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# UPDATED Version of The Practice of Statistics

## Sixth Edition| ©2020 Daren S. Starnes; Josh Tabor

*The Practice of Statistics* is the most trusted program for AP® Statistics because it provides teachers and students with everything they need to be successful in the statistics course and on the AP® Exam. With the expert authorship of high school AP® Statistics veterans, Daren Star...

*The Practice of Statistics* is the most trusted program for AP® Statistics because it provides teachers and students with everything they need to be successful in the statistics course and on the AP® Exam. With the expert authorship of high school AP® Statistics veterans, Daren Starnes and Josh Tabor and their supporting team of AP® teacher/leaders, * The UPDATED Practice of Statistics*, Sixth edition features a revised organization to match the new unit structure in the 2019-2020 Course Framework for AP® Statistic perfectly.

While developing this updated edition, the authors ensured that every College Board Learning Objective and Essential Knowledge statement in the 2019-2020 Course Framework is addressed fully. In addition, all of the required skills -- selecting statistical methods, data analysis, using probability and simulation, and statistical argumentation -- are integrated in the student edition and are clearly identified in the Updated Teacher’s Edition to help teachers reinforce them at point of use.

*The Updated Practice of Statistics* program combines a data analysis approach with the power of technology, innovative pedagogy, and an extensive support program entirely refreshed to reflect the changes that will allow teachers to use the revised College Board organization and content seamlessly. The Updated edition features an extensive set of resources including a robust online homework program, the extensively revised Test Bank, a comprehensive set of videos, and the Teacher’s Edition and Teacher’s Resource Materials, giving teachers and students everything they need to realize success on the exam and in the course.

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## The UPDATED Practice of Statistics, Sixth Edition

*The Practice of Statistics* is the most trusted program for AP® Statistics because it provides teachers and students with everything they need to be successful in the statistics course and on the AP® Exam. With the expert authorship of high school AP® Statistics veterans, Daren Starnes and Josh Tabor and their supporting team of AP® teacher/leaders, * The UPDATED Practice of Statistics*, Sixth edition features a revised organization to match the new unit structure in the 2019-2020 Course Framework for AP® Statistic perfectly.

While developing this updated edition, the authors ensured that every College Board Learning Objective and Essential Knowledge statement in the 2019-2020 Course Framework is addressed fully. In addition, all of the required skills -- selecting statistical methods, data analysis, using probability and simulation, and statistical argumentation -- are integrated in the student edition and are clearly identified in the Updated Teacher’s Edition to help teachers reinforce them at point of use.

*The Updated Practice of Statistics* program combines a data analysis approach with the power of technology, innovative pedagogy, and an extensive support program entirely refreshed to reflect the changes that will allow teachers to use the revised College Board organization and content seamlessly. The Updated edition features an extensive set of resources including a robust online homework program, the extensively revised Test Bank, a comprehensive set of videos, and the Teacher’s Edition and Teacher’s Resource Materials, giving teachers and students everything they need to realize success on the exam and in the course.

Features

**Examples with paired “Try “Problems** – At the heart of the TPS approach are the 175 worked examples, which are mapped to parallel exercises in the Section Exercises, to offer students both practice and support. A backward/forwards navigation system ensures that students who start by trying to work exercises and only then go back to read the text content will land at the right spot and will get the guided help they need. Each Example presents a ** detailed response in a “student font” to model a complete and well written solution**.

**Over 1600 Problems for Practice** – Each of the 12 chapters is organized into 2-3 sections with 4-7 Learning Targets in each. Integrated throughout the text are ** Check Your Understanding** exercises that offer “on the spot” practice for concepts and skills just learned. Each Section ends with comprehensive

**Section Exercises**, including short answer, Multiple Choice, and “review and recycle” problems, that ensures that key ideas learned earlier in the presentation are revisited as appropriate. Every Chapter concludes with a through

**Chapter Review and summary**, including a review table that identifies related examples and exercises for each Learning Target, a focused set of Chapter Review Exercises, and a

**Chapter AP® Statistics Practice Test**with M/C and FRQ questions.

Additional help is offered through the **350 worked Example and Exercise Videos**, identified by the play button, that feature an experienced AP® Statistics walking step-by-step through each one to offer additional help and support when students need it most. The can be accessed by clicking on the link in the student e-Book or viewed at the open access Student Site.

