Essential Statistics

Table of Contents

• Chapter 1: Introduction

  • Basic Definitions and Concepts
  • Overview
  • Presentation of Data

• Chapter 2: Descriptive Statistics

  • Three Popular Data Displays
  • Measures of Central Location
  • Measures of Variability
  • Relative Position of Data
  • The Empirical Rule and Chebyshev’s Theorem

• Chapter 3: Basic Concepts of Probability

  • Sample Spaces, Events, and Their Probabilities
  • Complements, Intersections, and Unions
  • Conditional Probability and Independent Events

• Chapter 4: Discrete Random Variables

  • Random Variables
  • Probability Distributions for Discrete Random Variables
  • The Binomial Distribution

• Chapter 5: Continuous Random Variables

  • Continuous Random Variables
  • The Standard Normal Distribution
  • Probability Computations for General Normal Random Variables
  • Areas of Tails of Distributions

• Chapter 6: Sampling Distributions

  • The Mean and Standard Deviation of the Sample Mean
  • The Sampling Distribution of the Sample Mean
  • The Sample Proportion

• Chapter 7: Estimation

  • Large Sample Estimation of a Population Mean
  • Small Sample Estimation of a Population Mean
  • Large Sample Estimation of a Population Proportion
  • Sample Size Considerations

• Chapter 8: Testing Hypotheses

  • The Elements of Hypothesis Testing
  • Large Sample Tests for a Population Mean
  • The Observed Significance of a Test
  • Small Sample Tests for a Population Mean
  • Large Sample Tests for a Population Proportion

• Chapter 9: Two-Sample Problems

  • Comparison of Two Population Means: Large, Independent Samples
  • Comparison of Two Population Means: Small, Independent Samples
  • Comparison of Two Population Means: Paired Samples
  • Comparison of Two Population Proportions
  • Sample Size Considerations

• Chapter 10: Correlation and Regression

  • Linear Relationships Between Variables
  • The Linear Correlation Coefficient
  • Modelling Linear Relationships with Randomness Present
  • The Least Squares Regression Line
  • Statistical Inferences About ?1
  • The Coefficient of Determination
  • Estimation and Prediction
  • A Complete Example
  • Formula List

• Chapter 11: Chi-Square Tests and F-Tests

  • Chi-Square Tests for Independence
  • Chi-Square One-Sample Goodness-of-Fit Tests
  • F-tests for Equality of Two Variances
  • F-Tests in One-Way ANOVA

• Appendix