Discovering the Fundamentals of Statistics [2 ed.] 9781429289627, 1429289627, 9781464110832, 1464110832, 9781464110993, 1464110999

Citation preview

Discovering the Fundamentals of

STATISTICS Second Edition

Daniel T. Larose

Central Connecticut State University

W. H. Freeman and Company A Macmillan Higher Education Company

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Publisher: Ruth Baruth Acquisitions Editor: Karen Carson Marketing Manager: Steve Thomas Marketing Assistant: Alissa Nigro Developmental Editor: Andrew Sylvester Senior Media Editor: Roland Cheyney Media Editor: Laura Judge Associate Editor: Jorge Amaral Associate Media Editor: Courtney Elezovic Editorial Assistant: Liam Ferguson Photo Editor: Cecilia Varas Photo Researcher: Julie Tesser Art Director: Diana Blume Text and Cover Design: Marsha Cohen Senior Project Editor: Elizabeth Geller Illustrations: MPS Limited Production Coordinator: Paul W. Rohloff Composition: MPS Limited Printing and Binding: RR Donnelley



TI-83™ screen shots are used with permission of the publisher: ©1996, Texas Instruments Incorporated. TI-83™ Graphic Calculator is a registered trademark of Texas Instruments Incorporated. Minitab is a registered trademark of Minitab, Inc. Microsoft© and Windows© are registered trademarks of the Microsoft Corporation in the United States and other countries. Excel screen shots are reprinted with permission from the Microsoft Corporation. Library of Congress Control Number: 2012949728



Paperback ISBN-13: 9781429289627 ISBN-10: 1429289627 Loose-Leaf ISBN-13: 9781464110832 ISBN-10: 1464110832 Instructor’s Edition ISBN-13: 9781464110993 ISBN-10: 1464110999 ©2014, 2011 by W. H. Freeman and Company All rights reserved Printed in the United States of America First printing W. H. Freeman and Company 41 Madison Avenue New York, NY 10010 Houndmills, Basingstoke RG21 6XS, England www.whfreeman.com

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BRIeF CONteNts

1

The Nature of Statistics

2

Describing Data Using Graphs and Tables

33

3

Describing Data Numerically

81

4

Correlation and Regression

149

5

Probability

193

6

Probability Distributions

251

7

Sampling Distributions

321

8

Confidence Intervals

353

9

Hypothesis Testing

405

10

Two-Sample Inference

483

11

Further Inference Methods

529

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Chapter 3

Describing Data Numerically

d e ta I L e d ta B L e O F C O N t e N t s

1

Preface to the Student About the Author

xi xxii

The Nature of Statistics Case study

1

Does Friday the 13th Change Human Behavior?

1.1 Data Stories: The People Behind the Numbers 1.2 An Introduction to Statistics

1, 6

2

5

What Is Statistics? 5 Descriptive Statistics: The Building Blocks of Data Analysis 8 Inferential Statistics: How Do We Get There from Here? 11

1.3 Gathering Data

17

Random Sampling 17 More Sampling Methods 20 Selection Bias and Questionnaire Design 23 Experimental Studies and Observational Studies

2

25

Chapter 1 Vocabulary 31 Chapter 1 Review Exercises 31 Chapter 1 Quiz 32

Describing Data Using Graphs and Tables Case study

The Caesar Cipher

33

33, 42

2.1 Graphs and Tables for Categorical Data

34

Frequency Distributions and Relative Frequency Distributions Bar Graphs and Pareto Charts 37 Pie Charts 38 Crosstabulations 39 Clustered Bar Graphs 40

2.2 Graphs and Tables for Quantitative Data

34

49

Frequency Distributions and Relative Frequency Distributions Histograms and Frequency Polygons 54 Stem-and-Leaf Displays and Dotplots 56 Distribution Shape, Symmetry, and Skewness 58

49

2.3 Further Graphs and Tables for Quantitative Data

66

Cumulative Frequency Distributions and Cumulative Relative Frequency Distributions 66 Ogives 67 Time Series Graphs 68

2.4 Graphical Misrepresentations of Data

73

Chapter 2 Vocabulary 78 Chapter 2 Review Exercises 79 Chapter 2 Quiz 80

iv

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3

Describing Data Numerically

81

Case study Can the Financial Experts Beat the Darts?

