, fax (201)748-6008, website http://www.wiley.com/go/permissions.
Evaluation copies are provided to qualified academics and professionals for review purposes only,
for use in their courses during the next academic year. These copies are licensed and may not
be sold or transferred to a third party. Upon completion of the review period, please return the
evaluation copy to Wiley. Return instructions and a free of charge return shipping label are
available at www.wiley.com/go/returnlabel. Outside of the United States, please contact your
local representative.
ISBN-13 978-0-470-40927-5
Printed in the United States of America
10 9 8 7 6 5 4 3 2 1
fpref.qxd
10/15/09
12:37 PM
Page v
Preface
THE NATURE OF THE BOOK
Conclusions, decisions, and actions that are data driven predominate in today’s
world. Statistics ? the subject of data analysis and data-based reasoning ? is necessarily playing a vital role in virtually all professions. Some familiarity with this subject is now an essential component of any college education. Yet, pressures to accommodate a growing list of academic requirements often necessitate that this
exposure be brief. Keeping these conditions in mind, we have written this book to
provide students with a first exposure to the powerful ideas of modern statistics. It
presents the key statistical concepts and the most commonly applied methods of
statistical analysis. Moreover, to keep it accessible to freshmen and sophomores
from a wide range of disciplines, we have avoided mathematical derivations. They
usually pose a stumbling block to learning the essentials in a short period of time.
This book is intended for students who do not have a strong background in
mathematics but seek to learn the basic ideas of statistics and their application
in a variety of practical settings. The core material of this book is common to almost all first courses in statistics and is designed to be covered well within a
one-semester course in introductory statistics for freshmen ? seniors. It is supplemented with some additional special-topics chapters.
ORIENTATION
The topics treated in this text are, by and large, the ones typically covered in an
introductory statistics course. They span three major areas: (i) descriptive statistics, which deals with summarization and description of data; (ii) ideas of probability and an understanding of the manner in which sample-to-sample variation
influences our conclusions; and (iii) a collection of statistical methods for analyzing the types of data that are of common occurrence. However, it is the treatment
of these topics that makes the text distinctive. Throughout, we have endeavored
to give clear and concise explanations of the concepts and important statistical
terminology and methods. By means of good motivation, sound explanations, and
an abundance of illustrations given in a real-world context, it emphasizes more
than just a superficial understanding.
v
fpref.qxd
10/15/09
vi
12:37 PM
Page vi
PREFACE
Each statistical concept or method is motivated by setting out its goal and then
focusing on an example to further elaborate important aspects and to illustrate its
application. The subsequent discussion is not only limited to showing how a
method works but includes an explanation of the why. Even without recourse to
mathematics, we are able to make the reader aware of possible pitfalls in the statistical analysis. Students can gain a proper appreciation of statistics only when they
are provided with a careful explanation of the underlying logic. Without this understanding, a learning of elementary statistics is bound to be rote and transient.
When describing the various methods of statistical analysis, the reader is
continually reminded that the validity of a statistical inference is contingent
upon certain model assumptions. Misleading conclusions may result when these
assumptions are violated. We feel that the teaching of statistics, even at an introductory level, should not be limited to the prescription of methods. Students
should be encouraged to develop a critical attitude in applying the methods and
to be cautious when interpreting the results. This attitude is especially important in the study of relationship among variables, which is perhaps the most
widely used (and also abused) area of statistics. In addition to discussing inference procedures in this context, we have particularly stressed critical examination of the model assumptions and careful interpretation of the conclusions.
SPECIAL FEATURES
1. Crucial elements are boxed to highlight important concepts and methods. These boxes provide an ongoing summary of the important items
essential for learning statistics. At the end of each chapter, all of its key
ideas and formulas are summarized.
2. A rich collection of examples and exercises is included. These are
drawn from a large variety of real-life settings. In fact, many data sets
stem from genuine experiments, surveys, or reports.
