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Introduction to Statistical Thinking
Benjamin Yakir
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Front Matter
Colophon
Preface
Note on This PreTeXt Edition
1
Introduction
1.1
Student Learning Objectives
1.2
Why Learn Statistics?
1.3
Statistics
1.4
Probability
1.5
Key Terms
1.6
The
R
Programming Environment
1.6.1
Some Basic
R
Commands
1.7
Exercises
1.8
Summary
1.8.1
Glossary
1.8.2
R
functions introduced in this chapter
1.8.3
Discuss in the forum
2
Sampling and Data Structures
2.1
Student Learning Objectives
2.2
The Sampled Data
2.2.1
Variation in Data
2.2.2
Variation in Samples
2.2.3
Frequency
2.2.4
Critical Evaluation
2.3
Reading External Data into
R
2.3.1
Saving the File and Setting the Working Directory
2.3.2
Reading a CSV File into
R
2.3.3
Data Types
2.4
Exercises
2.5
Summary
2.5.1
Glossary
2.5.2
R
functions introduced in this chapter
2.5.3
Discuss in the forum
3
Descriptive Statistics
3.1
Student Learning Objectives
3.2
Displaying Data
3.2.1
Histograms
3.2.2
Box Plots
3.3
Measures of the Center of Data
3.3.1
Skewness, the Mean and the Median
3.4
Measures of the Spread of Data
3.5
Exercises
3.6
Summary
3.6.1
Glossary
3.6.2
Discuss in the forum
3.6.3
Commonly Used Symbols
3.6.4
Commonly Used Expressions
3.6.5
Formulas
4
Probability
4.1
Student Learning Objectives
4.2
Different Forms of Variability
4.3
A Population
4.4
Random Variables
4.4.1
Sample Space and Events
4.4.2
Expectation and Standard Deviation
4.5
Probability and Statistics
4.6
Exercises
4.7
Summary
4.7.1
Glossary
4.7.2
Discussion in the Forum
4.7.3
Summary of Formulas
5
Random Variables
5.1
Student Learning Objectives
5.2
Discrete Random Variables
5.2.1
The Binomial Random Variable
5.2.2
The Poisson Random Variable
5.3
Continuous Random Variables
5.3.1
The Uniform Random Variable
5.3.2
The Exponential Random Variable
5.4
Exercises
5.5
Summary
5.5.1
Glossary
5.5.2
Discuss in the Forum
5.5.3
Summary of Formulas
6
The Normal Random Variable
6.1
Student Learning Objectives
6.2
The Normal Random Variable
6.2.1
The Normal Distribution
6.2.2
The Standard Normal Distribution
6.2.3
Computing Percentiles
6.2.4
Outliers and the Normal Distribution
6.3
Approximation of the Binomial Distribution
6.3.1
Approximate Binomial Probabilities and Percentiles
6.3.2
Continuity Corrections
6.4
Exercises
6.5
Summary
6.5.1
Glossary
6.5.2
Discuss in the Forum
7
The Sampling Distribution
7.1
Student Learning Objectives
7.2
The Sampling Distribution
7.2.1
A Random Sample
7.2.2
Sampling From a Population
7.2.3
Theoretical Models
7.3
Law of Large Numbers and Central Limit Theorem
7.3.1
The Law of Large Numbers
7.3.2
The Central Limit Theorem (CLT)
7.3.3
Applying the Central Limit Theorem
7.4
Exercises
7.5
Summary
7.5.1
Glossary
7.5.2
Discussion in the Forum
7.5.3
Summary of Formulas
8
Overview and Integration
8.1
Student Learning Objectives
8.2
An Overview
8.3
Integrated Applications
8.4
Discussion in the Forum
8.5
Summary
8.5.1
Glossary and Formulas
9
Introduction to Statistical Inference
9.1
Student Learning Objectives
9.2
Key Terms
9.3
The Cars Data Set
9.4
The Sampling Distribution
9.4.1
Statistics
9.4.2
The Sampling Distribution
9.4.3
Theoretical Distributions of Observations
9.4.4
Sampling Distribution of Statistics
9.4.5
The Normal Approximation
9.4.6
Simulations
9.5
Exercises
9.6
Summary
9.6.1
Glossary
9.6.2
Discuss in the forum
10
Point Estimation
10.1
Student Learning Objectives
10.2
Estimating Parameters
10.3
Estimation of the Expectation
10.3.1
The Accuracy of the Sample Average
10.3.2
Comparing Estimators
10.4
Estimation of the Variance and Standard Deviation
10.5
Estimation of Other Parameters
10.6
Exercises
10.7
Summary
10.7.1
Glossary
