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Elementary Statistics: Picturing the World / Edition 7
Elementary Statistics: Picturing the World / Edition 7
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Overview
Product Details
| ISBN-13: | 2900134683415 |
|---|---|
| Publication date: | 01/03/2018 |
| Pages: | 704 |
| Product dimensions: | 6.50(w) x 1.50(h) x 9.50(d) |
About the Author
Ron Larson received his Ph.D. in mathematics from the University of Colorado in 1970. At that time he accepted a position with Penn State University, and he currently holds the rank of professor of mathematics at the university. Larson is the lead author of more than two dozen mathematics textbooks that range from 6th grade through calculus levels. Many of his texts, such as the 10th Edition of his calculus text, are leaders in their markets. Larson is also one of the pioneers in the use of multimedia and the Internet to enhance the learning of mathematics. He has authored multimedia programs, extending from the elementary school through calculus levels. Larson is a member of several professional groups and is a frequent speaker at national and regional mathematics meetings.
Many thanks to Betsy Farber for her significant contributions to previous editions of the text. Sadly, Betsy passed away in 2013. She received her Bachelor's degree in mathematics from Penn State University and her Master's degree in mathematics from the College of New Jersey. Betsy taught all levels of mathematics at Bucks County Community College in Newtown, Pennsylvania for many years. She made many notable contributions throughout her career to developing new ways to make statistics relevant and interesting for both online and traditional students.
Read an Excerpt
PREFACE:
Preface
Welcome to Elementary Statistics: Picturing the World. This book has a variety of pedagogical features, all of which are designed to show students how statistics is used to picture and describe the world and to show them that statistics is used to make informed decisions. This message—picturing the world—begins with the cover, continues through the chapter openers, sections, exercise sets, and special features.
General Features
Versatile Course Coverage The table of contents of the text was developed to give instructors many options. For instance, by assigning the Extending the Basics exercises and spending time on the chapter projects, there is sufficient content to use the text in a two-semester course. More commonly, we expect the text to be used in a three-credit semester course. In such cases, instructors will have to pare down the text's 46 sections. If you want more information on sample syllabi, check the Web site that accompanies the text.
Choice of Table Our experience has shown that students find a cumulative density function (CDF) table easier to use than a "O-to-z" table. Using the CDF table to find the area under a normal curve is the topic of Section 5.2 on pages 202-208. Because we realize that many teachers prefer to use the "O-to-z" table, we have provided an alternative presentation of Section 5.2 using the "O-to-z" table in Appendix A of the book.
Graphical Approach As with most introductory statistics texts, we begin the descriptive statistics chapter with a survey of different ways to display data graphically. A differencebetween this text and many others is that we continue to incorporate the graphical display of data throughout the text. For example, see the use of stem-and-leaf plots to display data on pages 326 and 329. In all, the text has over 750 graphs—surpassing all other introductory statistics texts.
Variety of Real-Life Applications We have chosen real-life applications that are representative of the majors of the students taking introductory statistics courses. These include business, psychology, health sciences, sports, computer science, political science, and many others. Choosing meaningful applications for such a diverse audience is difficult. We wanted the applications to be authentic—but they also need to be accessible.
Data and Source Lines The data sets in the book were chosen for interest, variety, and their ability to illustrate concepts. Most of the over 200 data sets contain actual data with source lines. The remaining data sets contain simulated data that, though not actual, are representative of real-life situations. All data sets containing 20 or more entries are available in a variety of electronic forms, including disk and Internet. In the exercise sets, the data sets that are available electronically are indicated by the icon.
Accuracy Every effort was made to ensure the mathematical accuracy of the examples and exercise solutions. The examples and exercises were solved by two people independently. A third person compared the independent solutions and resolved differences. If you encounter errors that we missed, please contact us so that we can correct the problem in a subsequent printing.
