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Introduction to the Practice of Statistics


NINTH EDITION


David S. Moore George P. McCabe Bruce A. Craig Purdue University


Vice President, STEM: Ben Roberts Publisher: Terri Ward Senior Acquisitions Editor: Karen Carson Marketing Manager: Tom DeMarco Marketing Assistant: Cate McCaffery Development Editor: Jorge Amaral Senior Media Editor: Catriona Kaplan Assistant Media Editor: Emily Tenenbaum Director of Digital Production: Keri deManigold Senior Media Producer: Alison Lorber Associate Editor: Victoria Garvey Editorial Assistant: Katharine Munz Photo Editor: Cecilia Varas Photo Researcher: Candice Cheesman Director of Design, Content Management: Diana Blume Text and Cover Designer: Blake Logan Project Editor: Edward Dionne, MPS North America LLC Illustrations: MPS North America LLC Production Manager: Susan Wein Composition: MPS North America LLC Printing and Binding: LSC Communications Cover Illustration: Drawing Water: Spring 2011 detail (Midwest) by David Wicks “Look Back” Arrow: NewCorner/Shutterstock


Library of Congress Control Number: 2016946039


Student Edition Hardcover: ISBN-13: 978-1-319-01338-7 ISBN-10: 1-319-01338-4


Student Edition Loose-leaf: ISBN-13: 978-1-319-01362-2 ISBN-10: 1-319-01362-7


Instructor Complimentary Copy: ISBN-13: 978-1-319-01428-5 ISBN-10: 1-319-01428-3


© 2017, 2014, 2012, 2009 by W. H. Freeman and Company All rights reserved Printed in the United States of America First printing


W. H. Freeman and Company One New York Plaza Suite 4500 New York, NY 10004-1562 www.macmillanlearning.com


http://www.macmillanlearning.com

Brief Contents


To Teachers: About This Book To Students: What Is Statistics? About the Authors Data Table Index Beyond the Basics Index


PART I Looking at Data CHAPTER 1 Looking at Data—Distributions


CHAPTER 2 Looking at Data—Relationships


CHAPTER 3 Producing Data


PART II Probability and Inference CHAPTER 4 Probability: The Study of Randomness


CHAPTER 5 Sampling Distributions


CHAPTER 6 Introduction to Inference


CHAPTER 7 Inference for Means


CHAPTER 8 Inference for Proportions


PART III Topics in Inference CHAPTER 9 Inference for Categorical Data


CHAPTER 10 Inference for Regression


CHAPTER 11 Multiple Regression


CHAPTER 12 One-Way Analysis of Variance


CHAPTER 13 Two-Way Analysis of Variance Tables Answers to Odd-Numbered Exercises Notes and Data Sources Index


Contents


To Teachers: About This Book To Students: What Is Statistics? About the Authors Data Table Index Beyond the Basics Index


PART I Looking at Data CHAPTER 1 Looking at Data—Distributions Introduction


1.1 Data Key characteristics of a data set


Section 1.1 Summary Section 1.1 Exercises 1.2 Displaying Distributions with Graphs


Categorical variables: Bar graphs and pie charts Quantitative variables: Stemplots and histograms Histograms Data analysis in action: Don’t hang up on me Examining distributions Dealing with outliers Time plots


Section 1.2 Summary Section 1.2 Exercises 1.3 Describing Distributions with Numbers


Measuring center: The mean Measuring center: The median Mean versus median Measuring spread: The quartiles The five-number summary and boxplots The 1.5 × IQR rule for suspected outliers Measuring spread: The standard deviation Properties of the standard deviation Choosing measures of center and spread Changing the unit of measurement


Section 1.3 Summary Section 1.3 Exercises 1.4 Density Curves and Normal Distributions


Density curves


Measuring center and spread for density curves Normal distributions The 68–95–99.7 rule Standardizing observations Normal distribution calculations Using the standard Normal table Inverse Normal calculations Normal quantile plots


Beyond the Basics: Density estimation Section 1.4 Summary Section 1.4 Exercises Chapter 1 Exercises


CHAPTER 2 Looking at Data—Relationships Introduction


2.1 Relationships Examining relationships


Section 2.1 Summary Section 2.1 Exercises 2.2 Scatterplots


Interpreting scatterplots The log transformation Adding categorical variables to scatterplots Scatterplot smoothers Categorical explanatory variables


Section 2.2 Summary Section 2.2 Exercises 2.3 Correlation


The correlation r Properties of correlation


Section 2.3 Summary Section 2.3 Exercises 2.4 Least-Squares Regression


Fitting a line to data Prediction Least-squares regression Interpreting the regression line Facts about least-squares regression Correlation and regression Another view of r2


Section 2.4 Summary Section 2.4 Exercises 2.5 Cautions about Correlation and Regression


Residuals Outliers and influential observations


Beware of the lurking variable Beware of correlations based on averaged data Beware of restricted ranges


Beyond the Basics: Data mining Section 2.5 Summary Section 2.5 Exercises 2.6 Data Analysis for Two-Way Tables


