, Symbol Table
A complement of event A Σx y sum of the products of each x value multiplied by
H0 null hypothesis the corresponding y value
H1 alternative hypothesis n number of values in a sample
a alpha; probability of a type I error or the area of n! n factorial
the critical region N number of values in a finite population; also used
b beta; probability of a type II error as the size of all samples combined
r sample linear correlation coefficient k number of samples or populations or categories
r rho; population linear correlation coefficient x mean of the values in a sample
r2 coefficient of determination m mu; mean of all values in a population
rs Spearman’s rank correlation coefficient s standard deviation of a set of sample values
b1 point estimate of the slope of the regression line s lowercase sigma; standard deviation of all values
in a population
b0 point estimate of the y-intercept of the regression
line s2 variance of a set of sample values
2
ny predicted value of y s variance of all values in a population
d difference between two matched values z standard score
d mean of the differences d found from matched za>2 critical value of z
sample data t t distribution
sd standard deviation of the differences d found ta>2 critical value of t
from matched sample data
df number of degrees of freedom
se standard error of estimate
F F distribution
mx mean of the population of all possible sample
x2 chi-square distribution
means x
x2R right-tailed critical value of chi-square
sx standard deviation of the population of all
possible sample means x x2L left-tailed critical value of chi-square
E margin of error of the estimate of a population p probability of an event or the population proportion
parameter, or expected value q probability or proportion equal to 1 - p
Q1, Q2, Q3 quartiles pn sample proportion
D1, D2, c , D9 deciles qn sample proportion equal to 1 - pn
P1, P2, c , P99 percentiles p proportion obtained by pooling two samples
x data value q proportion or probability equal to 1 - p
f frequency with which a value occurs P(A) probability of event A
Σ capital sigma; summation P (A
B) probability of event A, assuming event B has occurred
Σx sum of the values nPr number of permutations of n items selected r at a
Σx 2 sum of the squares of the values time
(Σx)2 square of the sum of all values nCr number of combinations of n items selected r at a
time
,Essentials of Statistics
,This page intentionally left blank
,Essentials of Statistics
5th edition
Mario F. Triola
Boston Columbus Indianapolis New York San Francisco Upper Saddle River
Amsterdam Cape Town Dubai London Madrid Milan Munich Paris Montréal Toronto
Delhi Mexico City São Paulo Sydney Hong Kong Seoul Singapore Taipei Tokyo
,Editor in Chief: Deirdre Lynch
Executive Editor: Christopher Cummings
Senior Content Editors: Rachel Reeve and Chere Bemelmans
Assistant Editor: Sonia Ashraf
Senior Managing Editor: Karen Wernholm
Production Project Managers: Tracy Patruno and Mary Sanger
Associate Director of Design: Andrea Nix
Art Director and Cover Designer: Beth Paquin
Digital Assets Manager: Marianne Groth
Media Producer: Vicki Dreyfus
Software Developers: Mary Durnwald and Bob Carroll
Senior Marketing Manager: Erin Lane
Marketing Assistant: Kathleen DeChavez
Senior Author Support/Technology Specialist: Joe Vetere
Image Manager: Rachel Youdelman
Procurement Specialist: Debbie Rossi
Production Coordination, Composition, Illustrations:
®
Cenveo Publisher Services
Text Design: Leslie Haimes
Cover Images: (kites) Manuel Fernandes/Shutterstock;
(pencils) Diane Miller/iStockphoto
Credits appear on pages 655–656, which constitute a continuation of the copyright page.
Many of the designations used by manufacturers and sellers to distinguish their products are claimed as trademarks. Where those desig-
nations appear in this book, and Pearson was aware of a trademark claim, the designations have been printed in initial caps or all caps.
Library of Congress Cataloging-in-Publication Data
Triola, Mario F.
Essentials of statistics Mario F. Triola.--5th ed.
p. cm.
Includes index.