**Integrated AP® Support** – Our authors know from experience that success on the AP® Exam comes from practicing every day- not just during a last minute review session. In addition to strict adherence to the language, nomenclature, formulas and style of the new 2019-2020 AP® Exam, many special features are incorporated:

- AP® Exam Tips appear throughout the text to provide in situ hints and guidance on how to study and prepare for the exam and avoid common mistakes.
- Each Section ends with a comprehensive Section exercise set, including “review and recycle” problems that ensures that key ideas learned earlier in the presentation are revisited as appropriate. Every Chapter concludes with a through Chapter Review and summary, including a review table that identifies related examples and exercises for each Learning Target, a focused set of Chapter Review Exercises, and a Chapter AP® Statistics Practice Test.
- In addition, each chapter features a FRAPPY (Free Response AP® Problem, Yay!) activity that prepares students to answer the challenging FRQs, that comprise 50% of the score on the AP Exam.
- Four Cumulative AP® Practice Tests are interspersed at logical breaks in the text and build in level of complexity culminating in a complete model exam to help prepare students for success on the 2019-2020 AP® Statistics Exam.

**Technology Corners** – provide detailed instructions, with screen captures, for creating graphs and performing the most important statistical analyses on the TI-84 graphing calculator. TI-Nspire instructions are available on the Student Site and in the digital platform. In addition, a comprehensive set of Applets, available free to users, supports simulation and hands-on learning and are referenced at appropriate points in the text.

New to This Edition

*From Daren and Josh: *

In "Classic" 6e (and 4e/5e), inference chapters are organized by the **type of inference**: confidence intervals for single samples (Chapter 8), significance tests for single samples (Chapter 9), and significance tests and confidence intervals for two samples (Chapter 10). In "Updated" 6e, inference chapters are organized by **type of data**, to match the CED: inference for proportions (Chapters 8–9) and inference for means (Chapters 10–11). In both books, chi-square tests and inference for slope wrap up the chapters on inference.

—

A number of important structural changes were made in the UPDATED sixth edition to ensure tight alignment with the AP® Statistics Course and Exam Description, including:

- Transforming to achieve linearity moved from Section 12.2 to Section 3.3 in
*UPDATED TPS 6e*, so Chapter 3 now aligns with College Board’s Unit 2: Exploring Two-Variable Data in the Course Framework. - Sampling distribution of a difference in proportions moved from Section 10.1 to Section 7.
*2 in UPDATED TPS 6e*;**sampling distribution of a difference in means**moved from Section 10.2 to Section 7.3 in UPDATED TPS 6e. - Inference completely reorganized to match Course Framework units:

The 4-step “State-Plan-Do-Conclude” process that is primarily intended to help students answer inference questions on the AP® exam, is now only developed only in the inference chapters (8-12) of the Updated TPS6e. Further, a streamlined two-step process for **Normal distribution and Binomial distribution** calculations has been introduced in the UPDATED sixth edition to match recent AP® rubrics.

Here are specific content changes made in the UPDATED sixth edition based on the AP® Statistics Course Framework.

**Chapter 1**

- Added mosaic plots.
- Added margin note discussing mean ± 2 or 3 SD criterion for outliers.
- Emphasized terminology:

- discrete vs. continuous quantitative variables

- descriptive statistics vs. inferential statistics

- statistic vs. parameter

- unimodal (single-peaked), bimodal (double-peaked), approximately uniform

- variance vs. standard deviation

**Chapter 2**

- Changed definition of percentile to less than or equal to, with equivalent changes to cumulative relative frequency graphs.
- Emphasized terminology:

- empirical rule (68-95-99.7 rule)

**Chapter 3**

- Removed the term “outlier” in Section 3.1, as it has a more restrictive meaning in the course framework. Replaced with “unusual value.”
- Changed the equation of the least-squares regression line to .
- Introduced term “high-leverage point” as one whose x value is far from . Also, restricted the use of “outlier” to points with big residuals. Both high-leverage points and outliers can be influential points.
- Emphasized terminology:

- univariate vs. bivariate data

**Chapter 4**

- Added systematic random sampling.
- Emphasized terminology:

- homogeneous vs. heterogeneous

- prospective vs. retrospective observational studies

**Chapter 5**

- Changed “chance process” to “random process”.
- Emphasized terminology:

- trial

- empirical vs. theoretical probability

- disjoint (mutually exclusive)

- joint probability

**Chapter 6**

- Expanded discussion of 10% condition and independent observations.
- Increased coverage of geometric random variables to include shape, center (mean), and variability (SD) of the probability distribution.
- Emphasized terminology:

- probability distribution vs. population distribution; parameter

- cumulative probability distribution

- linear transformation vs. linear combination

**Chapter 7**

- Increased emphasis on the 10% condition, including idea that the traditional formulas for and overestimate the actual SD when sampling without replacement (but the difference is negligible when the 10% condition is met).
- Emphasized terminology:

- point estimator

- randomization distribution

- independent observations vs. independent samples

**Chapters 8–11**

- For each inference procedure, the conditions are introduced by stating that we need to check for independence in data collection methods (Random condition, 10% condition when sampling without replacement) and that the sampling distribution is approximately Normal (Large Counts, Normal/Large Sample).