The two-way table Joint distribution Marginal distributions Describing relations in two-way tables Conditional distributions Simpson’s paradox


Section 2.6 Summary Section 2.6 Exercises 2.7 The Question of Causation


Explaining association Establishing causation


Section 2.7 Summary Section 2.7 Exercises Chapter 2 Exercises


CHAPTER 3 Producing Data Introduction


3.1 Sources of Data Anecdotal data Available data Sample surveys and experiments


Section 3.1 Summary Section 3.1 Exercises 3.2 Design of Experiments


Comparative experiments Randomization Randomized comparative experiments How to randomize Randomization using software Randomization using random digits Cautions about experimentation Matched pairs designs Block designs


Section 3.2 Summary Section 3.2 Exercises 3.3 Sampling Design


Simple random samples How to select a simple random sample


Stratified random samples Multistage random samples Cautions about sample surveys


Beyond the Basics: Capture-recapture sampling Section 3.3 Summary Section 3.3 Exercises 3.4 Ethics


Institutional review boards Informed consent Confidentiality Clinical trials Behavioral and social science experiments


Section 3.4 Summary Section 3.4 Exercises Chapter 3 Exercises


PART II Probability and Inference CHAPTER 4 Probability: The Study of Randomness Introduction


4.1 Randomness The language of probability Thinking about randomness The uses of probability


Section 4.1 Summary Section 4.1 Exercises 4.2 Probability Models


Sample spaces Probability rules Assigning probabilities: Finite number of outcomes Assigning probabilities: Equally likely outcomes Independence and the multiplication rule Applying the probability rules


Section 4.2 Summary Section 4.2 Exercises 4.3 Random Variables


Discrete random variables Continuous random variables Normal distributions as probability distributions


Section 4.3 Summary Section 4.3 Exercises 4.4 Means and Variances of Random Variables


The mean of a random variable Statistical estimation and the law of large numbers


Thinking about the law of large numbers Beyond the Basics: More laws of large numbers


Rules for means The variance of a random variable Rules for variances and standard deviations


Section 4.4 Summary Section 4.4 Exercises 4.5 General Probability Rules


General addition rules Conditional probability General multiplication rules Tree diagrams Bayes’s rule Independence again


Section 4.5 Summary Section 4.5 Exercises Chapter 4 Exercises


CHAPTER 5 Sampling Distributions Introduction


5.1 Toward Statistical Inference Sampling variability Sampling distributions Bias and variability Sampling from large populations Why randomize?


Section 5.1 Summary Section 5.1 Exercises 5.2 The Sampling Distribution of a Sample Mean


The mean and standard deviation of x̅ The central limit theorem A few more facts


Beyond the Basics: Weibull distributions Section 5.2 Summary Section 5.2 Exercises 5.3 Sampling Distributions for Counts and Proportions


The binomial distributions for sample counts Binomial distributions in statistical sampling Finding binomial probabilities Binomial mean and standard deviation Sample proportions Normal approximation for counts and proportions The continuity correction Binomial formula The Poisson distributions


Section 5.3 Summary


Section 5.3 Exercises Chapter 5 Exercises


CHAPTER 6 Introduction to Inference Introduction Overview of inference 6.1 Estimating with Confidence


Statistical confidence Confidence intervals Confidence interval for a population mean How confidence intervals behave Choosing the sample size Some cautions


Section 6.1 Summary Section 6.1 Exercises 6.2 Tests of Significance


The reasoning of significance tests Stating hypotheses Test statistics P-values Statistical significance Tests for a population mean Two-sided significance tests and confidence intervals The P-value versus a statement of significance


Section 6.2 Summary Section 6.2 Exercises 6.3 Use and Abuse of Tests


Choosing a level of significance What statistical significance does not mean Don’t ignore lack of significance Statistical inference is not valid for all sets of data Beware of searching for significance


Section 6.3 Summary Section 6.3 Exercises 6.4 Power and Inference as a Decision


Power Increasing the power Inference as decision Two types of error Error probabilities The common practice of testing hypotheses


Section 6.4 Summary Section 6.4 Exercises Chapter 6 Exercises


CHAPTER 7 Inference for Means


Introduction


7.1 Inference for the Mean of a Population The t distributions The one-sample t confidence interval The one-sample t test Matched pairs t procedures Robustness of the t procedures


Beyond the Basics: The bootstrap Section 7.1 Summary Section 7.1 Exercises 7.2 Comparing Two Means


The two-sample z statistic The two-sample t procedures The two-sample t confidence interval The two-sample t significance test Robustness of the two-sample procedures Inference for small samples Software approximation for the degrees of freedom The pooled two-sample t procedures


Section 7.2 Summary Section 7.2 Exercises 7.3 Additional Topics on Inference


Choosing the sample size Inference for non-Normal populations


Section 7.3 Summary Section 7.3 Exercises Chapter 7 Exercises


CHAPTER 8 Inference for Proportions Introduction


8.1 Inference for a Single Proportion Large-sample confidence interval for a single proportion


Beyond the Basics: The plus four confidence interval for a single proportion Significance test for a single proportion Choosing a sample size for a confidence interval Choosing a sample size for a significance test