ISBN 0-321-92459-2
1. Statistics. I. Title.
QA276.12.T776 2011
519.5--dc22
2009013574
Copyright © 2015, 2011, 2008 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 written permission of the publisher. Printed in the United States of America. For information on obtaining
permission for use of material in this work, please submit a written request to Pearson Education, Inc., Rights and Contracts
Department, 501 Boylston Street, Suite 900, Boston, MA 02116, fax your request to 617-671-3447, or e-mail at http://
www.pearsoned.com/legal/permissions.htm.
1 2 3 4 5 6 7 8 9 10—CRK—17 16 15 14 13
ISBN-10: 0-321-92459-2
www.pearsonhighered.com ISBN-13: 978-0-321-92459-9
, .
To
Ginny
Marc, Dushana, and Marisa
Scott, Anna, Siena, and Kaia
,This page intentionally left blank
,About the Author
Mario F. Triola is a Professor
Emeritus of Mathematics at
Dutchess Community College,
where he has taught statistics
for over 30 years. Marty is the
author of Elementary Statistics,
12th edition, Elementary Sta-
tistics Using Excel, 5th edition,
Elementary Statistics Using the
TI-83/84 Plus Calculator, 4th
edition, and he is a co-author
of Biostatistics for the Biologi-
cal and Health Sciences, Sta-
tistical Reasoning for Everyday
Life, 4th edition, Business Sta-
tistics, and Introduction to Technical Mathematics, 5th edition. Elementary Statistics is
currently available as an International Edition, and it has been translated into several
foreign languages. Marty designed the original STATDISK statistical software, and
he has written several manuals and workbooks for technology supporting statistics
education. He has been a speaker at many conferences and colleges. Marty’s consult-
ing work includes the design of casino slot machines and fishing rods, and he has
worked with attorneys in determining probabilities in paternity lawsuits, analyzing
data in medical malpractice lawsuits, identifying salary inequities based on gender,
and analyzing disputed election results. He has also used statistical methods in ana-
lyzing medical school surveys, and analyzing survey results for the New York City
Transit Authority. Marty has testified as an expert witness in New York State Supreme
Court. The Text and Academic Authors Association has awarded Marty a “Texty” for
Excellence for his work on Elementary Statistics.
vii
, Contents
1 Introduction to Statistics
1-1 Review and Preview 4
2
1-2 Statistical and Critical Thinking 5
1-3 Types of Data 15
1-4 Collecting Sample Data 23
2 Summarizing and Graphing Data
2-1 Review and Preview 44
42
2-2 Frequency Distributions 44
2-3 Histograms 54
2-4 Graphs That Enlighten and Graphs That Deceive 60
3 Statistics for Describing, Exploring, and Comparing Data
3-1 Review and Preview 80
78
3-2 Measures of Center 80
3-3 Measures of Variation 96
3-4 Measures of Relative Standing and Boxplots 112
4 Probability
4-1 Review and Preview 134
132
4-2 Basic Concepts of Probability 135
4-3 Addition Rule 149
4-4 Multiplication Rule: Basics 156
4-5 Multiplication Rule: Complements and Conditional Probability 168
4-6 Counting 175
4-7 Probabilities through Simulations (on CD-ROM)
4-8 Bayes’ Theorem (on CD-ROM)
5 Discrete Probability Distributions
5-1 Review and Preview 196
194
5-2 Probability Distributions 196
5-3 Binomial Probability Distributions 210
5-4 Parameters for Binomial Distributions 223
6 Normal Probability Distributions
6-1 Review and Preview 238
236
6-2 The Standard Normal Distribution 239
6-3 Applications of Normal Distributions 252
6-4 Sampling Distributions and Estimators 266
6-5 The Central Limit Theorem 278
6-6 Assessing Normality 291
6-7 Normal as Approximation to Binomial 299
7 Estimates and Sample Sizes
7-1 Review and Preview 318
316
7-2 Estimating a Population Proportion 318
7-3 Estimating a Population Mean 337
7-4 Estimating a Population Standard Deviation or Variance 355
viii
A complement of event A Σx y sum of the products of each x value multiplied by
H0 null hypothesis the corresponding y value