**Chapter 8**

- Emphasized that a confidence interval is an interval estimate of plausible values for a parameter
*based on sample data.* - Emphasized that a confidence level represents the long-run capture rate when conditions are met.
- Modified generic formula for a confidence interval to use “standard error” rather than “standard deviation” to align with the new formula sheet.
- Emphasized that a confidence interval for a proportion can be used to create other intervals (e.g., for the total number of successes in a population).

**Chapter 9**

- Modified generic formula for a standardized test statistic to include standard deviation (error) of statistic in the denominator to align with the new formula sheet.
- Emphasized that the P-value is the probability of getting evidence for Ha as strong or stronger than the observed evidence when H0 is true, assuming the probability model is valid (
*conditions are met*). - Adjusted the decision rule for rejecting H0 to P-value ≤ α instead of P-value < α.
- For a two-sample z test of H0: p1 – p2 = 0, the Large Counts condition now uses expected counts calculated with the pooled (combined) proportion instead of observed counts.

**Chapters 10 and 11**

- Encouraged use of df from technology for two-sample t procedures.
- Placed paired data procedures immediately after two-sample procedures to help students differentiate these methods.

**Chapter 12**

- Emphasized that the chi-square statistic measures how far observed counts are from expected counts,
*relative to expected counts*. - Changed the equation of the population regression model to .

Modified the Normal condition for inference about slope: At each x value, the distribution of y values is approximately Normal OR n ≥ 30. - Added mention of a one-parameter model (with y intercept = 0) that uses df = n – 1 (otherwise df = n – 2 when estimating both the slope and y intercept).

In addition to the content changes, the Updated 6th edition has been refined to provide more and better support for the diverse population of students that takes AP® Statistics today.

**NEW** – Many of the Examples now include Teacher Talk boxes that feature the voice of the teacher to guide students through the appropriate steps in the solution.

**NEW** - More detailed **Chapter Review Exercise Videos** that augment the Section Example and Exercise Videos and help students prepare for the Chapter AP® Practice Test.

**Activities and NEW Chapter Projects** – with more than 30 built in Activities and 5 Chapter Projects, students are encouraged to learn by simulation and by “doing” statistics. The activities and projects may be used to support collaborative learning as well as deeper investigation and study

Look Inside

**
UPDATED Version of The Practice of Statistics**

Sixth Edition| ©2020

Daren S. Starnes; Josh Tabor

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**UPDATED Version of The Practice of Statistics**

Sixth Edition| 2020

Daren S. Starnes; Josh Tabor

## Table of Contents

**Unit 1: Exploring One-Variable Data**

Chapter 1: Data Analysis

Chapter 2: Modeling Distributions of Quantitative Data

**Unit 2: Exploring Two-Variable Data**

Chapter 3: Exploring Two-Variable Quantitative Data

**Unit 3: Collecting Data**Chapter 4: Collecting Data

**Unit 4: Probability, Random Variables, and Probability Distributions**

Chapter 5: Probability

Chapter 6: Random Variables and Probability Distributions

**Unit 5: Sampling Distributions**

Chapter 7: Sampling Distributions

**Unit 6: Inference for Categorical Data: Proportions**

Chapter 8: Estimating Proportions with Confidence

Chapter 9: Testing Claims about Proportions

**Unit 7: Inference for Quantitative Data: Means**

Chapter 10: Estimating Means with Confidence

Chapter 11: Testing Claims about Means

**Unit 8: Inference for Categorical Data: Chi-Square Unit 9: Inference for Quantitative Data: Slopes**

Chapter 12: Inference for Distributions and Relationships

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**UPDATED Version of The Practice of Statistics**

Sixth Edition| 2020

Daren S. Starnes; Josh Tabor

## Authors

### Daren S. Starnes

**Daren S. Starnes** is Mathematics Department Chair and holds the Robert S. and Christina Seix Dow Distinguished Master Teacher Chair in Mathematics at The Lawrenceville School near Princeton, New Jersey. He earned his MA in Mathematics from the University of Michigan and his BS in Mathematics from the University of North Carolina at Charlotte. Daren is also an alumnus of the North Carolina School of Science and Mathematics. Daren has led numerous one-day and weeklong AP® Statistics institutes for new and experienced teachers, and he has been a Reader, Table Leader, and Question Leader for the AP® Statistics exam since 1998. Daren is a frequent speaker at local, state, regional, national, and international conferences. He has written articles for *The Mathematics Teacher* and *CHANCE* magazine. From 2004 to 2009, Daren served on the ASA/NCTM Joint Committee on the Curriculum in Statistics and Probability (which he chaired in 2009). While on the committee, he edited the Guidelines for Assessment and Instruction in Statistics Education (GAISE) pre-K–12 report and coauthored (with Roxy Peck) *Making Sense of Statistical Studies*, a capstone module in statistical thinking for high school students. Daren is also coauthor of the popular on-level text *Statistics and Probability with Applications*.