3. Exercises are provided at the end of each major section. These provide the
reader with the opportunity to practice the ideas just learned. Occasionally, they supplement some points raised in the text. A larger collection of
exercises appears at the end of a chapter. The starred problems are relatively difficult and suited to the more mathematically competent student.
4. Using Statistics Wisely, a feature at the end of each chapter, provides
important guidelines for the appropriate use of the statistical procedures presented in the chapter.
5. Statistics in Context sections, in four of the beginning chapters, each
describe an important statistical application where a statistical approach
to understanding variation is vital. These extended examples reveal, early
on in the course, the value of understanding the subject of statistics.
6. P ? values are emphasized in examples concerning tests of hypotheses.
Graphs giving the relevant normal or t density curve, rejection region,
and P ? value are presented.
fpref.qxd
10/15/09
12:37 PM
Page vii
PREFACE
vii
7. Regression analysis is a primary statistical technique so we provide a
more thorough coverage of the topic than is usual at this level. The basics of regression are introduced in Chapter 11, whereas Chapter 12
stretches the discussion to several issues of practical importance. These
include methods of model checking, handling nonlinear relations, and
multiple regression analysis. Complex formulas and calculations are judiciously replaced by computer output so the main ideas can be learned
and appreciated with a minimum of stress.
8. Integrated Technology, at the end of most chapters, details the steps for using MINITAB, EXCEL,1 and TI-84 calculator. With this presentation available, with few exceptions, only computer output is needed in the text.
Software packages remove much of the drudgery of hand calculation
and they allow students to work with larger data sets where patterns are
more pronounced. Some computer exercises are included in all chapters where relevant.
9. Convenient Electronic Data Bank at the end of the book contains a substantial collection of data. These data sets, together with numerous others throughout the book, allow for considerable flexibility in the choice
between concept-orientated and applications-orientated exercises. The
Data Bank and the other larger data sets are available for download on
the accompanying Web site located at www.wiley.com/college/johnson.
10. Technical Appendix A presents a few statistical facts of a mathematical
nature. These are separated from the main text so that they can be left
out if the instructor so desires.
ABOUT THE SIXTH EDITION
The sixth edition of STATISTICS ? Principles and Methods maintains the objectives and level of presentation of the earlier editions. The goals are the developing (i) of an understanding of the reasonings by which findings from sample
data can be extended to general conclusions and (ii) a familiarity with some
basic statistical methods. There are numerous data sets and computer outputs
which give an appreciation of the role of the computer in modern data analysis.
Clear and concise explanations introduce the concepts and important statistical terminology and methods. Real-life settings are used to motivate the
statistical ideas and well organized discussions proceed to cover statistical
methods with heavy emphasis on examples. The sixth edition enhances these
special features. The major improvements are:
Bayes? Theorem. A new section is added to Chapter 4 to highlight the reasoning underlying Bayes?s theorem and to present applications.
Approximate t. A new subsection is added to Chapter 7, which describes
the approximate two sample t statistic that is now pervasive in statistical software programs. For normal distributions, with unequal variances, this has become the preferred approach.
1Commands and the worksheets with data sets pertain to EXCEL 2003.
fpref.qxd
10/15/09
viii
12:37 PM
Page viii
PREFACE
New Examples. A substantial number of new examples are included, especially in the core chapters, Chapter 11 on regression, and Chapter 13 on contingency tables.
More Data-Based Exercises. Most of the new exercises are keyed to new
data-based examples in the text. New data are also presented in the exercises.
Other new exercises are based on the credit card use and opinion data that are
added to the data bank.
New Exercises. Numerous new exercises provide practice on understanding
the concepts and others address computations. These new exercises, which augment the already rich collection, are placed in real-life settings to help promote
a greater appreciation of the wide span of applicability of statistical methods.
