Statistics (12e)

Classic, yet contemporary. Theoretical, yet applied. McClave & Sincich’s Statistics gives you the best of both worlds. This text offers a trusted, comprehensive introduction to statistics that emphasizes inference and integrates real data throughout. The authors stress the development of statistical thinking, the assessment of credibility, and value of the inferences made from data.

The Twelfth Edition infuses a new focus on ethics, which is critically important when working with statistical data. Chapter Summaries have a new, study-oriented design, helping students stay focused when preparing for exams. Data, exercises, technology support, and Statistics in Action cases are updated throughout the book. In addition, MyStatLab will have increased exercise coverage and two new banks of questions to draw from: Getting Ready for Stats and Conceptual Question Library.

Ideal for one- or two-semester courses in introductory statistics, this text assumes a mathematical background of basic algebra. Flexibility is built in for instructors who teach a more advanced course, with optional footnotes about calculus and the underlying theory.

1. Statistics, Data, and Statistical Thinking

1.1 The Science of Statistics

1.2 Types of Statistical Applications

1.3 Fundamental Elements of Statistics

1.4 Types of Data

1.5 Collecting Data

1.6 The Role of Statistics in Critical Thinking

Statistics in Action: Social Media Networks and the Millennial Generation

Using Technology: Creating and Listing Data

2. Methods for Describing Sets of Data

2.1 Describing Qualitative Data

2.2 Graphical Methods for Describing Quantitative Data

2.3 Summation Notation

2.4 Numerical Measures of Central Tendency

2.5 Numerical Measures of Variability

2.6 Interpreting the Standard Deviation

2.7 Numerical Measures of Relative Standing

2.8 Methods for Detecting Outliers: Box Plots and z-Scores

2.9 Graphing Bivariate Relationships (Optional)

2.10 Distorting the Truth with Descriptive Techniques

Statistics In Action: Body Image Dissatisfaction: Real or Imagined?

Using Technology: Describing Data

3. Probability

3.1 Events, Sample Spaces, and Probability

3.2 Unions and Intersections

3.3 Complementary Events

3.4 The Additive Rule and Mutually Exclusive Events

3.5 Conditional Probability

3.6 The Multiplicative Rule and Independent Events

3.7 Random Sampling

3.8 Some Additional Counting Rules (Optional)

3.9 Bayes’ Rule (Optional)

Statistics In Action: Lotto Buster! –Can You Improve Your Chances of Winning the Lottery?

Using Technology: Generating a Random Sample

4. Discrete Random Variables

4.1 Two Types of Random Variables

4.2 Probability Distributions for Discrete Random Variables

4.3 Expected Values of Discrete Random Variables

4.4 The Binomial Random Variable

4.5 The Poisson Random Variable (Optional)

4.6 The Hypergeometric Random Variable (Optional)

Statistics in Action: Probability in a Reverse Cocaine Sting– Was Cocaine Really Sold?

Using Technology: Discrete Probabilities

5. Continuous Random Variables

5.1 Continuous Probability Distributions

5.2 The Uniform Distribution

5.3 The Normal Distribution

5.4 Descriptive Methods for Assessing Normality

5.5 Approximating a Binomial Distribution with a Normal Distribution (Optional)

5.6 The Exponential Distribution (Optional)

Statistics in Action: Super Weapons Development — Is the Hit Ratio Optimized?

Using Technology: Continuous Random Variables, Probabilities, and Normal Probability Plots

6. Sampling Distributions

6.1 What is a Sampling Distribution?

6.2 Properties of Sampling Distributions: Unbiasedness and Minimum Variance

6.3 The Sampling Distribution of (x-bar) and the Central Limit Theorem

Statistics in Action: The Insomnia Pill–Will It Take Less Time to Fall Asleep?