3.1 Measures of Center

81, 91, 108

82

The Mean 82 The Median 86 The Mode 88 Skewness and Measures of Center

3.2 Measures of Variability

90

96

The Range 96 Population Variance and Population Standard Deviation 98 Compute the Sample Variance and Sample Standard Deviation The Empirical Rule 105 Chebyshev’s Rule 107

3.3 Working with Grouped Data

102

114

The Weighted Mean 114 Estimating the Mean for Grouped Data 115 Estimating the variance and Standard Deviation for Grouped Data

3.4 Measures of Relative Position and Outliers z-Scores 120 Detecting Outliers Using the z-Score Method Percentiles and Percentile Ranks 125 Quartiles and the Interquartile Range 128 The Five-Number Summary 135 The Boxplot 136 Detecting Outliers Using the IQR Method Chapter 3 Formulas and Vocabulary Chapter 3 Review Exercises 145 Chapter 3 Quiz 147

117

120

124

3.5 Five-Number Summary and Boxplots

4

v

134

139

144

Correlation and Regression Case study Worldwide Patterns of Cell Phone Usage

4.1 Scatterplots and Correlation

149 149, 171

150

Scatterplots 150 Correlation Coefficient 152 Test for Linear Correlation 158

4.2 Introduction to Regression The Regression Line 164 Predictions and Prediction Error

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164

168

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Chapter 3Table Detailed Describing of Contents Data Numerically

4.3 Further Topics in Regression Analysis

178

Sum of Squares Error (SSE) and Standard Error of the Estimate s SST, SSR, and SSE 181 Coefficient of Determination r 2 183 Chapter 4 Formulas and Vocabulary Chapter 4 Review Exercises 189 Chapter 4 Quiz 190

5

189

Probability

193

Case study The ELISA Test for the Presence of HIV

5.1 Introducing Probability

5.2 Combining Events

197

209

Complement, Union, and Intersection Addition Rule 211

5.3 Conditional Probability

209

217

Introduction to Conditional Probability 217 Independent Events 219 Multiplication Rule 221 Approximating Probabilities for Dependent Events

5.4 Counting Methods

224

234

Multiplication Rule for Counting 234 Permutations and Combinations 237 Computing Probabilities Using Combinations Chapter 5 Formulas and Vocabulary Chapter 5 Review Exercises 247 Chapter 5 Quiz 248

242

246

Probability Distributions Case study Text Messaging

251

251, 274

6.1 Discrete Random Variables

252

Random Variables 252 Discrete Probability Distributions 255 Mean and Variability of a Discrete Random Variable

6.2 Binomial Probability Distribution Binomial Experiment 266 Binomial Probability Distribution Formula

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193, 228

194

Building Blocks of Probability 194 Classical Method of Assigning Probability Relative Frequency Method 200

6

178

257

266 268

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Binomial Distribution Tables  272 Binomial Mean, Variance, Standard Deviation, and Mode  273

6.3 Continuous Random Variables and the Normal Probability Distribution  279 Continuous Probability Distributions  280 Calculating Probabilities for the Uniform Probability Distribution  281 Introduction to Normal Probability Distribution  282

6.4 Standard Normal Distribution  288 Finding Areas Under the Standard Normal Curve for a Given Z-Value  288 Finding Standard Normal Z-Values for a Given Area  293

6.5 Applications of the Normal Distribution  298 Finding Probabilities for Any Normal Distribution  298 Finding a Normal Data Value for a Given Area or Probability  302

6.6 Normal Approximation to the Binomial Probability Distribution  311 Using the Normal Distribution to Approximate Probabilities of the Binomial Distribution  311 Chapter 6 Formulas and Vocabulary  316 Chapter 6 Review Exercises  317 Chapter 6 Quiz  318

7

Sampling Distributions

321

Case Study Trial of the Pyx: How Much Gold Is in Your Gold Coins?  321, 337

7.1 Introduction to Sampling Distributions  322 _

Sampling Distribution of the Sample Mean x​ ​    323 _ Sampling Distribution of ​x​ for a Normal Population  325 Finding Probabilities and Percentiles Using a Sampling Distribution  326