Balanced Approach The text strikes a balance between computation, decision making, and conceptual understanding. We have provided many Examples, Exercises, and Try It problems that go beyond mere computation. For instance, look at Exercises 31 and 32 on page 43. Students are not just asked to construct a relative frequency histogram for the given data, they are asked to go a step further and use the histogram to make a decision.
Prerequisites Statistics contains many formulas and variables, including radicals, summation notation, Greek letters, and subscripts. So, some familiarity with algebra and evaluation of algebraic expressions is a prerequisite. Nevertheless, we have made every effort to keep algebraic manipulations to a minimum-often we display informal versions of formulas using words in place of variables. For instance, see the definition of class width on page 30.
Flexible Technology Although most formulas in the book are illustrated with tabular "hand" calculations, we assume that most students who take this course have access to some form of technology tool, such as Minitab, Excel, or the TI-83. Because the use of technology varies widely, we have made the text flexible. It can be used in courses with no more technology than a scientific calculator—or it can be used in courses that require frequent use of sophisticated technology tools. For those who want specific instructions on particular technology tools, separate technology manuals are available to augment the text. Whatever your use of technology, we are sure that you agree with us that the goal of this course is not computation. Rather, it is to gain an understanding of the basic concepts and uses of statistics.
The Cover Each chapter begins with a photographic introduction that includes real-life data. In keeping with the theme of "picturing the world," one photo from each of the chapter openers was used to create the eleven "upper" sides of a dodecahedron. The image was created electronically using a three-dimensional modeling program. On the cover, only 6 of the sides are visible. But on the title screens of electronic versions of the text and supplements, all 11 of the upper sides are visible as the dodecahedron spins. We like this image because it resembles our spinning planet.
Page Layout We believe that statistics is more accessible to students when it is carefully formatted on each page with a consistent open lay out. This text is the first college level statistics book to be written to design, which means that none of its features (Examples, Try It problems, Definitions, or Guidelines) are split from one page to the next. Although this process requires extra planning and work in the development stage, the result is a presentation that is clean and clear.
MAA, AMATYC, NCTM Standards This text answers the call for a student-friendly text that emphasizes the uses of statistics and not just the computation of its myriad of formulas. Our experience indicates that our job as instructors of an introductory course in statistics is not to produce statisticians but to produce informed consumers of statistical reports. For this reason, we have included many exercises that require students to provide written explanations, find patterns, and make decisions.
Chapter Features
Chapter Openers Each chapter begins with a two-page description of a real-life problem. For example, look at the opener to Chapter 2.The data set contains the ages of the entire population of the fishing village of Akhiok, Alaska. As the chapter is developed, students are asked to return to the data set given in the chapter opener. For instance, on page 32 students are asked to construct a frequency distribution for the ages of the 77 residents of Akhiok. Each chapter opener has two special features called Where You've Been and Where You're Going. The first of these shows students how the chapter fits into the bigger picture of statistics, and the second gives students an overview of the chapter.
Chapter Case Study Each chapter includes a full-page case study with actual data and a series of thought-provoking questions that are designed to illustrate the important concepts of the chapter. For instance, the case study on page 329 was taken from the Journal of the American Medical Association and illustrates how hypothesis testing can be used to show that the normal human body temperature is not 98.6 degrees, as is commonly believed. The case studies can be assigned as individual projects or as group projects to be worked in class or outside of class.
Chapter Technology Project Each chapter has a full-page technology project that gives students additional insight into the way technology is used to handle large data sets or complex real-life questions. For instance, the technology project on page 346 shows students how hypothesis testing was used to show gender bias in the selection of jurors in the trial of Dr. Spock.
Chapter Summary Each chapter concludes with a chapter summary that answers the questions What did you learn? and Why did you learn it? The chapter summary is designed to be used as a study aid in conjunction with the chapter review exercises. In addition to showing the real-life uses of the material in the chapter, each summary points out one or more common abuses of statistics.