Using Technology: Simulating a Sampling Distribution

7. Inferences Based on a Single Sample: Estimation with Confidence Intervals

7.1 Identifying and Estimating the Target Parameter

7.2 Confidence Interval for a Population Mean: Normal (z) Statistic

7.3 Confidence Interval for a Population Mean: Student's t-statistic

7.4 Large-Sample Confidence Interval for a Population Proportion

7.5 Determining the Sample Size

7.6 Confidence Interval for a Population Variance (Optional)

Statistics in Action: Medicare Fraud Investigations

Using Technology: Confidence Intervals

8. Inferences Based on a Single Sample: Tests of Hypothesis

8.1 The Elements of a Test of Hypothesis

8.2 Formulating Hypotheses and Setting Up the Rejection Region

8.3 Test of Hypothesis About a Population Mean: Normal (z) Statistic

8.4 Observed Significance Levels: p-Values

8.5 Test of Hypothesis About a Population Mean: Student's t-statistic

8.6 Large-Sample Test of Hypothesis About a Population Proportion

8.7 Calculating Type II Error Probabilities: More About β (Optional)

8.8 Test of Hypothesis About a Population Variance (Optional)

Statistics in Action: Diary of a Kleenex User–How Many Tissues in a Box?

Using Technology: Tests of Hypothesis

9. Inferences Based on a Two Samples: Confidence Intervals and Tests of Hypotheses

9.1 Identifying the Target Parameter

9.2 Comparing Two Population Means: Independent Sampling

9.3 Comparing Two Population Means: Paired Difference Experiments

9.4 Comparing Two Population Proportions: Independent Sampling

9.5 Determining the Sample Size

9.6 Comparing Two Population Variances: Independent Sampling (Optional)

Statistics in Action: Zixit Corp. vs. Visa USA Inc.–A Libel Case

Using Technology: Two-Sample Inferences

10. Analysis of Variance: Comparing More Than Two Means

10.1 Elements of a Designed Study

10.2 The Completely Randomized Design: Single Factor

10.3 Multiple Comparisons of Means

10.4 The Randomized Block Design

10.5 Factorial Experiments: Two Factors

Statistics in Action: On the Trail of the Cockroach: Do Roaches Travel at Random?

Using Technology: Analysis of Variance

11. Simple Linear Regression

11.1 Probabilistic Models

11.2 Fitting the Model: The Least Squares Approach

11.3 Model Assumptions

11.4 Assessing the Utility of the Model: Making Inferences About the Slope β1

11.5 The Coefficients of Correlation and Determination

11.6 Using the Model for Estimation and Prediction

11.7 A Complete Example

Statistics in Action: Can "Dowsers" Really Detect Water?

Using Technology: Simple Linear Regression

12. Multiple Regression and Model Building

12.1 Multiple Regression Models

12.2 The First-Order Model: Inferences About the Individual β-Parameters

12.3 Evaluating the Overall Utility of a Model

12.4 Using the Model for Estimation and Prediction

12.5 Model Building: Interaction Models

12.6 Model Building: Quadratic and other Higher-Order Models

12.7 Model Building: Qualitative (Dummy) Variable Models

12.8 Model Building: Models with both Quantitative and Qualitative Variables

12.9 Model Building: Comparing Nested Models (Optional)

12.10 Model Building: Stepwise Regression (Optional)

12.11 Residual Analysis: Checking the Regression Assumptions

12.12 Some Pitfalls: Estimability, Multicollinearity, and Extrapolation

Statistics in Action: Modeling Condo Sales: Are There Differences in Auction Prices?

Using Technology: Multiple Regression

13. Categorical Data Analysis

13.1 Categorical Data and the Multinomial Distribution

13.2 Testing Categorical Probabilities: One-Way Table

13.3 Testing Categorical Probabilities: Two-Way (Contingency) Table

13.4 A Word of Caution About Chi-Square Tests

Statistics in Action: College Students and Alcohol–Is Drinking Frequency Related to Amount?

Using Technology: Chi-Square Analyses

14. Nonparametric Statistics*

14.1 Introduction: Distribution-Free Tests

14.2 Single Population Inferences

14.3 Comparing Two Populations: Independent Samples

14.4 Comparing Two Populations: Paired Difference Experiment

14.5 Comparing Three or More Populations: Completely Randomized Design

14.6 Comparing Three or More Populations: Randomized Block Design

14.7 Rank Correlation

Statistics in Action: How Vulnerable are Wells to Groundwater Contamination?