7.2 Central Limit Theorem for Means  332 Assessing Normality Using Normal Probability Plots  332 _ Sampling Distribution of x​ ​  for Skewed Populations  333 Applying the Central Limit Theorem for Means  334

7.3 Central Limit Theorem for Proportions  342 ˆ​    342 Sampling Distribution of the Sample Proportion p​ Applying the Central Limit Theorem for Proportions  345 Chapter 7 Formulas and Vocabulary  350 Chapter 7 Review Exercises  351 Chapter 7 Quiz  351

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Chapter 3Table Detailed Describing of Contents Data Numerically

8

Confidence Intervals

353

Case study Health Effects of the Deepwater Horizon Oil Spill 353, 388

8.1 Z Interval for the Population Mean

354

Calculate a Point Estimate of the Population Mean 354 The Z Interval for the Population Mean 355 Ways to Reduce the Margin of Error 362 Sample Size for Estimating the Population Mean 364

8.2 t Interval for the Population Mean

370

Introducing the t Distribution 370 t Interval for the Population Mean 373

8.3 Z Interval for the Population Proportion Point Estimate pˆ of the Population Proportion p 382 Z Interval for the Population Proportion p 383 Margin of Error for the Z Interval for p 385 Sample Size for Estimating the Population Proportion

382

386

8.4 Confidence Intervals for the Population Variance and Standard Deviation 392 Properties of the x2 (Chi-Square) Distribution 393 Constructing Confidence Intervals for the Population Variance and Standard Deviation 395

9

Chapter 8 Formulas and Vocabulary Chapter 8 Review Exercises 401 Chapter 8 Quiz 402

400

Hypothesis Testing Case study The Golden Ratio

405 405, 445

9.1 Introduction to Hypothesis Testing

406

Constructing the Hypotheses 407 Type I and Type II Errors 410

9.2 Z Test for the Population Mean: Critical-Value Method The Essential Idea About Hypothesis Testing for the Mean 413 Performing the Z Test for the Mean, Using the Critical-Value Method

9.3 Z Test for the Population Mean: p-Value Method

413 415

422

The p-Value Method of Performing the Z Test for the Mean 422 Assessing the Strength of Evidence Against the Null Hypothesis 428 The Relationship Between the p-Value Method and the Critical-Value Method 429 Using Confidence Intervals for µ to Perform Two-Tailed Hypothesis Tests About µ 430

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9.4 t Test for the Population Mean  437 t Test for µ Using the Critical-Value Method  437 t Test for µ Using the p-Value Method  440 Using Confidence Intervals to Perform Two-Tailed t Tests  444

9.5 Z Test for the Population Proportion  452 The Z Test for p Using the Critical-Value Method  452 Z Test for p: the p-Value Method  455 Using Confidence Intervals for p to Perform Two-Tailed Hypothesis Tests About p  458

9.6 Chi-Square Test for the Population Standard Deviation  463 x2 (Chi-Square) Test for s Using the Critical-Value Method  463 x2 Test for s Using the p-Value Method  466 Using Confidence Intervals for s to Perform Two-Tailed Hypothesis Tests for s  468

9.7 Probability of Type II Error and the Power of a Hypothesis Test  472 Probability of a Type II Error  472 Power of a Hypothesis Test  474 Chapter 9 Formulas and Vocabulary  478 Chapter 9 Review Exercises  478 Chapter 9 Quiz  480

10

Two-Sample Inference

483

Case Study Do Prior Student Evaluations Influence Students’ Ratings of Professors?  483, 505

10.1 Inference for Mean Difference—Dependent Samples  484 Independent Samples and Dependent Samples  484 Dependent Sample t Test for the Population Mean of the Differences  485 t Intervals for the Population Mean Difference for Dependent Samples  491 Use a t Interval for µd to Perform t Tests About µd  492

10.2 Inference for Two Independent Means  497 Independent Sample t Test for µ1 – µ2  497 t Confidence Intervals for µ1 – µ2  503 Using Confidence Intervals to Perform Hypothesis Tests  504 t Inference for µ1 – µ2 Using Pooled Variance  506 Z Inference for µ1 – µ2 When s1 and s2 Are Known  508

