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OPTIMA Statistics
Jonathan Duncan
Contents
Index
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Contents
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Front Matter
Colophon
Preface
I
Descriptive Statistics and Probability
1
Collecting and Describing Data
Understanding Data
Describing Data Graphically
Describing Data Numerically: Measures of Center and Spread
Describing Data Numerically: Measures of Relative Standing
2
Understanding Randomness and Probability
Randomness and Simulation
Basic Counting Rules
Probability and Probability Rules
Conditional Probability and Independence
3
Exploring Probability Distributions
Random Variables and Discrete Probability distributions
Families of Discrete Distributions: Uniform and Binomial
The Normal Distribution
Normal Approximation to the Binomial Distribution
Sampling Distributions and the Central Limit Theorem
II
Inferential Statistics
4
Estimating Means and Proportions
Introduction to Estimation and Confidence intervals
Confidence Intervals for a Mean
Confidence Intervals for a Proportion
Confidence Intervals for the Difference Between Means or Proportions
Confidence Intervals for Means Using Small Samples
5
Testing Hypotheses for Means and Proportions
Introduction to Hypothesis Testing
Hypothesis Tests for a Mean
Hypothesis Tests for a Proportion
Hypothesis Tests for Differences Between Means and Proportions
Hypothesis Tests for Means Using Small Samples
6
Other Tests of Significance
Analysis of Variance
Goodness-of-Fit Tests
Tests of Independence and Homogeneity
Back Matter
A
Reference
Common Critical Values
B
Distribution Tables
Standard Normal Distribution
Student's t Distribution
Chi-Squared Distribution
Index
Authored in PreTeXt
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OPTIMA Statistics
Jonathan Duncan
Department of Mathematics
Walla Walla University
jonathan.duncan@wallawalla.edu
June 22, 2021
Colophon
Preface