Using Technology: Nonparametric Analyses

Appendix A. Tables

Table I. Random Numbers

Table II. Binomial Probabilities

Table III. Poisson Probabilities

Table IV. Normal Curve Areas

Table V. Exponentials

Table VI. Critical Values of t

Table VII. Critical Values of x2

Table VIII. Percentage Points of the F Distribution, α=.10

Table IX. Percentage Points of the F Distribution, α=.05

Table X. Percentage Points of the F Distribution, α=.025

Table XI. Percentage Points of the F Distribution, α=.01

Table XII. Critical Values of TL and TU for the Wilcoxon Rank Sum Test

Table XIII. Critical Values of T0 in the Wilcoxon Signed Rank Test

Table XIV. Critical Values of Spearman's Rank Correlation Coefficient

Appendix B. Calculation Formulas for Analysis of Variance

Short Answers to Selected Odd-Numbered Exercises

*This chapter is included on the CD-ROM that comes with the textbook.

• Ethics Boxes were added where appropriate to highlight the importance of ethical behavior when collecting, analyzing, and interpreting data with statistics.
• In the “Where We’re Going” sections, which begin each chapter, section numbers now appear next to each learning objective, to show where each concept will be discussed in the chapter.
• End-of-Chapter Summaries are redesigned to be a more effective study aid for students. Important points are reinforced through flow graphs (which aid in selecting the appropriate statistical method) and boxed notes with key words, formulas, definitions, lists, and key concepts.
• Approximately 20% of more than 1,800 exercises are revised and updated. Many new and updated exercises, based on contemporary studies and real data, have been added; most foster and promote critical thinking skills.
• Five of the 14 Statistics in Action cases are new or revised, and each is based on real data from a recent study.
• Updated technology—All printouts from statistical software (SAS, SPSS, MINITAB, and the TI-83/84 Plus Graphing Calculator) and corresponding instructions for use have been revised to reflect the latest versions of the software.

Content Changes:

• Chapter 7 (Confidence Intervals): The methodology for finding a confidence interval for a population mean is developed based on using either a normal (z) statistic (Section 7.2) or a Student's t-statistic (Section 7.3). An optional section (Section 7.6) on estimating a population variance has been added.
• Chapter 8 (Tests of Hypothesis): A new section emphasizing the formulation of the null and alternative hypotheses (Section 8.2) has been added.
• Chapter 12 (Multiple Regression and Model Building): For pedagogical purposes, the chapter is divided into three parts: First Order Models with Quantitative Independent Variables, Model Building, and Multiple Regression Diagnostics.
• Chapter 13 (Categorical Data Analysis): A subsection on contingency tables with fixed marginals as been added to Section 13.3.

McClave and Sincich provide support to students when they are learning to solve problems and when they are studying and reviewing the material.

• “Where We’re Going” bullets begin each chapter, to offer learning objectives and to provide section numbers that correspond to where each concept is discussed in the chapter.
• Examples foster problem-solving skills by taking a three-step approach: (1) "Problem", (2) "Solution", and (3) "Look Back" (or "Look Ahead"). This step-by-step process provides students with a defined structure by which to approach problems and enhances their problem-solving skills.
• The "Look Back" feature often gives helpful hints to solving the problem and/or provides a further reflection or insight into the concept or procedure that is covered.
• A “Now Work” exercise suggestion follows each Example, which provides a practice exercise that is similar in style and concept to the example. Students test and confirm their understanding immediately.
• Redesigned! End-of-Chapter Summaries now serve as a more effective study aid for students. Important points are reinforced through flow graphs (which aid in selecting the appropriate statistical method) and boxed notes with key words, formulas, definitions, lists, and key concepts.

More than 1,800 exercises are included, based on a wide variety of applications in various disciplines and research areas, and more than 20% have been updated for the new edition. Some students have difficulty learning the mechanics of statistical techniques while applying the techniques to real applications. For this reason, exercise sections are divided into four parts:

• Learning the Mechanics: These exercises allow students to test their ability to comprehend a mathematical concept or a definition.
• Applying the Concepts—Basic: Based on applications taken from a wide variety of journals, newspapers, and other sources, these short exercises help students begin developing the skills necessary to diagnose and analyze real-world problems.
• Applying the Concepts—Intermediate: Based on more detailed real-world applications, these exercises require students to apply their knowledge of the technique presented in the section.
• Applying the Concepts—Advanced: These more difficult real-data exercises require students to use critical thinking skills.
• Critical Thinking Challenges: Students apply critical thinking skills to solve one or two challenging real-life problems. These expose students to real-world problems with solutions that are derived from careful, logical thought and use of the appropriate statistical analysis tool.