10.3 Inference for Two Independent Proportions  514 Independent Sample Z Tests for p1 – p2  514 Independent Sample Z Interval for p1 – p2  520 Use Z Confidence Intervals to Perform Z Tests for p1 – p2  521 Chapter 10 Formulas and Vocabulary  525 Chapter 10 Review Exercises  526 Chapter 10 Quiz  526

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Detailed Table of Contents

11

Further Inference Methods

529

Case Study Online Dating  529, 550

11.1 x2 Goodness of Fit Test  530 The Multinomial Random Variable  531 What Is a x2 Goodness of Fit Test?  532 Performing the x2 Goodness of Fit Test  534

11.2 x2 Tests for Independence and for Homogeneity of Proportions  543 Introduction to the x2 Test for Independence  543 Performing the x2 Test for Independence  545 Test for the Homogeneity of Proportions  548

11.3 Analysis of Variance  557 F Distribution  557 How Analysis of Variance (ANOVA) Works  558 Performing One-Way ANOVA  565

11.4 Inference in Regression  575 The Regression Model and the Regression Assumptions  575 Hypothesis Tests for Slope b1  579 Confidence Interval for b1  583 Using Confidence Intervals to Perform the t Test for Slope b1  584 Chapter 11 Formulas and Vocabulary  589 Chapter 11 Review Exercises  590 Chapter 11 Quiz  592 Answers to Odd-Numbered Exercises and Chapter Quizzes  A-1 Tables Appendix  T-1 Table A: Random numbers  T-2 Table B: Binomial distribution  T-3 Table C: Standard normal distribution  T-9 Table D: t-Distribution  T-11 Table E: Chi-square (x 2 ) distribution  T-12 Table F: F-Distribution critical values  T-13 Table G: Critical values for correlation coefficient  T-17 Notes and Data Sources  N-1 Index  I-1

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P R e Fa C e t O t H e s t u d e N t

xi

Our 21st century world is flooded with data. Stock market returns and sports results snake across our TV screens in a nonstop stream. Grocery purchases are beep-beeped into data warehouses that enable the retailer to analayze the purchases and recommend individualized offers to their customers. Political candidates recite statistical facts and figures often massaged to support their positions on the issues. To develop a deeper sense of meaning and comprehension of data, students today need to turn to statistics: the art and science of collecting, analyzing, presenting, and interpreting data. Discovering the Fundamentals of Statistics will help you develop the quantitative and analytical tools needed to understand statistics in today’s data-saturated world.

The Introductory Statistics Course Discovering the Fundamentals of Statistics is intended for an algebra-based, undergraduate, one- or two-semester course in general introductory statistics for non-majors. The only prerequisite is basic algebra. Discovering the Fundamentals of Statistics will prepare you to work with data in fields such as psychology, business, nursing, education, and liberal arts, to name a few. The GAISE guidelines, endorsed by the American Statistical Association, include the following recommendations: 1. 2. 3. 4. 5. 6.

Emphasize statistical literacy and develop statistical thinking Use real data Stress conceptual understanding rather than mere knowledge of procedures Foster active learning in the classroom Use technology for developing conceptual understanding and analyzing data Use assessments to improve and evaluate student learning

Discovering the Fundamentals of Statistics adopts these guidelines verbatim as the course pedagogical objectives, with the following single adjustment: (3) Stress conceptual understanding in addition to knowledge of procedures. To these, the text adds two course pedagogical objectives: 7. Use case studies to show how newly acquired analytic tools may be applied to a familiar problem. 8. Encourage student motivation.

Approach of Discovering the Fundamentals of Statistics, Second Edition Balanced analytical and computational coverage. The text integrates data interpretation and discovery-based methods with complete computational coverage of introductory statistics topics. Through unique and careful use of pedagogy, the text helps you develop your “statistical sense”—understanding the meaning behind the numbers. Equally, the text includes integrated and comprehensive computational coverage, including step-by-step solutions within examples. Select examples include screen shots and computer output from TI-83/84, Excel, Minitab, and CrunchIt!, with keystroke instructions located in the Step-by-Step Technology Guides at the ends of sections. Communication of results. Discovering the Fundamentals of Statistics, Second Edition emphasizes how, in the real world and in your future careers, you will need to explain statistical results to others who have never taken a statistics course.

xi

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Preface to the Student

Emphasis on variability. The importance of variability in the introductory statistics curriculum cannot be overstated. Without a solid appreciation of how statistics may vary, there is little chance that you will be able to understand the crucial topic of sampling distributions. Use of powerful, current examples with real data. The Deepwater Horizon oil spill, the use of cell-phone apps, and celebrity-followers on Twitter represent the variety of examples included in Discovering the Fundamentals of Statistics, Second Edition. Example and exercise topics reflect real-world problems and engage your interest in their solution. Real data (with sources cited) are frequently used to further demonstrate relevance of topics.