Chapter Review Exercises Following each chapter summary, we have compiled a set of review exercises that students can use as a preparation for a chapter test. The order of the exercises follows the order that the topics were presented in the chapter. The answers to all odd-numbered review exercises are given in the back of the book. The worked out solutions are available in the Student's Solutions Manual.
Chapter Quizzes and Cumulative Tests The third part of the "endof-chapter" self-evaluation materials is a chapter quiz. In addition, cumulative tests appear after Chapters 3, 6, 9, and 11. The answers to all quiz and test questions are given in the back of the book.
Section Features
Section Organization Each section is organized by learning objectives. These objectives are presented in everyday language in a margin feature called What You Should Learn. The same objectives are then used as subsection titles throughout the section.
Titled Examples Every concept in the text is clearly illustrated with one or more step-by-step examples. Each of the more than 200 examples is numbered and titled for easy reference. In presenting the examples, we used an open format with a step-by-step display that students can use as a model when solving the exercises.
Try Its Each example in the text is followed by a similar problem called Try It Yourself The answers to these problems are given in the back of the book, and the workedout solutions are given in the Student's Solutions Manual. The Try It Yourself questions are a major strength of the text as more than just a collection of exercises, but as a bona fide learning instrument. Few students who take this course understand that one cannot learn statistics by simply reading about it. Instead, one learns statistics by reading and doing statistics. Please encourage your students to use this feature-it requires effort, but it pays off in student success.
Study Tips Most sections contain one or more study tips placed on yellow "sticky notes" in the margin.These tend to be informal learning aids, which show how to read a table, use technology, or interpret a result or a graph. For instance, the study tip on page 44 points out that a stem-and-leaf plot has as many leaves as there are entries in the original data set.
Insights Most sections also contain one or more insights placed on blue "sticky notes" in the margin. The purpose of each insight is to help drive home an important interpretation or help connect different concepts. For instance, the insight on page 212 helps students interpret z-scores by pointing out that z-scores that are less than -3 or greater than 3 are very unusual.
Definitions The critical definitions of statistics are set off with gold screens. In writing the definitions, we strived for two goals—simplicity and mathematical accuracy. Consequently, the formal definitions are often followed by studentfriendly guidelines that explain, in everyday English, how to apply the definition. For instance, see the definition of population standard deviation on page 70.
Guidelines Throughout the book, the presentation of a statistical formula is followed by a step-by-step set of guidelines for applying the formula. The guidelines are divided into two columns titled In Words and In Symbols. See page 70 for an example.
Picturing the World Each section contains a real-life "mini case study" that illustrates the important concept or concepts of the section. Each Picturing the World concludes with a question, and can be used for general class discussion or group work. For instance, the Picturing the World on page 88 asks students to interpret a boxand-whisker plot that represents the ages of U.S. presidents.
Technology Examples Many sections contain a worked example that shows how technology can be used to calculate formulas, perform tests, or display data. For instance, Example 5 on page 72 shows how to use Minitab, Excel, and the TI-83 to find the mean and standard deviation of a data set. Note that this example shows the screen displays within the presentation of the example. Additional screen displays are given at the ends of selected chapters. For instance, note the technology reference for Example 7 on page 50.
Section Exercise Sets Each section concludes with a set of exercises carefully written to nurture student understanding and proficiency.
- Abundance of Exercises The text contains over 1700 exercises, more than twice the number of most introductory statistics books. Our goal is to provide instructors with a versatile teaching instrument that offers a wide range of exercises that move from basic concepts and skill development to more challenging and interpretive problems.
- Exercises are Labeled Most exercises are labeled for easy reference. For instance, Exercises 9-12 on page 336 are labeled Graphical Analysis because students are asked to use the graphs provided to answer the questions.
- Paired Format Almost all exercises are given in "paired format" so that the odd-numbered exercise, whose answer is given in the back of the book, is paired with an even-numbered exercise, whose answer is not given. This paired format is commonly used in mathematics texts, but is less common in statistics texts.