ORGANIZATION
This book is organized into fifteen chapters, an optional technical appendix
(Appendix A), and a collection of tables (Appendix B). Although designed for a
one-semester or a two-quarter course, it is enriched with ample additional material to allow the instructor some choices of topics. Beyond Chapter 1, which sets
the theme of statistics and distinguishes population and sample, the subject
matter could be classified as follows:
Topic
Descriptive study of data
Probability and distributions
Sampling variability
Core ideas and methods
of statistical inference
Special topics of
statistical inference
Chapter
2, 3
4, 5, 6
7
8, 9, 10
11, 12, 13, 14, 15
We regard Chapters 1 to 10 as constituting the core material of an introductory statistics course, with the exception of the starred sections in Chapter 6. Although this material is just about enough for a one-semester course, many
instructors may wish to eliminate some sections in order to cover the basics of regression analysis in Chapter 11. This is most conveniently done by initially skipping
Chapter 3 and then taking up only those portions that are linked to Chapter 11.
Also, instead of a thorough coverage of probability that is provided in Chapter 4,
the later sections of that chapter may receive a lighter coverage.
SUPPLEMENTS
Instructor?s Solution Manual. (ISBN 978-0-470-53519-6) This manual contains complete solutions to all exercises.
fpref.qxd
10/15/09
12:37 PM
Page ix
PREFACE
ix
Test Bank. (Available on the accompanying website: www.wiley.com/
college/johnson) Contains a large number of additional questions for each
chapter.
Student Solutions Manual. (ISBN 978-0-470-53521-9) This manual contains complete solutions to all odd-numbered exercises.
Electronic Data Bank. (Available on the accompanying website: www.
wiley.com/college/johnson) Contains interesting data sets used in the text but that
can be used to perform additional analyses with statistical software packages.
WileyPLUS. This powerful online tool provides a completely integrated suite
of teaching and learning resources in one easy-to-use website. WileyPLUS offers
an online assessment system with full gradebook capabilities and algorithmically
generated skill building questions. This online teaching and learning environment
also integrates the entire digital textbook. To view a demo of WileyPLUS, contact
your local Wiley Sales Representative or visit: www.wiley.com/college/wileyplus.
ACKNOWLEDGMENTS
We thank Minitab (State College, Pa.) and the SAS Institute (Cary, N.C.) for permission to include commands and output from their software packages. A special
thanks to K. T. Wu and Kam Tsui for many helpful suggestions and comments on
earlier editions. We also thank all those who have contributed the data sets which
enrich the presentation and all those who reviewed the previous editions. The
following people gave their careful attention to this edition:
Hongshik Ahn, Stony Brook University
Prasanta Basak, Penn State University Altoona
Andrea Boito, Penn State University Altoona
Patricia M. Buchanan, Penn State University
Nural Chowdhury, University of Saskatchewan
S. Abdul Fazal, California State University Stanislaus
Christian K. Hansen, Eastern Washington University
Susan Kay Herring, Sonoma State University
Hui-Kuang Hsieh, University of Massachusetts Amherst
Hira L. Koul, Michigan State University
Melanie Martin, California State University Stanislaus