H1 alternative hypothesis n number of values in a sample
a alpha; probability of a type I error or the area of n! n factorial
the critical region N number of values in a finite population; also used
b beta; probability of a type II error as the size of all samples combined
r sample linear correlation coefficient k number of samples or populations or categories
r rho; population linear correlation coefficient x mean of the values in a sample
r2 coefficient of determination m mu; mean of all values in a population
rs Spearman’s rank correlation coefficient s standard deviation of a set of sample values
b1 point estimate of the slope of the regression line s lowercase sigma; standard deviation of all values
in a population
b0 point estimate of the y-intercept of the regression
line s2 variance of a set of sample values
2
ny predicted value of y s variance of all values in a population
d difference between two matched values z standard score
d mean of the differences d found from matched za>2 critical value of z
sample data t t distribution
sd standard deviation of the differences d found ta>2 critical value of t
from matched sample data
df number of degrees of freedom
se standard error of estimate
F F distribution
mx mean of the population of all possible sample
x2 chi-square distribution
means x
x2R right-tailed critical value of chi-square
sx standard deviation of the population of all
possible sample means x x2L left-tailed critical value of chi-square
E margin of error of the estimate of a population p probability of an event or the population proportion
parameter, or expected value q probability or proportion equal to 1 - p
Q1, Q2, Q3 quartiles pn sample proportion
D1, D2, c , D9 deciles qn sample proportion equal to 1 - pn
P1, P2, c , P99 percentiles p proportion obtained by pooling two samples
x data value q proportion or probability equal to 1 - p
f frequency with which a value occurs P(A) probability of event A
Σ capital sigma; summation P (A
B) probability of event A, assuming event B has occurred
Σx sum of the values nPr number of permutations of n items selected r at a
Σx 2 sum of the squares of the values time
(Σx)2 square of the sum of all values nCr number of combinations of n items selected r at a
time
,Essentials of Statistics
,This page intentionally left blank
,Essentials of Statistics
5th edition
Mario F. Triola
Boston Columbus Indianapolis New York San Francisco Upper Saddle River
Amsterdam Cape Town Dubai London Madrid Milan Munich Paris Montréal Toronto
Delhi Mexico City São Paulo Sydney Hong Kong Seoul Singapore Taipei Tokyo
,Editor in Chief: Deirdre Lynch
Executive Editor: Christopher Cummings
Senior Content Editors: Rachel Reeve and Chere Bemelmans
Assistant Editor: Sonia Ashraf
Senior Managing Editor: Karen Wernholm
Production Project Managers: Tracy Patruno and Mary Sanger
Associate Director of Design: Andrea Nix
Art Director and Cover Designer: Beth Paquin
Digital Assets Manager: Marianne Groth
Media Producer: Vicki Dreyfus
Software Developers: Mary Durnwald and Bob Carroll
Senior Marketing Manager: Erin Lane
Marketing Assistant: Kathleen DeChavez
Senior Author Support/Technology Specialist: Joe Vetere
Image Manager: Rachel Youdelman
Procurement Specialist: Debbie Rossi
Production Coordination, Composition, Illustrations:
®
Cenveo Publisher Services
Text Design: Leslie Haimes
Cover Images: (kites) Manuel Fernandes/Shutterstock;
(pencils) Diane Miller/iStockphoto
Credits appear on pages 655–656, which constitute a continuation of the copyright page.
Many of the designations used by manufacturers and sellers to distinguish their products are claimed as trademarks. Where those desig-
nations appear in this book, and Pearson was aware of a trademark claim, the designations have been printed in initial caps or all caps.
Library of Congress Cataloging-in-Publication Data
Triola, Mario F.
Essentials of statistics Mario F. Triola.--5th ed.
p. cm.
Includes index.