New to This Edition •

• •

• •

•

Additional topics have been added throughout the text. These additions include coverage of percentile ranks in Chapter 3, approximating probabilities for dependent events in Chapter 5, t inference for μ1 — μ2 using pooled variance, Z inference for μ1 — μ2, inference for two independent standard deviations in Chapter 10. For more information on content coverage, see “Key Chapter Changes” on page xiv. An increased number of examples and exercises offers extra support and provides a variety of relative examples to review and exercises to practice. Examples and exercises cover a wide range of applications and use updated, real data. Now You Can Do Exercises feature, found in the margin next to most examples, cues you to try related Practicing the Techniques exercises. These callouts are intended to prompt you toward practicing the techniques shown in the example. When working a particular exercise, you can also easily look back through the section to find the callout to a related example. Bringing It All Together exercises within each section offer a culmination of everything you have learned in a particular section, using a related set of Applying the Concepts exercises to tie together the main concepts and techniques learned. Chapter 9, “Hypothesis Testing,” has been rewritten to accommodate instructor preference with regard to teaching (a) the critical-value method only, (b) the p-value method only, or (c) both methods. (a) For those who like to cover the critical-value method but not the p-value method, simply cover Section 9.2 but not Section 9.3. (b) For those who like to cover the p-value method but not the critical-value method, cover only Objective 1 from Section 9.2, and then cover Section 9.3. (c) For those who like to cover both methods, simply cover both Section 9.2 and Section 9.3. For all hypothesis tests, coverage of the critical-value method has been moved ahead of the p-value method. This aligns our coverage with that of most of our competitors, making it easier for instructors who have previously taught using a different book, to use Discovering Statistics. In Chapters 9 and 10, the null hypothesis now always contains an equal sign. For example, the previous usage was: The new notation is:

H0 : μ ≤ μ0 versus Ha : μ  μ0 H0 : μ 5 μ0 versus Ha : μ  μ0

•

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The rejection rules is as follows, to be applied throughout the book: • Critical-value method (right-tailed test example): Changed from “Reject H0 if test statistic > critical value” to “Reject H0 if test statistic ≥ critical-value.” • p-value method: Changed from “Reject H0 if p-value < a” to “Reject H0 if p-value ≤ a.”

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xiii

CrunchIt!® Statistical Software is now included in the Step-by-Step Technology Guides at the end of select sections. This easily accessible and easy to use software offers all the basic statistical routines covered in introductory statistics courses. Data sets, available in a variety of software formats, are each named and marked with an icon in the text. You can locate the data sets on the CD in the back of the book or at www.whfreeman.com/discofun2e. The Try This in Class feature has been moved to the IRCD and is now integrated with the In-Class Activities for each chapter of the Instructor’s Edition.