Mark McKibben, Goucher College
Charles H. Morgan, Jr., Lock Haven University of Pennsylvania
Perpetua Lynne Nielsen, Brigham Young University
Ashish Kumar Srivastava, St. Louis University
James Stamey, Baylor University
Masoud Tabatabai, Penn State University Harrisburg
Jed W. Utsinger, Ohio University
R. Patrick Vernon, Rhodes College
fpref.qxd
10/15/09
x
12:37 PM
Page x
PREFACE
Roumen Vesselinov, University of South Carolina
Vladimir Vinogradov, Ohio University
A. G. Warrack, North Carolina A&T State University
Richard A. Johnson
Gouri K. Bhattacharyya
ftoc.qxd
10/15/09
12:38 PM
Page xi
Contents
1
INTRODUCTION
1
2
3
4
5
6
7
8
9
10
2
1
What Is Statistics? 3
Statistics in Our Everyday Life 3
Statistics in Aid of Scientific Inquiry 5
Two Basic Concepts ? Population and Sample 8
The Purposeful Collection of Data 14
Statistics in Context 15
Objectives of Statistics 17
Using Statistics Wisely 18
Key Ideas 18
Review Exercises 19
ORGANIZATION AND DESCRIPTION OF DATA
21
1 Introduction 23
2 Main Types of Data 23
3 Describing Data by Tables and Graphs 24
3.1 Categorical Data 24
3.2 Discrete Data 28
3.3 Data on a Continuous Variable 29
4 Measures of Center 40
5 Measures of Variation 48
6 Checking the Stability of the Observations over Time 60
7 More on Graphics 64
8 Statistics in Context 66
9 Using Statistics Wisely 68
10 Key Ideas and Formulas 68
11 Technology 70
12 Review Exercises 73
xi
ftoc.qxd
10/15/09
xii
3
12:38 PM
Page xii
CONTENTS
DESCRIPTIVE STUDY OF BIVARIATE DATA
1
2
3
4
5
6
7
8
9
10
4
81
Introduction 83
Summarization of Bivariate Categorical Data 83
A Designed Experiment for Making a Comparison 88
Scatter Diagram of Bivariate Measurement Data 90
The Correlation Coefficient ? A Measure of Linear Relation 93
Prediction of One Variable from Another (Linear Regression) 104
Using Statistics Wisely 109
Key Ideas and Formulas 109
Technology 110
Review Exercises 111
PROBABILITY
115
1 Introduction 117
2 Probability of an Event 118
3 Methods of Assigning Probability 124
3.1 Equally Likely Elementary Outcomes ?
The Uniform Probability Model 124
3.2 Probability As the Long-Run Relative Frequency 126
4 Event Relations and Two Laws of Probability 132
5 Conditional Probability and Independence 141
6 Bayes? Theorem 140
7 Random Sampling from a Finite Population 155
8 Using Statistics Wisely 162
9 Key Ideas and Formulas 162
10 Technology 164
11 Review Exercises 165
5
PROBABILITY DISTRIBUTIONS
1
2
3
4
5
6
7
8
9
10
11
Introduction 173
Random Variables 173
Probability Distribution of a Discrete Random Variable 176
Expectation (Mean) and Standard Deviation
of a Probability Distribution 185
Successes and Failures ? Bernoulli Trials 193
The Binomial Distribution 198
The Binomial Distribution in Context 208
Using Statistics Wisely 211
Key Ideas and Formulas 212
Technology 213
Review Exercises 215
171
ftoc.qxd
10/15/09
12:38 PM
Page xiii
CONTENTS
6
THE NORMAL DISTRIBUTION
xiii
221
1 Probability Model for a Continuous
Random Variable 223
2 The Normal Distribution ? Its General Features 230
3 The Standard Normal Distribution 233
4 Probability Calculations with Normal Distributions 238
5 The Normal Approximation to the Binomial 242
*6 Checking the Plausibility of a Normal Model 248
*7 Transforming Observations to Attain
Near Normality 251
8 Using Statistics Wisely 254
9 Key Ideas and Formulas 255
10 Technology 256
11 Review Exercises 257
7
VARIATION IN REPEATED SAMPLES ?