10.7.2
Discuss in the forum
10.7.3
Formulas
11
Confidence Intervals
11.1
Student Learning Objectives
11.2
Intervals for Mean and Proportion
11.2.1
Examples of Confidence Intervals
11.2.2
Confidence Intervals for the Mean
11.2.3
Confidence Intervals for a Proportion
11.3
Intervals for Normal Measurements
11.3.1
Confidence Intervals for a Normal Mean
11.3.2
Confidence Intervals for a Normal Variance
11.4
Choosing the Sample Size
11.5
Exercises
11.6
Summary
11.6.1
Glossary
11.6.2
Discuss in the forum
11.6.3
Formulas for Confidence Intervals, 95% Confidence Level
12
Testing Hypotheses
12.1
Student Learning Objectives
12.2
The Theory of Hypothesis Testing
12.2.1
An Example of Hypothesis Testing
12.2.2
The Structure of a Statistical Test of Hypotheses
12.2.3
Error Types and Error Probabilities
12.2.4
\(p\)
-Values
12.3
Testing Hypothesis on Expectation
12.4
Testing Hypothesis on Proportion
12.5
Exercises
12.6
Summary
12.6.1
Glossary
12.6.2
Discuss in the forum
12.6.3
Formulas
13
Comparing Two Samples
13.1
Student Learning Objectives
13.2
Comparing Two Distributions
13.3
Comparing the Sample Means
13.3.1
An Example of a Comparison of Means
13.3.2
Confidence Interval for the Difference
13.3.3
The t-Test for Two Means
13.4
Comparing Sample Variances
13.5
Exercises
13.6
Summary
13.6.1
Glossary
13.6.2
Discuss in the Forum
13.6.3
Formulas
14
Linear Regression
14.1
Student Learning Objectives
14.2
Points and Lines
14.2.1
The Scatter Plot
14.2.2
Linear Equation
14.3
Linear Regression
14.3.1
Fitting the Regression Line
14.3.2
Inference
14.3.3
R-squared and the Variance of Residuals
14.4
R-squared and the Variance of Residuals
14.5
Exercises
14.6
Summary
14.6.1
Glossary
14.6.2
Formulas
15
A Bernoulli Response
15.1
Student Learning Objectives
15.2
Comparing Sample Proportions
15.3
Logistic Regression
15.4
Exercises
15.5
Summary
15.5.1
Glossary
15.5.2
Discuss in the Forum
15.5.3
Formulas
16
Case Studies
16.1
Student Learning Objectives
16.2
A Review
16.3
Case Studies
16.3.1
Physicians’ Reactions to the Size of a Patient
16.3.2
Physical Strength and Job Performance
16.4
Summary
16.4.1
Concluding Remarks
16.4.2
Discussion in the Forum
Backmatter
A
Solutions to Selected Exercises
A.1
Chapter 1: Introduction
A.1.1
Exercise 1.1
A.1.2
Exercise 1.2
A.2
Chapter 2: Sampling and Data Structures
A.2.1
Exercise 2.1
A.2.2
Exercise 2.2
A.3
Chapter 3: Descriptive Statistics
A.3.1
Exercise 3.1
A.3.2
Exercise 3.2
A.4
Chapter 4: Probability
A.4.1
Exercise 4.1
A.4.2
Exercise 4.2
A.5
Chapter 5: Random Variables
A.5.1
Exercise 5.1
A.5.2
Exercise 5.2
A.6
Chapter 6: The Normal Random Variable
A.6.1
Exercise 6.1
A.6.2
Exercise 6.2
A.7
Chapter 7: The Sampling Distribution
A.7.1
Exercise 7.1
A.7.2
Exercise 7.2
A.8
Chapter 9: Introduction to Statistical Inference
A.8.1
Exercise 9.1
A.8.2
Exercise 9.2
A.9
Chapter 10: Point Estimation
A.9.1
Exercise 10.1
A.9.2
Exercise 10.2
A.10
Chapter 11: Confidence Intervals
A.10.1
Exercise 11.1
A.10.2
Exercise 11.2
A.10.3
Exercise 11.3
A.11
Chapter 12: Testing Hypotheses
A.11.1
Exercise 12.1
A.11.2
Exercise 12.2
A.11.3
Exercise 12.3
A.12
Chapter 13: Comparing Two Samples
A.12.1
Exercise 13.1
A.12.2
Exercise 13.2
A.12.3
Exercise 13.3
A.13
Chapter 14: Linear Regression
A.13.1
Exercise 14.1
A.13.2
Exercise 14.2
A.13.3
Exercise 14.3
A.13.4
Exercise 14.4
A.13.5
Exercise 14.5
A.13.6
Exercise 14.6
A.14
Chapter 15: A Bernoulli Response
A.14.1
Exercise 15.1
A.14.2
Exercise 15.2
Index
Colophon
Colophon
Website
github.com/PreTeXtBooks/statthink
©2011–2026 Benjamin Yakir
This book is an open source and may be used by anyone who wishes to do so under the conditions of the Creative Commons Attribution License (CC-BY 3.0).
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