Key Chapter Changes • •

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Chapter 2: Crosstabulations and clustered bar graphs are now covered in Section 2.1, “Graphs and Tables for Categorical Data.” Chapter 3: Section 3.1 now contains exercises covering the trimmed mean, the midrange, the harmonic mean, and the geometric mean. Section 3.2 now offers exercises on the coefficient of variation, the mean absolute deviation, and the coefficient of skewness. Quartiles and the interquartile range are now covered in Section 3.4 Measures of Position and Outliers. Chebyshev’s Rule and the Empirical Rule have been moved to their more natural position as applications of the standard deviation in Section 3.2, “Measures of Variability.” Chapter 4 is newly titled “Correlation and Regression.” Chapter 4 begins with a brand new case study, “Worldwide Patterns of Cell Phone Usage”, where students use the methods learned in this chapter to examine whether residents of richer countries tend to use their cell phones to browse the Internet more often than residents of poor countries. Section 4.1 covers the closely related topics of scatterplots and the correlation coefficient. The regression equation has been changed from ˆy 5 b0  b1x to y 5 b1x + b0, so that instructors who also teach algebra may be comfortable moving from the y 5 mx  b notation. Chapter 6 is now titled “Probability Distributions.” The chapter begins with a new case study, “Text Messaging,” where students will learn that they must be careful what they assume. Section 6.2 offers new exercises on the geometric, hypergeometric, and multinomial distributions. Section 6.4 now covers the uniform probability distribution. NEW Section 6.6 covers the Normal Approximation to the Binomial Probability Distribution. Chapter 7: The point estimate topic has been moved to Section 8.1, where it appears more naturally just before confidence intervals. The awkward term standard deviation of the sampling distribution of the sample mean has been replaced with the more succinct standard error of the mean. Similarly, the standard deviation of the sampling distribution of the sample proportion is replaced with standard error of the proportion. Normal probability plots are now covered in Section 7.2, just in time for when they are needed. Overall, the coverage has been streamlined so that instructors may get to the Central Limit Theorem more quickly. Chapter 8 opens with a NEW Case Study: Health Effects of the Deepwater Horizon Oil Spill. Section 8.1, “Z Interval for the Population Mean” now covers point estimates. The material on the Z confidence interval has been rewritten, making it simpler and increasing the pace. Chapter 9: The critical-value method is now covered before the p-value method. Starting in Section 9.4, in the Applying the Concepts exercises, the method to be used (critical value method or p-value method) is not specified. However, the Practicing the Techniques exercises continue to specify which method to be used. The null hypothesis and rejection rule formulas have been changed (see description above). There is a NEW Section 9.7 on probability of a type II error and the power of a hypothesis test.

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Preface to the Student

•

Chapter 10: The null hypothesis formula has been changed (see description above). Starting with this chapter, coverage of hypothesis testing is moved ahead of confidence intervals for the remainder of the book, in line with common practice. Section 10.2, “Inference for Two Independent Means,” covers two new topics: (a) t inference for µ1 – µ2 using pooled variance and (b) Z inference for µ1 – µ2 when s1 and s2 are known.

Features of Discovering the Fundamentals of Statistics, Second Edition The Second Edition retains many of the successful features from the First Edition. Case Studies. A case study begins each chapter and is developed throughout the section examples, using the new set of tools that the section provides.

The Big Picture. Brief, bulleted lists at the beginning of each chapter look at “where we are coming from, and where we are headed…”. (Chapter 2, page 34)

Matched Objectives. Each section begins with a list of numbered objectives headed “By the end of this section, I will be able to…”. The objective numbers are matched with the numbered topics within each section as well as the end-of-section summary. (Chapter 7, pages 332, 339)

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Developing Your Statistical Sense. This feature empowers students with some useful perspectives that real-world data analysts need to know. You will learn to think like real-world statistical analysts. This feature implements the GAISE guideline “develop statistical thinking.” (Chapter. 9, page 411)

What Does This Mean? Feature boxes foster an intuitive approach and interpretation of results. Whenever a new formula or statistic is being introduced, the emphasis is on “What does this really mean?” Developing this understanding is just as important as getting the right answer, especially when the software can do the calculations. In the workplace, you may need to explain to your manager what the statistical results really mean. This feature helps to implement the GAISE guideline “stress conceptual understanding.” (Chapter 8, page 358)

What If Scenarios. The scenarios help you focus on statistical thinking rather than rote computation. Because of the availability of powerful statistical computer packages, statistical analysis is easy to do badly. The wrong analysis is worse than useless. It can cost companies lots of money, may convince lawmakers to pass legislation affecting millions of people, can incorrectly determine effects of pharmaceuticals or environmental pollution, and can have many other serious ramifications. The What If? scenarios are extensions of examples or exercises aimed at honing students’ critical-thinking skills. In What If? exercises, the original problem set-up is altered in a specific but nonquantifiable way. You are then asked to think about how that change would percolate through the results, without recourse to calculations. The exercises as well as the scenarios are marked with the What If? icon. (Chapter 3, page 89)

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Preface to the Student

Stepped Example Solutions. In selected examples, you are guided through the key steps needed to work through the calculations and find the solution. (Chapter 9, page 418)

What Results Might We Expect? This feature, located in example solutions, challenges you to predict what the result of a particular problem will be. You are presented with a graphical view of the situation, and, before performing any calculations, you are asked to bring your intuition and common sense to bear on the problem and to state what results we might expect once we do the number crunching. (Chapter 9, page 426) Definitions and Formulas. Easily located in highlighted boxes, key definitions and formulas are important for you to understand when working examples and exercises. Important vocabulary and formulas are also listed (with page references) at the end of each chapter. (Chapter 1, page 6)

Exercises. Discovering the Fundamentals of Statistics, Second Edition, contains a rich and varied collection of section and chapter exercises.