SAMPLING DISTRIBUTIONS
263
1 Introduction 265
2 The Sampling Distribution of a Statistic 266
3 Distribution of the Sample Mean and
the Central Limit Theorem 273
4 Statistics in Context 285
5 Using Statistics Wisely 289
6 Key Ideas and Formulas 289
7 Review Exercises 290
8 Class Projects 292
9 Computer Project 293
8
DRAWING INFERENCES FROM LARGE SAMPLES
1
2
3
4
5
6
7
8
9
Introduction 297
Point Estimation of a Population Mean 299
Confidence Interval for a Population Mean 305
Testing Hypotheses about a Population Mean 314
Inferences about a Population Proportion 329
Using Statistics Wisely 337
Key Ideas and Formulas 338
Technology 340
Review Exercises 343
295
ftoc.qxd
10/15/09
xiv
9
12:38 PM
Page xiv
CONTENTS
SMALL-SAMPLE INFERENCES
FOR NORMAL POPULATIONS
349
1 Introduction 351
2 Student?s t Distribution 351
3 Inferences about ? Small Sample Size 355
3.1 Confidence Interval for 355
3.2 Hypotheses Tests for 358
4 Relationship between Tests and Confidence Intervals 363
5 Inferences about the Standard Deviation
(The Chi-Square Distribution) 366
6 Robustness of Inference Procedures 371
7 Using Statistics Wisely 372
8 Key Ideas and Formulas 373
9 Technology 375
10 Review Exercises 376
10
COMPARING TWO TREATMENTS
1
2
3
4
5
6
7
8
9
10
11
12
13
11
381
Introduction 383
Independent Random Samples from Two Populations 386
Large Samples Inference about Difference of Two Means 388
Inferences from Small Samples: Normal Populations with
Equal Variances 394
Inferences from Small Samples: Normal Populations with Unequal
Variances 400
5.1 A Conservative t Test 400
5.2 An Approximate t Test?Satterthwaite Correction 402
Randomization and Its Role in Inference 407
Matched Pairs Comparisons 409
7.1 Inferences from a Large Number of Matched Pairs 412
7.2 Inferences from a Small Number of Matched Pairs 413
7.3 Randomization with Matched Pairs 416
Choosing between Independent Samples and a Matched Pairs Sample 418
Comparing Two Population Proportions 420
Using Statistics Wisely 426
Key Ideas and Formulas 427
Technology 431
Review Exercises 434
REGRESSION ANALYSIS ? I
Simple Linear Regression
1 Introduction 441
2 Regression with a Single Predictor 443
439
ftoc.qxd
10/15/09
12:38 PM
Page xv
CONTENTS
xv
3 A Straight-Line Regression Model 446
4 The Method of Least Squares 448
5 The Sampling Variability of the Least Squares Estimators ?
Tools for Inference 456
6 Important Inference Problems 458
6.1. Inference Concerning the Slope 1 458
6.2. Inference about the Intercept 0 460
6.3. Estimation of the Mean Response for a Specified x Value 460
6.4. Prediction of a Single Response for a Specified x Value 463
7 The Strength of a Linear Relation 471
8 Remarks about the Straight Line Model Assumptions 476
9 Using Statistics Wisely 476
10 Key Ideas and Formulas 477
11 Technology 480
12 Review Exercises 481
12
REGRESSION ANALYSIS ? II
Multiple Linear Regression and Other Topics
1
2
3
4
5
6
7
8
13
485
Introduction 487
Nonlinear Relations and Linearizing Transformations 487
Multiple Linear Regression 491
Residual Plots to Check the Adequacy of a Statistical Model 503
Using Statistics Wisely 507
Key Ideas and Formulas 507
Technology 508
Review Exercises 509
ANALYSIS OF CATEGORICAL DATA
513
1 Introduction 515
2 Pearson?s 2 Test for Goodness of Fit 518
3 Contingency Table with One Margin Fixed
(Test of Homogeneity) 522
4 Contingency Table with Neither Margin Fixed (Test of Independence) 531
5 Using Statistics Wisely 537
6 Key Ideas and Formulas 537
7 Technology 539
8 Review Exercises 540
14
ANALYSIS OF VARIANCE (ANOVA)
