# Introductory Statistics

### Resources

## Description

## 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)
- 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

## Product details

- No. of pages: 828
- Language: English
- Copyright: © Academic Press 2017
- Published: January 26, 2017
- Imprint: Academic Press
- Hardcover ISBN: 9780128043172
- eBook ISBN: 9780128043615