• • • •

Clarifying the Concepts (conceptual) Practicing the Techniques (skill-based) Applying the Concepts (real-world applications) NEW Bringing It All Together

These exercises bring together everything you have learned in a particular section, using a related set of Applying the Concepts exercises to tie together the main concepts and techniques learned in the section.

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NEW Now You Can Do Exercises feature

Connects the Practicing the Techniques exercises to specific examples from the section. For example, in the margin at the end of Example 4.2 on page 152, you will find “Now You Can Do Exercises 13–18.” This callout lets you know that you can use the example as a model when completing the exercise set.

•

Construct Your Own Data Sets

In these exercises, students are challenged to make up their own small set of numbers fulfilling some particular requirement, such as the mean being greater than the median. These exercises reinforce the statistical concepts beyond just rote calculation of the answers. At the end of each chapter, Review Exercises and a Chapter Quiz help to test your overall understanding of each chapter’s concepts and to practice for exams. The answers to odd-numbered exercises and all chapter quiz exercises are given in the back of the book. Step-by-Step Technology Guide. This feature covers TI83/84 calculators, Excel, Minitab, and CrunchIt!, providing stepped keystroke instructions for working through selected examples in the text. Screen shots of the results are often provided as well, either within the Step-by-Step Technology Guide or in the corresponding example. (Chapter 4, page 159)

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Preface to the Student LET PP

Applets. Interactive statistical applets are located on the book’s companion Web site: www.whfreeman.com/discofun2e. Applet icons in the text mark the related chapter material and exercises.

UTION CA

Caution notes. Signaled by the Caution icon, these warnings in the text help you avoid common errors and misconceptions.

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Supplements The following electronic and print supplements are available with Discovering the Fundamentals of Statistics, Second Edition: courses.bfwpub.com/discofun2e (Access code required. Available packaged with Discovering the Fundamentals of Statistics, Second Edition, or for purchase online.) StatsPortal is the digital gateway to Discovering the Fundamentals of Statistics, Second Edition, designed to enrich the course and enhance your study skills through a collection of Web-based tools. StatsPortal integrates a rich suite of diagnostic, assessment, tutorial, and enrichment features, enabling you to master statistics at your own pace. StatsPortal is organized around the following learning components: Interactive eBook offers a complete and customizable online version of the text, fully integrated with all the media resources available with Discovering the Fundamentals of Statistics, Second Edition. The eBook allows you to quickly search the text, highlight key areas, and add notes about what you are reading. Resources organizes all the resources for Discovering the Fundamentals of Statistics, Second Edition, into one location for ease of use. These resources include the following:

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NEW! is a formative assessment tool that tests your conceptual knowledge of the material in the text. As you progress through each Learning Curve activity, the system will customize the questions based on your performance so that you are tested more rigorously in those areas where you need the most work. NEW! Stepped Tutorials These new exercise tutorials (2-3 per chapter) feature algorithmically generated quizzing with step-by-step feedback and are easily assignable for homework. Statistical Video Series consisting of StatClips, StatClips Step-by-Step Examples, and Statistically Speaking “Snapshots.” View animated lecture videos, whiteboard lessons, and documentary-style footage that illustrate key statistical concepts and help you visualize statistics in real world scenarios. StatTutor Tutorials offer over 150 audio-multimedia tutorials, including video, applets, and animations. Stats@Work Simulations put you in the role of a statistical consultant, helping you to better understand statistics interactively within the context of real-life scenarios. You are asked to interpret and analyze data presented in report form, as well as to interpret current events. NEW! Statistical Applets are interactive applications that allow you to work exercises from the text and practice key statistical procedures, such as correlation and regression, probability, and random sampling. CrunchIt! Statistical Software allows users to analyze data from any online location. Designed with the beginner in mind, the software is not only easily accessible but also easy to use. CrunchIt! offers all the basic statistical routines covered in introductory statistics courses and more. EESEE Case Studies developed by The Ohio State University Statistics Department, teach you to apply your statistical skills by exploring actual case studies using real data.

