Statistics

For courses in introductory statistics.

A Contemporary Classic

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. This new edition is extensively revised with an eye on clearer, more concise language throughout the text and in the exercises.

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.

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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 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.

Preface

Applications Index

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: Sampling and Related Issues

1.6 The Role of Statistics in Critical Thinking and Ethics

            Statistics in Action: Social Media Network Usage–Are You Linked In?

            Using Technology: MINITAB: Accessing 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 Numerical Measures of Central Tendency

2.4 Numerical Measures of Variability

2.5 Using the Mean and Standard Deviation to Describe Data

2.6 Numerical Measures of Relative Standing

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

2.8 Graphing Bivariate Relationships (Optional)

2.9 Distorting the Truth with Descriptive Statistics

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

            Using Technology: MINITAB: Describing Data

            TI-83/TI—84 Plus Graphing Calculator: 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 Some Additional Counting Rules (Optional)

3.8 Bayes’s Rule (Optional)

            Statistics in Action: Lotto Buster! Can You Improve Your Chance of Winning?

            Using Technology: TI-83/TI-84 Plus Graphing Calculator: Combinations and Permutations

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: MINITAB: Discrete Probabilities

            TI-83/TI-84 Plus Graphing Calculator: Discrete Random Variables and 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: MINITAB: Continuous Random Variable Probabilities and Normal Probability Plots

            TI-83/TI-84 Plus Graphing Calculator: Normal Random Variable and Normal Probability Plots

6. Sampling Distributions

6.1 The Concept of 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

6.4 The Sampling Distribution of the Sample Proportion

            Statistics in Action: The Insomnia Pill: Is It Effective?

            Using Technology: MINITAB: 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: MINITAB: Confidence Intervals

            TI-83/TI-84 Plus Graphing Calculator: 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 Observed Significance Levels: p-Values

8.4 Test of Hypothesis about a Population Mean: Normal (z) Statistic

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: MINITAB: Tests of Hypotheses

            TI-83/TI-84 Plus Graphing Calculator: Tests of Hypotheses

9. Inferences Based on 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. v. Visa USA Inc.–A Libel Case

            Using Technology: MINITAB: Two-Sample Inferences

            TI-83/TI-84 Plus Graphing Calculator: 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: Voice versus Face Recognition–Does One Follow the Other?

            Using Technology: MINITAB: Analysis of Variance

            TI-83/TI-84 Plus Graphing Calculator: 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: MINITAB: Simple Linear Regression

            TI-83/TI-84 Plus Graphing Calculator: Simple Linear Regression

12. Multiple Regression and Model Building

12.1 Multiple-Regression Models

PART I: First-Order Models with Quantitative Independent Variables

12.2 Estimating and Making Inferences about the β Parameters

12.3 Evaluating Overall Model Utility

12.4 Using the Model for Estimation and Prediction

PART II: Model Building in Multiple Regression

12.5 Interaction Models

12.6 Quadratic and Other Higher Order Models

12.7 Qualitative (Dummy) Variable Models

12.8 Models with Both Quantitative and Qualitative Variables (Optional)

12.9 Comparing Nested Models (Optional)

12.10 Stepwise Regression (Optional)

PART III: Multiple Regression Diagnostics

12.11 Residual Analysis: Checking the Regression Assumptions

12.12 Some Pitfalls: Estimability, Multicollinearity, and Extrapolation

            Statistics in Action: Modeling Condominium Sales: What Factors Affect Auction Price?

            Using Technology: MINITAB: Multiple Regression

            TI-83/TI-84 Plus Graphing Calculator: Multiple Regression

13. Categorical Data Analysis

13.1 Categorical Data and the Multinomial Experiment

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: The Case of the Ghoulish Transplant Tissue

            Using Technology: MINITAB: Chi-Square Analyses

            TI-83/TI-84 Plus Graphing Calculator: Chi-Square Analyses

14. Nonparametric Statistics (available online)

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 14-48

            Statistics in Action: Pollutants at a Housing Development: A Case of Mishandling Small Samples 14-2

            Using Technology: MINITAB: Nonparametric Tests 14-65

Appendices

Appendix A. Summation Notation

Appendix B. Tables

Table I Binomial Probabilities

Table II Normal Curve Areas

Table III Critical Values of t

Table IV Critical Values of x ²

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

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

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

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

Table IX Critical Values of T_L and T_U for the Wilcoxon Rank Sum Test: Independent Samples

Table X Critical Values of T₀ in the Wilcoxon Paired Difference Signed Rank Test

Table XI Critical Values of Spearman’s Rank Correlation Coefficient

Table XII Critical Values of the Studentized Range, α = .05

Table XIII Critical Values of the Studentized Range, α = .01

Appendix C. Calculation Formulas for Analysis of Variance

Short Answers to Selected Odd-Numbered Exercises

Index

Photo Credits