# Introductory Statistics

## 4th Edition

**Author:**Sheldon Ross

**eBook ISBN:**9780128043615

**Hardcover ISBN:**9780128043172

**Imprint:**Academic Press

**Published Date:**7th February 2017

**Page Count:**828

## Description

*Introductory Statistics, Fourth Edition, *reviews statistical concepts and techniques in a manner that will teach students not only how and when to utilize the statistical procedures developed, but also how to understand why these procedures should be used. The text's main merits are the clarity of presentation, contemporary examples and applications from diverse areas, an explanation of intuition, and the ideas behind the statistical methods.

Concepts are motivated, illustrated, and explained in a way that attempts to increase one's intuition. To quote from the preface, it is only when a student develops a feel or intuition for statistics that she or he is really on the path toward making sense of data. Ross achieves this goal through a coherent mix of mathematical analysis, intuitive discussions, and examples.

Applications and examples refer to real-world issues, such as gun control, stock price models, health issues, driving age limits, school admission ages, use of helmets, sports, scientific fraud, and many others. Examples relating to data mining techniques using the number of Google queries or Twitter tweets are also considered.

For this fourth edition, new topical coverage includes sections on Pareto distribution and the 80-20 rule, Benford's law, added material on odds and joint distributions and correlation, logistic regression, A-B testing, and more modern (big data) examples and exercises.

## Key Features

- Includes new section on Pareto distribution and the 80-20 rule, Benford’s law, odds, joint distribution and correlation, logistic regression, A-B testing, and examples from the world of analytics and big data
- Comprehensive edition that includes the most commonly used statistical software packages (SAS, SPSS, Minitab), ISM, SSM, and an online graphing calculator manual
- Presents a unique, historical perspective, profiling prominent statisticians and historical events to motivate learning by including interest and context
- Provides exercises and examples that help guide the student towards indpendent learning using real issues and real data, e.g. stock price models, health issues, gender issues, sports, and scientific fraud

## Readership

This text is written for the introductory non-calculus based statistics course offered in mathematics and/or statistics departments for undergraduate students of any major who take a semester course in basic Statistics or a year course in Probability and Statistics

## Table of Contents

Chapter 1: Introduction to Statistics

- Abstract
- 1.1. Introduction
- 1.2. The Nature of Statistics
- 1.3. Populations and Samples
- 1.4. A Brief History of Statistics
- Key Terms
- The Changing Definition of Statistics
- Review Problems

Chapter 2: Describing Data Sets

- Abstract
- 2.1. Introduction
- 2.2. Frequency Tables and Graphs
- Problems
- 2.3. Grouped Data and Histograms
- Problems
- 2.4. Stem-and-Leaf Plots
- Problems
- 2.5. Sets of Paired Data
- Problems
- 2.6. Some Historical Comments
- Key Terms
- Summary
- Review Problems

Chapter 3: Using Statistics to Summarize Data Sets

- Abstract
- 3.1. Introduction
- 3.2. Sample Mean
- Problems
- 3.3. Sample Median
- Problems
- Problems
- 3.4. Sample Mode
- Problems
- 3.5. Sample Variance and Sample Standard Deviation
- Problems
- 3.6. Normal Data Sets and the Empirical Rule
- Problems
- 3.7. Sample Correlation Coefficient
- Problems
- 3.8. The Lorenz Curve and Gini Index
- Problems
- 3.9. Using R
- Key Terms
- Summary
- Review Problems

Chapter 4: Probability

- Abstract
- 4.1. Introduction
- 4.2. Sample Space and Events of an Experiment
- Problems
- 4.3. Properties of Probability
- Problems
- 4.4. Experiments Having Equally Likely Outcomes
- Problems
- 4.5. Conditional Probability and Independence
- Problems
- *4.6. Bayes' Theorem
- Problems
- *4.7. Counting Principles
- Problems
- Key Terms
- Summary
- Review Problems

Chapter 5: Discrete Random Variables

- Abstract
- 5.1. Introduction
- 5.2. Random Variables
- Problems
- 5.3. Expected Value
- Problems
- 5.4. Variance of Random Variables
- Problems
- 5.5. Jointly Distributed Random Variables
- Problems
- 5.6. Binomial Random Variables
- Problems
- *5.7. Hypergeometric Random Variables
- Problems
- *5.8. Poisson Random Variables
- Problems
- 5.9. Using R to calculate Binomial and Poisson Probabilities
- Key Terms
- Summary
- Review Problems