### Josh Tabor

**Josh Tabor** has enjoyed teaching on-level and AP® Statistics to high school students for more than 23 years, most recently at his alma mater, Canyon del Oro High School in Oro Valley, Arizona. He received a BS in Mathematics from Biola University, in La Mirada, California. In recognition of his outstanding work as an educator, Josh was named one of the five finalists for Arizona Teacher of the Year in 2011. He is a past member of the AP® Statistics Development Committee (2005–2009) and has been a Reader, Table Leader, and Question Leader at the AP® Statistics Reading since 1999. In 2013, Josh was named to the SAT® Mathematics Development Committee. Each year, Josh leads one-week AP® Summer Institutes and College Board workshops around the world and frequently speaks at local, national, and international conferences. In addition to teaching and speaking, Josh has published articles in *The American Statistician*, *The Mathematics Teacher*, *STATS Magazine*, and *The Journal of Statistics Education*. He is the coauthor with Daren Starnes of two other popular statistics textbooks, *The Practice of Statistics for the AP® Exam*, Sixth Edition, and *Statistics and Probability with Applications*, Third Edition, for on-level statistics. Outside of work, Josh enjoys gardening, traveling, and playing board games with his family.

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**UPDATED Version of The Practice of Statistics**

Sixth Edition| 2020

Daren S. Starnes; Josh Tabor

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# Program Resources

### Chapter 8 Examview Sample Test

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### Sample Chapter 8 Teacher's Edition

### UPDATED ExamView Assessment Suite for The Practice of Statistics

Daren S. Starnes; Josh Tabor | Sixth Edition | ©2020 | ISBN:9781319269357*The Practice of Statistics*is the most trusted program for AP® Statistics because it provides teachers and students with everything they need...

*The Practice of Statistics*is the most trusted program for AP® Statistics because it provides teachers and students with everything they need to be successful in the statistics course and on the AP® Exam. With the expert authorship of high school AP® Statistics veterans, Daren Starnes and Josh Tabor and their supporting team of AP® teacher/leaders,

*The Practice of Statistics*, Sixth edition (TPS6) has been crafted to follow the topical outline of the AP® Statistics course with careful attention paid to the style, nomenclature, and language used on the AP® Statistics exam. It combines a data analysis approach with the power of technology, innovative pedagogy, and an extensive support program built entirely for the sixth edition. New resources, including a robust online homework program and an extensively revised TestBank, give teachers and students everything they need to realize success on the exam and in the course.

### UPDATED Teacher's Edition for The Practice of Statistics

Daren S. Starnes; Josh Tabor | Sixth Edition | ©2020 | ISBN:9781319269326*The Practice of Statistics*is the most trusted program for AP® Statistics because it provides teachers and students with everything they need...

*The Practice of Statistics*is the most trusted program for AP® Statistics because it provides teachers and students with everything they need to be successful in the statistics course and on the AP® Exam. With the expert authorship of high school AP® Statistics veterans, Daren Starnes and Josh Tabor and their supporting team of AP® teacher/leaders,

*The Practice of Statistics*, Sixth edition (TPS6) has been crafted to follow the topical outline of the AP® Statistics course with careful attention paid to the style, nomenclature, and language used on the AP® Statistics exam. It combines a data analysis approach with the power of technology, innovative pedagogy, and an extensive support program built entirely for the sixth edition. New resources, including a robust online homework program and an extensively revised TestBank, give teachers and students everything they need to realize success on the exam and in the course.

### UPDATED Teacher's Resource Flash Drive for The Practice of Statistics

Daren S. Starnes; Josh Tabor | Sixth Edition | ©2020 | ISBN:9781319269371*The Practice of Statistics*is the most trusted program for AP® Statistics because it provides teachers and students with everything they need...

*The Practice of Statistics*is the most trusted program for AP® Statistics because it provides teachers and students with everything they need to be successful in the statistics course and on the AP® Exam. With the expert authorship of high school AP® Statistics veterans, Daren Starnes and Josh Tabor and their supporting team of AP® teacher/leaders,

*The Practice of Statistics*, Sixth edition (TPS6) has been crafted to follow the topical outline of the AP® Statistics course with careful attention paid to the style, nomenclature, and language used on the AP® Statistics exam. It combines a data analysis approach with the power of technology, innovative pedagogy, and an extensive support program built entirely for the sixth edition. New resources, including a robust online homework program and an extensively revised TestBank, give teachers and students everything they need to realize success on the exam and in the course.

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**UPDATED Version of The Practice of Statistics**

Sixth Edition| 2020

Daren S. Starnes; Josh Tabor

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**UPDATED Version of The Practice of Statistics**

Sixth Edition| 2020

Daren S. Starnes; Josh Tabor

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