1 Introduction 545
2 Comparison of Several Treatments ?
The Completely Randomized Design 545
543
ftoc.qxd
10/15/09
xvi
12:38 PM
Page xvi
CONTENTS
3 Population Model and Inferences
for a Completely Randomized Design 553
4 Simultaneous Confidence Intervals 557
5 Graphical Diagnostics and Displays
to Supplement ANOVA 561
6 Randomized Block Experiments
for Comparing k Treatments 563
7 Using Statistics Wisely 571
8 Key Ideas and Formulas 572
9 Technology 573
10 Review Exercises 574
15
NONPARAMETRIC INFERENCE
577
1 Introduction 579
2 The Wilcoxon Rank-Sum Test for Comparing
Two Treatments 579
3 Matched Pairs Comparisons 590
4 Measure of Correlation Based on Ranks 599
5 Concluding Remarks 603
6 Using Statistics Wisely 604
7 Key Ideas and Formulas 604
8 Technology 605
9 Review Exercises 605
APPENDIX A1
SUMMATION NOTATION
609
APPENDIX A2
RULES FOR COUNTING
614
APPENDIX A3
EXPECTATION AND
STANDARD DEVIATION?PROPERTIES
617
THE EXPECTED VALUE AND_
STANDARD DEVIATION OF X
622
APPENDIX A4
ftoc.qxd
10/15/09
12:38 PM
Page xvii
CONTENTS
APPENDIX B
TABLES
xvii
624
Table 1
Table 2
Table 3
Table 4
Table 5
Table 6
Table 7
Random Digits 624
Cumulative Binomial Probabilities 627
Standard Normal Probabilities 634
Percentage Points of t Distributions 636
Percentage Points of 2 Distributions 637
Percentage Points of F ( v1 , v2 ) Distributions 638
Selected Tail Probabilities for the Null Distribution of
Wilcoxon?s Rank-Sum Statistic 640
Table 8 Selected Tail Probabilities for the Null Distribution
of Wilcoxon?s Signed-Rank Statistic 645
DATA BANK
647
ANSWERS TO SELECTED ODD-NUMBERED EXERCISES
665
INDEX
681
ftoc.qxd
10/15/09
12:38 PM
Page xviii
c01.qxd
10/15/09
11:59 AM
Page 1
1
Introduction
1.
2.
3.
4.
5.
6.
7.
8.
What Is Statistics?
Statistics in Our Everyday Life
Statistics in Aid of Scientific Inquiry
Two Basic Concepts?Population and Sample
The Purposeful Collection of Data
Statistics in Context
Objectives of Statistics
Review Exercises
c01.qxd
10/15/09
11:59 AM
Page 2
Surveys Provide Information
About the Population
What is your favorite spectator sport?
Football
Baseball
Basketball
Other
36.4%
12.7%
12.5%
38.4%
College and professional sports are combined in our summary.1 Clearly, football
is the most popular spectator sport. Actually, the National Football League by
itself is more popular than baseball.
Until the mid 1960s, baseball was most popular according to similar surveys.
Surveys, repeated at different times, can detect trends in opinion.
Hometown fans attending today?s game are but a sample of the population of all local
football fans. A self-selected sample may not be entirely representative of the population
on issues such as ticket price increases. Kiichiro Sato/ ? AP/Wide World Photos
1
These percentages are similar to those obtained by the ESPN Sports Poll, a service of TNS, in a
2007 poll of over 27,000 fans.
c01.qxd
10/15/09
11:59 AM
Page 3
2. STATISTICS IN OUR EVERYDAY LIFE
3
1. WHAT IS STATISTICS?
The word statistics originated from the Latin word ?status,? meaning ?state.? For a
long time, it was identified solely with the displays of data and charts pertaining
to the economic, demographic, and political situations prevailing in a country.
Even today, a major segment of the general public thinks of statistics as synonymous with forbidding arrays of numbers and myriad graphs. This image is enhanced by numerous government reports that contain a massive compilation of
numbers and carry the word statistics in their titles: ?Statistics of Farm Production,? ?Statistics of Trade and Shipping,? ?Labor Statistics,? to name a few. However, gigantic advances during the twentieth century have enabled statistics to
grow and assume its present importance as a discipline of data-based reasoning.