Case studies, applications, and biographies keep students motivated and show the relevance of statistics.

• NEW! Ethics Boxes have been added where appropriate to highlight the importance of ethical behavior when collecting, analyzing, and interpreting statistical data.
• Statistics in Action begins each chapter with a case study based on an actual contemporary, controversial, or high-profile issue. Relevant research questions and data from the study are presented and the proper analysis demonstrated in short "Statistics in Action Revisited" sections throughout the chapter.
• Brief Biographies of famous statisticians and their achievements are presented within the main chapter, as well as in marginal boxes. Students develop an appreciation for the statistician's efforts and the discipline of statistics as a whole.

Support for statistical software is integrated throughout the text and online, so instructors can focus less time on teaching the software and more time teaching statistics.

• Each statistical analysis method presented is demonstrated using output from SAS, SPSS, and MINITAB. These outputs appear in examples and exercises, exposing students to the output they will encounter in their future careers.
• Using Technology boxes at the end of each chapter offer statistical software tutorials, with step-by-step instructions and screen shots for MINITAB and, where appropriate, the TI-83/84 Plus Graphing Calculator.
• To complement the text, support for the statistical software is available in MyStatLab’s Technology Instruction Videos and the three-hole punched, tri-fold Technology Study Cards. Student discounts on select statistical software packages are also available. Ask your Pearson sales representative for details.

A Resource CD-ROM accompanies the text, with files for text examples, exercises, Statistics in Action and Real-World case data sets marked with a CD icon. All data files are available as .csv, .txt, and TI files. The CD also contains Chapter 14, Nonparametric Statistics, and a set of appletsthat allowstudents to run simulations that visually demonstrate some of the difficult statistical concepts (e.g., sampling distributions and confidence intervals.)

Flexibility in Coverage

• Probability and Counting Rules:
• Probability poses a challenge for instructors because they must decide on the level of presentation, and students find it a difficult subject to comprehend.
• Unlike other texts that combine probability and counting rules, McClave/Sincich includes the counting rules (with examples) in an appendix rather than in the body of the chapter on probability; the instructor can control the level of coverage of probability covered.

• Multiple Regression and Model Building:
• Two full chapters are devoted to discussing the major types of inferences that can be derived from a regression analysis, showing how these results appear in the output from statistical software, and, most important, selecting multiple regression models to be used in an analysis.
• The instructor has the choice of a one-chapter coverage of simple linear regression (Chapter 11), a two-chapter treatment of simple and multiple regression (excluding the sections on model building in Chapter 12), or complete coverage of regression analysis, including model building and regression diagnostics.
• This extensive coverage of such useful statistical tools will provide added evidence to the student of the relevance of statistics to real-world problems.

Role of calculus:

• Although the text is designed for students without a calculus background, footnotes explain the role of calculus in various derivations.
• Footnotes are also used to inform the student about some of the theory underlying certain methods of analysis. They provide additional flexibility in the mathematical and theoretical level at which the material is presented.

Dr. Jim McClave is currently President and CEO of Info Tech, Inc., a statistical consulting and software development firm with an international clientele. He is also currently an Adjunct Professor of Statistics at the University of Florida, where he was a full-time member of the faculty for twenty years.

Dr. Terry Sincich obtained his PhD in Statistics from the University of Florida in 1980. He is an Associate Professor in the Information Systems & Decision Sciences Department at the University of South Florida in Tampa. Dr. Sincich is responsible for teaching basic statistics to all undergraduates, as well as advanced statistics to all doctoral candidates, in the College of Business Administration. He has published articles in such journals as the Journal of the American Statistical Association, International Journal of Forecasting, Academy of Management Journal, and the Auditing: A Journal of Practice & Theory. Dr. Sincich is a co-author of the texts Statistics, Statistics for Business & Economics, Statistics for Engineering & the Sciences, and A Second Course in Statistics: Regression Analysis.