Chapter 6: Normal Random Variables

- Abstract
- 6.1. Introduction
- 6.2. Continuous Random Variables
- Problems
- 6.3. Normal Random Variables
- Problems
- 6.4. Probabilities Associated with a Standard Normal Random Variable
- Problems
- 6.5. Finding Normal Probabilities: Conversion to the Standard Normal
- 6.6. Additive Property of Normal Random Variables
- Problems
- 6.7. Percentiles of Normal Random Variables
- Problems
- 6.8. Calculating Normal Probabilities with R
- Key Terms
- Summary
- Review Problems

Chapter 7: Distributions of Sampling Statistics

- Abstract
- 7.1. A Preview
- 7.2. Introduction
- 7.3. Sample Mean
- Problems
- 7.4. Central Limit Theorem
- Problems
- 7.5. Sampling Proportions from a Finite Population
- Problems
- 7.6. Distribution of the Sample Variance of a Normal Population
- Problems
- Key Terms
- Summary
- Review Problems

Chapter 8: Estimation

- Abstract
- 8.1. Introduction
- 8.2. Point Estimator of a Population Mean
- Problems
- 8.3. Point Estimator of a Population Proportion
- Problems
- Problems
- 8.4. Estimating a Population Variance
- Problems
- 8.5. Interval Estimators of the Mean ofa Normal Population with Known Population Variance
- Problems
- 8.6. Interval Estimators of the Mean ofa Normal Population with Unknown Population Variance
- Problems
- 8.7. Interval Estimators of a Population Proportion
- Problems
- 8.8. Use of R
- Key Terms
- Summary
- Review Problems

Chapter 9: Testing Statistical Hypotheses

- Abstract
- 9.1. Introduction
- 9.2. Hypothesis Tests and Significance Levels
- Problems
- 9.3. Tests Concerning the Mean of a Normal Population: Case of Known Variance
- Problems
- Problems
- 9.4. The t Test for the Mean of a Normal Population: Case of Unknown Variance
- Problems
- 9.5. Hypothesis Tests Concerning Population Proportions
- Problems
- 9.6. Use of R in Running a One Sample t-test
- Key Terms
- Summary
- Review Problems and Proposed Case Studies

Chapter 10: Hypothesis Tests Concerning Two Populations

- Abstract
- 10.1. Introduction
- 10.2. Testing Equality of Means of Two Normal Populations: Case of Known Variances
- Problems
- 10.3. Testing Equality of Means: Unknown Variances and Large Sample Sizes
- Problems
- 10.4. Testing Equality of Means: Small-Sample Tests when the Unknown Population Variances Are Equal
- Problems
- 10.5. Paired-Sample t Test
- Problems
- 10.6. Testing Equality of Population Proportions
- Problems
- 10.7. Use of R in Running a Two Sample t-Test
- Key Terms
- Summary
- Review Problems

Chapter 11: Analysis of Variance

- Abstract
- 11.1. Introduction
- 11.2. One-Factor Analysis of Variance
- Problems
- 11.3. Two-Factor Analysis of Variance: Introduction and Parameter Estimation
- Problems
- 11.4. Two-Factor Analysis of Variance: Testing Hypotheses
- Problems
- 11.5. Final Comments
- Key Terms
- Summary
- Review Problems

Chapter 12: Linear Regression

- Abstract
- 12.1. Introduction
- 12.2. Simple Linear Regression Model
- Problems
- 12.3. Estimating the Regression Parameters
- Problems
- 12.4. Error Random Variable
- Problems
- 12.5. Testing the Hypothesis that β=0
- Problems
- 12.6. Regression to the Mean
- Problems
- 12.7. Prediction Intervals for Future Responses
- Problems
- 12.8. Coefficient of Determination
- Problems
- 12.9. Sample Correlation Coefficient
- Problems
- 12.10. Analysis of Residuals: Assessingthe Model
- Problems
- 12.11. Multiple Linear Regression Model
- Problems
- 12.12. Logistic Regression
- 12.13. Use of R in Regression
- Key Terms
- Summary
- Review Problems

Chapter 13: Chi-Squared Goodness-of-Fit Tests

- Abstract
- 13.1. Introduction
- 13.2. Chi-Squared Goodness-of-Fit Tests
- Problems
- 13.3. Testing for Independence in Populations Classified According to Two Characteristics
- Problems
- 13.4. Testing for Independence in Contingency Tables with Fixed Marginal Totals
- Problems
- 13.5. Use of R
- Key Terms
- Summary
- Review Problems