Section 8.1 Summary Section 8.1 Exercises 8.2 Comparing Two Proportions


Large-sample confidence interval for a difference in proportions Beyond the Basics: The plus four confidence interval for a difference in proportions


Significance test for a difference in proportions Choosing a sample size for two sample proportions


Beyond the Basics: Relative risk Section 8.2 Summary


Section 8.2 Exercises Chapter 8 Exercises


PART III Topics in Inference CHAPTER 9 Inference for Categorical Data Introduction


9.1 Inference for Two-Way Tables The hypothesis: No association Expected cell counts The chi-square test Computations Computing conditional distributions The chi-square test and the z test


Beyond the Basics: Meta-analysis Section 9.1 Summary Section 9.1 Exercises 9.2 Goodness of Fit Section 9.2 Summary Section 9.2 Exercises Chapter 9 Exercises


CHAPTER 10 Inference for Regression Introduction


10.1 Simple Linear Regression Statistical model for linear regression Preliminary data analysis and inference considerations Estimating the regression parameters Checking model assumptions Confidence intervals and significance tests Confidence intervals for mean response Prediction intervals Transforming variables


Beyond the Basics: Nonlinear regression Section 10.1 Summary Section 10.1 Exercises 10.2 More Detail about Simple Linear Regression


Analysis of variance for regression The ANOVA F test Calculations for regression inference Inference for correlation


Section 10.2 Summary Section 10.2 Exercises Chapter 10 Exercises


CHAPTER 11 Multiple Regression Introduction


11.1 Inference for Multiple Regression Population multiple regression equation Data for multiple regression Multiple linear regression model Estimation of the multiple regression parameters Confidence intervals and significance tests for regression coefficients ANOVA table for multiple regression Squared multiple correlation R2


Section 11.1 Summary Section 11.1 Exercises 11.2 A Case Study


Preliminary analysis Relationships between pairs of variables Regression on high school grades Interpretation of results Examining the residuals Refining the model Regression on SAT scores Regression using all variables Test for a collection of regression coefficients


Beyond the Basics: Multiple logistic regression Section 11.2 Summary Section 11.2 Exercises Chapter 11 Exercises


CHAPTER 12 One-Way Analysis of Variance Introduction


12.1 Inference for One-Way Analysis of Variance Data for one-way ANOVA Comparing means The two-sample t statistic An overview of ANOVA The ANOVA model Estimates of population parameters Testing hypotheses in one-way ANOVA The ANOVA table The F test Software


Beyond the Basics: Testing the equality of spread Section 12.1 Summary Section 12.1 Exercises 12.2 Comparing the Means


Contrasts


Multiple comparisons Power


Section 12.2 Summary Section 12.2 Exercises Chapter 12 Exercises


CHAPTER 13 Two-Way Analysis of Variance Introduction


13.1 The Two-Way ANOVA Model Advantages of two-way ANOVA The two-way ANOVA model Main effects and interactions


13.2 Inference for Two-Way ANOVA The ANOVA table for two-way ANOVA


Chapter 13 Summary Chapter 13 Exercises Tables Answers to Odd-Numbered Exercises Notes and Data Sources Index


To Teachers: About This Book


Statistics is the science of data. Introduction to the Practice of Statistics (IPS) is an introductory text based on this principle. We present methods of basic statistics in a way that emphasizes working with data and mastering statistical reasoning. IPS is elementary in mathematical level but conceptually rich in statistical ideas. After completing a course based on our text, we would like students to be able to think objectively about conclusions drawn from data and use statistical methods in their own work.


In IPS, we combine attention to basic statistical concepts with a comprehensive presentation of the elementary statistical methods that students will find useful in their work. IPS has been successful for several reasons:


1. IPS examines the nature of modern statistical practice at a level suitable for beginners. We focus on the production and analysis of data as well as the traditional topics of probability and inference.


2. IPS has a logical overall progression, so data production and data analysis are a major focus, while inference is treated as a tool that helps us draw conclusions from data in an appropriate way.


3. IPS presents data analysis as more than a collection of techniques for exploring data. We emphasize systematic ways of thinking about data. Simple principles guide the analysis: always plot your data; look for overall patterns and deviations from them; when looking at the overall pattern of a distribution for one variable, consider shape, center, and spread; for relations between two variables, consider form, direction, and strength; always ask whether a relationship between variables is influenced by other variables lurking in the background. We warn students about pitfalls in clear cautionary discussions.


4. IPS uses real examples to drive the exposition. Students learn the technique of least-squares regression and how to interpret the regression slope. But they also learn the conceptual ties between regression and correlation and the importance of looking for influential observations.


5. IPS is aware of current developments both in statistical science and in teaching statistics. Brief, optional Beyond the Basics sections give quick overviews of topics such as density estimation, scatterplot smoothers, data mining, nonlinear regression, and meta-analysis. Chapter 16 gives an elementary introduction to the bootstrap and other computer-intensive statistical methods.

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