- Extending the Basics Each exercise set ends with a group of exercises called Extending the Basics. These exercises go beyond the material presented in the section—they tend to be more challenging and are not required as prerequisites of subsequent sections.
- Answers and Solutions The answers to all odd-numbered exercises are given in the back of the book, and the worked-out solutions are available in the Student's Solutions Manual.
Table of Contents
| Preface | x | |
| Features | xiii | |
| Supplements | xxi | |
| Acknowledgments | xxiii | |
| How to Study Statistics | xxiv | |
| Chapter 1 | Introduction to Statistics | 0 |
| Chapter 2 | Descriptive Statistics | 30 |
| Chapter 3 | Probability | 108 |
| Chapter 4 | Discrete Probability Distributions | 160 |
| Chapter 5 | Normal Probability Distributions | 204 |
| Chapter 6 | Confidence Intervals | 268 |
| Chapter 7 | Hypothesis Testing with One Sample | 318 |
| Chapter 8 | Hypothesis Testing with Two Samples | 388 |
| Chapter 9 | Correlation and Regression | 440 |
| Chapter 10 | Chi-Square Tests and the F-Distribution | 492 |
| Chapter 11 | Nonparametric Tests | 544 |
| Appendices | ||
| Index | 1 |
Preface
Preface
Welcome to Elementary Statistics: Picturing the World. This book has a variety of pedagogical features, all of which are designed to show students how statistics is used to picture and describe the world and to show them that statistics is used to make informed decisions. This message—picturing the world—begins with the cover, continues through the chapter openers, sections, exercise sets, and special features.
General Features
Versatile Course Coverage The table of contents of the text was developed to give instructors many options. For instance, by assigning the Extending the Basics exercises and spending time on the chapter projects, there is sufficient content to use the text in a two-semester course. More commonly, we expect the text to be used in a three-credit semester course. In such cases, instructors will have to pare down the text's 46 sections. If you want more information on sample syllabi, check the Web site that accompanies the text.
Choice of Table Our experience has shown that students find a cumulative density function (CDF) table easier to use than a "O-to-z" table. Using the CDF table to find the area under a normal curve is the topic of Section 5.2 on pages 202-208. Because we realize that many teachers prefer to use the "O-to-z" table, we have provided an alternative presentation of Section 5.2 using the "O-to-z" table in Appendix A of the book.
Graphical Approach As with most introductory statistics texts, we begin the descriptive statistics chapter with a survey of different ways to display data graphically. Adifferencebetween this text and many others is that we continue to incorporate the graphical display of data throughout the text. For example, see the use of stem-and-leaf plots to display data on pages 326 and 329. In all, the text has over 750 graphs—surpassing all other introductory statistics texts.
Variety of Real-Life Applications We have chosen real-life applications that are representative of the majors of the students taking introductory statistics courses. These include business, psychology, health sciences, sports, computer science, political science, and many others. Choosing meaningful applications for such a diverse audience is difficult. We wanted the applications to be authentic—but they also need to be accessible.
Data and Source Lines The data sets in the book were chosen for interest, variety, and their ability to illustrate concepts. Most of the over 200 data sets contain actual data with source lines. The remaining data sets contain simulated data that, though not actual, are representative of real-life situations. All data sets containing 20 or more entries are available in a variety of electronic forms, including disk and Internet. In the exercise sets, the data sets that are available electronically are indicated by the icon.
Accuracy Every effort was made to ensure the mathematical accuracy of the examples and exercise solutions. The examples and exercises were solved by two people independently. A third person compared the independent solutions and resolved differences. If you encounter errors that we missed, please contact us so that we can correct the problem in a subsequent printing.
Balanced Approach The text strikes a balance between computation, decision making, and conceptual understanding. We have provided many Examples, Exercises, and Try It problems that go beyond mere computation. For instance, look at Exercises 31 and 32 on page 43. Students are not just asked to construct a relative frequency histogram for the given data, they are asked to go a step further and use the histogram to make a decision.