Chapter 14: Nonparametric Hypotheses Tests

- Abstract
- 14.1. Introduction
- 14.2. Sign Test
- Problems
- 14.3. Signed-Rank Test
- Problems
- 14.4. Rank-Sum Test for Comparing Two Populations
- Problems
- 14.5. Runs Test for Randomness
- Problems
- 14.6. Testing the Equality of Multiple Probability Distributions
- Problems
- 14.7. Permutation Tests
- Problems
- Key Terms
- Summary
- Review Problems

Chapter 15: Quality Control

- Abstract
- 15.1. Introduction
- 15.2. The X‾ Control Chart for Detecting a Shift in the Mean
- Problems
- Problems
- 15.3. Control Charts for Fraction Defective
- Problems
- 15.4. Exponentially Weighted Moving-Average Control Charts
- Problems
- 15.5. Cumulative-Sum Control Charts
- Problems
- Key Terms
- Summary
- Review Problems

Chapter 16: Machine Learning and Big Data

- Abstract
- 16.1. Introduction
- 16.2. Late Flight Probabilities
- 16.3. The Naive Bayes Approach
- Problems
- 16.4. Distance Based Estimators the k-Nearest Neighbors Rule
- Problems
- 16.5. Assessing the Approaches
- Problems
- 16.6. Choosing the Best Probability: A Bandit Problem
- Problems

Appendix A: A Data Set

Appendix B: Mathematical Preliminaries

- B.1. Summation
- B.2. Absolute Value
- B.3. Set Notation

Appendix C: How to Choose a Random Sample

Appendix D: Tables

Appendix E: Programs

Answers to Odd-Numbered Problems

- Chapter 1 Problems
- Chapter 2 Review
- Chapter 3 Review
- Chapter 4 Review
- Chapter 5 Review
- Chapter 6 Review
- Chapter 7 Review
- Chapter 8 Review
- Chapter 9 Review
- Chapter 10 Review
- Chapter 11 Review
- Chapter 12 Review
- Chapter 13 Review
- Chapter 14 Review
- Chapter 15 Review

Index

Introductory Statistics

- 1. Introduction to Statistics
- 2. Describing Data Sets
- 3. Using Statistics to Summarize Data Sets
- 4. Probability
- 5. Discrete Random Variables
- 6. Normal Random Variables
- 7. Distributions of Sampling Statistics
- 8. Estimation
- 9. Testing Statistical Hypotheses
- 10. Hypotheses Tests Concerning Two Populations
- 11. Analysis of Variance
- 12. Linear Regression
- 13. Chi-squared Goodness of Fit Tests
- 14. Nonparametric Hypotheses
- 15. Quality Control

## Details

- No. of pages:
- 828

- Language:
- English

- Copyright:
- © Academic Press 2017

- Published:
- 7th February 2017

- Imprint:
- Academic Press

- eBook ISBN:
- 9780128043615

- Hardcover ISBN:
- 9780128043172

## About the Author

### Sheldon Ross

Dr. Sheldon M. Ross is a professor in the Department of Industrial and Systems Engineering at the University of Southern California. He received his PhD in statistics at Stanford University in 1968. He has published many technical articles and textbooks in the areas of statistics and applied probability. Among his texts are A First Course in Probability, Introduction to Probability Models, Stochastic Processes, and Introductory Statistics. Professor Ross is the founding and continuing editor of the journal Probability in the Engineering and Informational Sciences. He is a Fellow of the Institute of Mathematical Statistics, a Fellow of INFORMS, and a recipient of the Humboldt US Senior Scientist Award.

### Affiliations and Expertise

Professor, Department of Industrial and Systems Engineering, University of Southern California, Los Angeles, USA

## Reviews

"The coverage is careful and slow, with many worked examples and plenty of problems, half of which have answers. ...Illuminating examples abound. Those who are less than wholly confident about any of the material will find it a rich and unthreatening resource of information and also of questions (even if they are almost all derived from a US context). I have been looking for some time for a properly academic superior to M.J. Moroney’s invaluable if outdated *Facts from figures* which I have used for forty years, and this would seem to fill the bill." **--The Mathematical Gazette**

"There are some interesting topics included that are not in most introductory stats texts, such as the Gini index, bandit problems, and quality control." --**MAA Reviews**