Table of Contents

1. Introduction to Statistical Investigations

1.1 Preliminary: Introduction to the six-step method

1.2 Preliminary: Exploring data

1.3 Preliminary: Exploring random processes

1.4 Data and formulas

2. Significance

2.1 Example: Introduction to chance models

2.2 Example: Measuring the strength of evidence

2.3 Example: Alternative measure of strength of evidence

2.4 Example: What impacts strength of evidence?

2.5 Example: Inference on a single proportion: Theory-based approach

2.6 Supplemental Exploration: Introduction to chance models

2.7 Supplemental Exploration: Measuring the strength of evidence

2.8 Supplemental Exploration: Do People Use Facial Prototyping?

2.9 Supplemental Exploration: Competitive Advantage to Uniform Colors?

2.10 Supplemental Exploration: Eye Dominance

2.11 Investigation: Tire story falls flat

2.12 Tools, data, and formulas

3. Generalization

3.1 Example: Sampling from a finite population

3.2 Example: Inference for a single quantitative variable

3.3 Example: Theory-based Inference for a Population Mean

3.4 Example: Other Statistics

3.5 Supplemental Exploration: Sampling Words

3.6 Supplemental Exploration: Inference for a single quantitative variable

3.7 Supplemental Exploration: Sleepless Nights?

3.8 Supplemental Exploration: Other statistics

3.9 Investigation: Faking cell phone calls

3.10 Tools, data, and formulas

4. Estimation

4.1 Example: Statistical inference: Confidence intervals

4.2 Example: 2SD and theory-based confidence intervals for a single proportion

4.3 Example: 2SD and theory-based confidence intervals for a single mean

4.4 Example: Factors that affect the width of a confidence interval

4.5 Supplemental Exploration: Statistical inference: Confidence intervals

4.6 Supplemental Exploration: 2SD and theory-based confidence intervals for a single proportion

4.7 Supplemental Exploration: 2SD and theory-based confidence intervals for a single mean

4.8 Supplemental Exploration A: Factors that affect the width of a confidence interval

4.9 Supplemental Exploration B: Factors that affect the width of a confidence interval

4.10 Investigation: Cell phones while driving

4.11 Tools, data, and formulas

5. Causation

5.1 Example: Association and confounding

5.2 Example: Observational studies vs. experiments

5.3 Supplemental Exploration: Association and confounding

5.4 Supplemental Exploration: Observational studies versus experiments

5.5 Investigation: High anxiety and sexual attraction

5.6 Tools and data

6. Comparing Two Proportions

6.1 Example: Comparing two groups: Categorical response

6.2 Example: Comparing two proportions: Simulation-based approach

6.3 Example: Comparing two proportions: Theory-based approach

6.4 Supplemental Exploration: Comparing two groups: Categorical response

6.5 Supplemental Exploration: Comparing two proportions: Simulation-based approach

6.6 Supplemental Exploration: Comparing two proportions: Theory-based approach

6.7 Investigation: Does vitamin C improve your health?

6.8 Tools, data, and formulas

7. Comparing Two Means

7.1 Example: Comparing two groups: Quantitative response

7.2 Example: Comparing two means: Simulation-based approach

7.3 Example: Comparing two means: Theory-based approach

7.4 Supplemental Exploration: Comparing two groups: Quantitative response

7.5 Supplemental Exploration: Comparing two means: Simulation-based approach

7.6 Supplemental Exploration: Comparing two means: Theory-based approach

7.7 Investigation: Memorizing letters

7.8 Tools, data, and formulas

8. Paired Data

8.1 Example: Paired designs

8.2 Example: Simulation-based approach for analyzing paired data

8.3 Example: Theory-based approach to analyzing data from paired samples

8.4 Supplemental Exploration: Paired designs

8.5 Supplemental Exploration: Simulation-based approach for analyzing paired data

8.6 Supplemental Exploration: Theory-based approach for analyzing paired data

8.7 Investigation: Filtering water in Cameroon

8.8 Tools, data, and formulas

9. Comparing More Than Two Proportions