Prerequisites Statistics contains many formulas and variables, including radicals, summation notation, Greek letters, and subscripts. So, some familiarity with algebra and evaluation of algebraic expressions is a prerequisite. Nevertheless, we have made every effort to keep algebraic manipulations to a minimum-often we display informal versions of formulas using words in place of variables. For instance, see the definition of class width on page 30.
Flexible Technology Although most formulas in the book are illustrated with tabular "hand" calculations, we assume that most students who take this course have access to some form of technology tool, such as Minitab, Excel, or the TI-83. Because the use of technology varies widely, we have made the text flexible. It can be used in courses with no more technology than a scientific calculator—or it can be used in courses that require frequent use of sophisticated technology tools. For those who want specific instructions on particular technology tools, separate technology manuals are available to augment the text. Whatever your use of technology, we are sure that you agree with us that the goal of this course is not computation. Rather, it is to gain an understanding of the basic concepts and uses of statistics.
The Cover Each chapter begins with a photographic introduction that includes real-life data. In keeping with the theme of "picturing the world," one photo from each of the chapter openers was used to create the eleven "upper" sides of a dodecahedron. The image was created electronically using a three-dimensional modeling program. On the cover, only 6 of the sides are visible. But on the title screens of electronic versions of the text and supplements, all 11 of the upper sides are visible as the dodecahedron spins. We like this image because it resembles our spinning planet.
Page Layout We believe that statistics is more accessible to students when it is carefully formatted on each page with a consistent open lay out. This text is the first college level statistics book to be written to design, which means that none of its features (Examples, Try It problems, Definitions, or Guidelines) are split from one page to the next. Although this process requires extra planning and work in the development stage, the result is a presentation that is clean and clear.
MAA, AMATYC, NCTM Standards This text answers the call for a student-friendly text that emphasizes the uses of statistics and not just the computation of its myriad of formulas. Our experience indicates that our job as instructors of an introductory course in statistics is not to produce statisticians but to produce informed consumers of statistical reports. For this reason, we have included many exercises that require students to provide written explanations, find patterns, and make decisions.
Chapter Features
Chapter Openers Each chapter begins with a two-page description of a real-life problem. For example, look at the opener to Chapter 2.The data set contains the ages of the entire population of the fishing village of Akhiok, Alaska. As the chapter is developed, students are asked to return to the data set given in the chapter opener. For instance, on page 32 students are asked to construct a frequency distribution for the ages of the 77 residents of Akhiok. Each chapter opener has two special features called Where You've Been and Where You're Going. The first of these shows students how the chapter fits into the bigger picture of statistics, and the second gives students an overview of the chapter.
Chapter Case Study Each chapter includes a full-page case study with actual data and a series of thought-provoking questions that are designed to illustrate the important concepts of the chapter. For instance, the case study on page 329 was taken from the Journal of the American Medical Association and illustrates how hypothesis testing can be used to show that the normal human body temperature is not 98.6 degrees, as is commonly believed. The case studies can be assigned as individual projects or as group projects to be worked in class or outside of class.
Chapter Technology Project Each chapter has a full-page technology project that gives students additional insight into the way technology is used to handle large data sets or complex real-life questions. For instance, the technology project on page 346 shows students how hypothesis testing was used to show gender bias in the selection of jurors in the trial of Dr. Spock.
Chapter Summary Each chapter concludes with a chapter summary that answers the questions What did you learn? and Why did you learn it? The chapter summary is designed to be used as a study aid in conjunction with the chapter review exercises. In addition to showing the real-life uses of the material in the chapter, each summary points out one or more common abuses of statistics.
Chapter Review Exercises Following each chapter summary, we have compiled a set of review exercises that students can use as a preparation for a chapter test. The order of the exercises follows the order that the topics were presented in the chapter. The answers to all odd-numbered review exercises are given in the back of the book. The worked out solutions are available in the Student's Solutions Manual.