ISBN 0-321-92459-2
1. Statistics. I. Title.
QA276.12.T776 2011
519.5--dc22
2009013574
Copyright © 2015, 2011, 2008 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 written permission of the publisher. Printed in the United States of America. For information on obtaining
permission for use of material in this work, please submit a written request to Pearson Education, Inc., Rights and Contracts
Department, 501 Boylston Street, Suite 900, Boston, MA 02116, fax your request to 617-671-3447, or e-mail at http://
www.pearsoned.com/legal/permissions.htm.
1 2 3 4 5 6 7 8 9 10—CRK—17 16 15 14 13
ISBN-10: 0-321-92459-2
www.pearsonhighered.com ISBN-13: 978-0-321-92459-9
, .
To
Ginny
Marc, Dushana, and Marisa
Scott, Anna, Siena, and Kaia
,This page intentionally left blank
,About the Author
Mario F. Triola is a Professor
Emeritus of Mathematics at
Dutchess Community College,
where he has taught statistics
for over 30 years. Marty is the
author of Elementary Statistics,
12th edition, Elementary Sta-
tistics Using Excel, 5th edition,
Elementary Statistics Using the
TI-83/84 Plus Calculator, 4th
edition, and he is a co-author
of Biostatistics for the Biologi-
cal and Health Sciences, Sta-
tistical Reasoning for Everyday
Life, 4th edition, Business Sta-
tistics, and Introduction to Technical Mathematics, 5th edition. Elementary Statistics is
currently available as an International Edition, and it has been translated into several
foreign languages. Marty designed the original STATDISK statistical software, and
he has written several manuals and workbooks for technology supporting statistics
education. He has been a speaker at many conferences and colleges. Marty’s consult-
ing work includes the design of casino slot machines and fishing rods, and he has
worked with attorneys in determining probabilities in paternity lawsuits, analyzing
data in medical malpractice lawsuits, identifying salary inequities based on gender,
and analyzing disputed election results. He has also used statistical methods in ana-
lyzing medical school surveys, and analyzing survey results for the New York City
Transit Authority. Marty has testified as an expert witness in New York State Supreme
Court. The Text and Academic Authors Association has awarded Marty a “Texty” for
Excellence for his work on Elementary Statistics.
vii
, Contents
1 Introduction to Statistics
1-1 Review and Preview 4
2
1-2 Statistical and Critical Thinking 5
1-3 Types of Data 15
1-4 Collecting Sample Data 23
2 Summarizing and Graphing Data
2-1 Review and Preview 44
42
2-2 Frequency Distributions 44
2-3 Histograms 54
2-4 Graphs That Enlighten and Graphs That Deceive 60
3 Statistics for Describing, Exploring, and Comparing Data
3-1 Review and Preview 80
78
3-2 Measures of Center 80
3-3 Measures of Variation 96
3-4 Measures of Relative Standing and Boxplots 112
4 Probability
4-1 Review and Preview 134
132
4-2 Basic Concepts of Probability 135
4-3 Addition Rule 149
4-4 Multiplication Rule: Basics 156
4-5 Multiplication Rule: Complements and Conditional Probability 168
4-6 Counting 175
4-7 Probabilities through Simulations (on CD-ROM)
4-8 Bayes’ Theorem (on CD-ROM)
5 Discrete Probability Distributions
5-1 Review and Preview 196
194
5-2 Probability Distributions 196
5-3 Binomial Probability Distributions 210
5-4 Parameters for Binomial Distributions 223
6 Normal Probability Distributions
6-1 Review and Preview 238
236
6-2 The Standard Normal Distribution 239
6-3 Applications of Normal Distributions 252
6-4 Sampling Distributions and Estimators 266
6-5 The Central Limit Theorem 278
6-6 Assessing Normality 291
6-7 Normal as Approximation to Binomial 299
7 Estimates and Sample Sizes
7-1 Review and Preview 318
316
7-2 Estimating a Population Proportion 318
7-3 Estimating a Population Mean 337
7-4 Estimating a Population Standard Deviation or Variance 355
viii