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Preface to the Student

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Student Solutions Manual provides solutions to the odd-numbered exercises, with stepped out solutions to select problems. • WHFStat Macros for Excel • Data sets are available in ASCII, Excel, TI, Minitab, SPSS, and JMP formats. • Statistical Software Manuals for TI-83/84, Excel, Minitab, SPSS, and JMP provide instruction, examples, and exercises using specific statistical software packages. • (Instructors Only) SolutionMaster is a Web-based version of the instructor’s solutions manual. This easy-to-use tool allows instructors to create homework assignments, quizzes, and tests from textbook exercises and generate a separate solution guide. Assignments and solutions can be downloaded in PDF format for convenient printing and posting. For more information or a demonstration, contact your local W. H. Freeman sales representative. Assignment Center (for instructor use only) organizes assignments and grades through an easy-to-create assignment process providing access to questions from the Test Bank, Web Quizzes, and Exercises from Discovering the Fundamentals of Statistics, Second Edition. Companion Web site: www.whfreeman.com/discostat2e is an open-access Web site includes statistical applets, data sets, and quizzes. Printed Student Solutions Manual offers detailed solutions for key exercises from each section of Discovering the Fundamentals of Statistics, Second Edition. ISBN: 1464110808 EESEE (Electronic Encyclopedia of Statistical Examples and Exercises) Case Studies. Developed by The Ohio State University Statistics Department, these electronic case studies provide a wide variety of timely, real examples with real data. EESEE case studies are available via an access code-protected Web site. Access codes are included with new copies of Discovering the Fundamentals of Statistics, Second Edition, or subscriptions can be purchased online. Instructors can access EESEE through the companion Web site.

For Instructors Only Instructor’s Guide with Solutions The solutions manual offers teaching tips, chapter commentaries, lists of teaching resources, and solutions to all exercises from Discovering the Fundamentals of Statistics, Second Edition. Available electronically within the StatsPortal, the Online Study Center, and IRCD, as well as in print form. Test Bank The Test Bank contains hundreds of multiple-choice questions to generate quizzes and tests. Available electronically on CD-ROM (for Windows and Mac), where questions can be downloaded, edited, and resequenced to suit each instructor’s needs. Enhanced Instructor’s Resource CD-ROM Allows instructors to search and export (by key term or chapter) all the material from the student Web site, plus:

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All text images and tables Instructor’s Guide with Solutions PowerPoint lecture slides Test bank files ISBN: 1464110980 Course Management Systems W. H. Freeman and Company provides courses for Blackboard, WebCT (Campus Edition and Vista), and Angel course management systems. They are completely integrated courses that you can easily customize and adapt to meet your teaching goals and course objectives. Visit http://www.macmillanhighered.com/Catalog/other/Coursepack for more information.

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Acknowledgments

i-clicker is a two-way radio-frequency classroom response solution developed by educators for educators. University of Illinois physicists Tim Stelzer, Gary Gladding, Mats Selen, and Benny Brown created the i-clicker system after using competing classroom response solutions and discovering they were neither classroom-appropriate nor student-friendly. Each step of i-clicker’s development has been informed by teaching and learning. i-clicker is superior to other systems from both pedagogical and technical standpoints. To learn more about packaging i-clicker with this textbook, please contact your local sales rep or visit www.iclicker.com.

Acknowledgments I would like to join W. H. Freeman and Company in thanking the reviewers who offered comments that assisted in the development and refinement of the second edition of Discovering the Fundamentals of Statistics: Holly Ashton, Pikes Peak Community College John Beyers, University of Maryland University College Dean Burbank, Gulf Coast State College Ferry Butar Butar, Sam Houston State University Ann Cannon, Cornell College Ayona Chatterjee, University of West Georgia Zhao Chen, Florida Gulf Coast University Geoffrey Dietz, Gannon University Wanda Eanes, M