Passive display of numbers and charts is now a minor aspect of statistics, and
few, if any, of today?s statisticians are engaged in the routine activities of tabulation and charting.
What, then, are the role and principal objectives of statistics as a scientific
discipline? Stretching well beyond the confines of data display, statistics deals
with collecting informative data, interpreting these data, and drawing conclusions
about a phenomenon under study. The scope of this subject naturally extends to
all processes of acquiring knowledge that involve fact finding through collection
and examination of data. Opinion polls (surveys of households to study sociological, economic, or health-related issues), agricultural field experiments (with new
seeds, pesticides, or farming equipment), clinical studies of vaccines, and cloud
seeding for artificial rain production are just a few examples. The principles and
methodology of statistics are useful in answering questions such as, What kind
and how much data need to be collected? How should we organize and interpret
the data? How can we analyze the data and draw conclusions? How do we assess
the strength of the conclusions and gauge their uncertainty?
Statistics as a subject provides a body of principles and methodology for
designing the process of data collection, summarizing and interpreting
the data, and drawing conclusions or generalities.
2. STATISTICS IN OUR EVERYDAY LIFE
Fact finding through the collection and interpretation of data is not confined to professional researchers. In our attempts to understand issues of environmental protection, the state of unemployment, or the performance of competing football teams,
numerical facts and figures need to be reviewed and interpreted. In our day-to-day
life, learning takes place through an often implicit analysis of factual information.
We are all familiar to some extent with reports in the news media on important statistics.
c01.qxd
10/15/09
4
11:59 AM
Page 4
CHAPTER 1/INTRODUCTION
Employment. Monthly, as part of the Current Population Survey, the
Bureau of Census collects information about employment status from a sample of
about 65,000 households. Households are contacted on a rotating basis with threefourths of the sample remaining the same for any two consecutive months.
The survey data are analyzed by the Bureau of Labor Statistics, which reports monthly unemployment rates.

Cost of Living. The consumer price index (CPI) measures the cost of a
fixed market basket of over 400 goods and services. Each month, prices are obtained from a sample of over 18,000 retail stores that are distributed over 85
metropolitan areas. These prices are then combined taking into account the relative quantity of goods and services required by a hypothetical ?1967 urban wage
earner.? Let us not be concerned with the details of the sampling method and
calculations as these are quite intricate. They are, however, under close scrutiny
because of the importance to the hundreds of thousands of Americans whose

earnings or retirement benefits are tied to the CPI.
Election time brings the pollsters into the limelight.
Gallup Poll. This, the best known of the national polls, produces estimates of the percentage of popular vote for each candidate based on interviews
with a minimum of 1500 adults. Beginning several months before the presidential election, results are regularly published. These reports help predict winners
and track changes in voter preferences.

Our sources of factual information range from individual experience to reports
in news media, government records, and articles in professional journals. As consumers of these reports, citizens need some idea of statistical reasoning to properly
interpret the data and evaluate the conclusions. Statistical reasoning provides criteria for determining which conclusions are supported by the data and which are not.
The credibility of conclusions also depends greatly on the use of statistical methods
at the data collection stage. Statistics provides a key ingredient for any systematic
approach to improve any type of process from manufacturing to service.
Quality and Productivity Improvement. In the past 30 years, the
United States has faced increasing competition in the world marketplace. An international revolution in quality and productivity improvement has heightened
the pressure on the U.S. economy. The ideas and teaching of W. Edwards Deming helped rejuvenate Japan?s industry in the late 1940s and 1950s. In the 1980s
and 1990s, Deming stressed to American executives that, in order to survive,
they must mobilize their work force to make a continuing commitment to quality improvement. His ideas have also been applied to government. The city of
Madison, WI, has implemented quality improvement projects in the police department and in bus repair and scheduling. In each case, the project goal was
better service at less cost. Treating citizens as the customers of government services, the first step was to collect information from them in order to identify situations that needed improvement. One end result was the strategic placement
of