Chapter Quizzes and Cumulative Tests The third part of the "endof-chapter" self-evaluation materials is a chapter quiz. In addition, cumulative tests appear after Chapters 3, 6, 9, and 11. The answers to all quiz and test questions are given in the back of the book.
Section Features
Section Organization Each section is organized by learning objectives. These objectives are presented in everyday language in a margin feature called What You Should Learn. The same objectives are then used as subsection titles throughout the section.
Titled Examples Every concept in the text is clearly illustrated with one or more step-by-step examples. Each of the more than 200 examples is numbered and titled for easy reference. In presenting the examples, we used an open format with a step-by-step display that students can use as a model when solving the exercises.
Try Its Each example in the text is followed by a similar problem called Try It Yourself The answers to these problems are given in the back of the book, and the workedout solutions are given in the Student's Solutions Manual. The Try It Yourself questions are a major strength of the text as more than just a collection of exercises, but as a bona fide learning instrument. Few students who take this course understand that one cannot learn statistics by simply reading about it. Instead, one learns statistics by reading and doing statistics. Please encourage your students to use this feature-it requires effort, but it pays off in student success.
Study Tips Most sections contain one or more study tips placed on yellow "sticky notes" in the margin.These tend to be informal learning aids, which show how to read a table, use technology, or interpret a result or a graph. For instance, the study tip on page 44 points out that a stem-and-leaf plot has as many leaves as there are entries in the original data set.
Insights Most sections also contain one or more insights placed on blue "sticky notes" in the margin. The purpose of each insight is to help drive home an important interpretation or help connect different concepts. For instance, the insight on page 212 helps students interpret z-scores by pointing out that z-scores that are less than -3 or greater than 3 are very unusual.
Definitions The critical definitions of statistics are set off with gold screens. In writing the definitions, we strived for two goals—simplicity and mathematical accuracy. Consequently, the formal definitions are often followed by studentfriendly guidelines that explain, in everyday English, how to apply the definition. For instance, see the definition of population standard deviation on page 70.
Guidelines Throughout the book, the presentation of a statistical formula is followed by a step-by-step set of guidelines for applying the formula. The guidelines are divided into two columns titled In Words and In Symbols. See page 70 for an example.
Picturing the World Each section contains a real-life "mini case study" that illustrates the important concept or concepts of the section. Each Picturing the World concludes with a question, and can be used for general class discussion or group work. For instance, the Picturing the World on page 88 asks students to interpret a boxand-whisker plot that represents the ages of U.S. presidents.
Technology Examples Many sections contain a worked example that shows how technology can be used to calculate formulas, perform tests, or display data. For instance, Example 5 on page 72 shows how to use Minitab, Excel, and the TI-83 to find the mean and standard deviation of a data set. Note that this example shows the screen displays within the presentation of the example. Additional screen displays are given at the ends of selected chapters. For instance, note the technology reference for Example 7 on page 50.
Section Exercise Sets Each section concludes with a set of exercises carefully written to nurture student understanding and proficiency.
- Abundance of Exercises The text contains over 1700 exercises, more than twice the number of most introductory statistics books. Our goal is to provide instructors with a versatile teaching instrument that offers a wide range of exercises that move from basic concepts and skill development to more challenging and interpretive problems.
- Exercises are Labeled Most exercises are labeled for easy reference. For instance, Exercises 9-12 on page 336 are labeled Graphical Analysis because students are asked to use the graphs provided to answer the questions.
- Paired Format Almost all exercises are given in "paired format" so that the odd-numbered exercise, whose answer is given in the back of the book, is paired with an even-numbered exercise, whose answer is not given. This paired format is commonly used in mathematics texts, but is less common in statistics texts.
- Extending the Basics Each exercise set ends with a group of exercises called Extending the Basics. These exercises go beyond the material presented in the section—they tend to be more challenging and are not required as prerequisites of subsequent sections.
- Answers and Solutions The answers to all odd-numbered exercises are given in the back of the book, and the worked-out solutions are available in the Student's Solutions Manual.