9.1 Example: Comparing multiple proportions: Simulation-based approach

9.2 Example: Comparing multiple proportions: Theory-based approach

9.3 Example: Chi-square goodness-of-fit test

9.4 Supplemental Exploration: Comparing multiple proportions: Simulation-based approach

9.5 Supplemental Exploration A: Comparing multiple proportions: Theory-based approach

9.6 Supplemental Exploration B: Comparing multiple proportions: Theory-based approach

9.7 Supplemental Exploration: Chi-square goodness-of-fit test

9.8 Investigation: Who yields to pedestrians?

9.9 Tools, data, and formulas

10. Comparing More Than Two Means

10.1 Example: Comparing multiple means: Simulation-based approach

10.2 Example: Comparing multiple means: Theory-based approach

10.3 Supplemental Exploration: Comparing multiple means: Simulation-based approach

10.4 Supplemental Exploration: Comparing multiple means: Theory-based approach

10.5 Investigation: Aggression

10.6 Tools, data, and formulas

11. Two Quantitative Variables

11.1 Example: Two quantitative variables: Scatterplot and correlation

11.2 Example: Inference for correlation coefficient: A simulation-based approach

11.3 Example: Least squares regression

11.4 Example: Inference for regression slope: Simulation-based approach

11.5 Example: Inference for regression slope: Theory-based approach

11.6 Supplemental Exploration: Two quantitative variables: Scatterplot and correlation

11.7 Supplemental Exploration: Inference for correlation coefficient: A simulation-based approach

11.8 Supplemental Exploration: Least squares regression

11.9 Supplemental Exploration: Inference for regression slope: Simulation-based approach

11.10 Supplemental Exploration: Inference for regression slope: Theory-based approach

11.11 Investigation: Association between hand span and candy?

11.12 Tools, data, and formulas

12. Modeling Randomness

12.1 Example: Basics of probability

12.2 Example: Probability rules

12.3 Example: Conditional probability and independence

12.4 Example: Discrete random variables

12.5 Example: Random variable rules

12.6 Example: Binomial and geometric random variables

12.7 Example: Continuous random variables and normal distribution

12.8 Example: Revisiting theory-based approximations of sampling distributions

12.9 Supplemental Exploration: Basics of probability

12.10 Supplemental Exploration: Probability rules

12.11 Supplemental Exploration A: Conditional probability and independence

12.12 Supplemental Exploration B: Conditional probability and independence

12.13 Supplemental Exploration: Discrete random variables

12.14 Supplemental Exploration: Random variable rules

12.15 Supplemental Exploration: Binomial and geometric random variables

12.16 Supplemental Exploration A: Continuous random variables and normal distribution

12.17 Supplemental Exploration B: Continuous random variables and normal distribution

12.18 Supplemental Exploration A: Revisiting theory-based approximations of sampling distributions

12.19 Supplemental Exploration B: Revisiting theory-based approximations of sampling distributions

13. Instructor Resources

13.1 Under the Spiral: How the ISI zyBook teaches the Statistical Investigation Process

13.2 Examples and Explorations

## What You’ll Find In This zyBook:

**More action with less text.**

- Bring text author’s SBI approach to learning statistics into a new course management platform
- Students interact with assignable reading made up of embedded in the text guided animations, simulation tools and learning questions with answer-specific feedback
- Build confidence and conceptual understanding of the statistical process
- Challenge Activities deliver higher stakes assessment

#### Scaffolding in the ISI zyBook:

## What is a zyBook?

**Introduction to Statistical Investigations** is a web-native, interactive zyBook that helps students visualize concepts to learn faster and more effectively than with a traditional textbook. (Check out our research.)

Since 2012, over 1,200 universities and colleges across the country have adopted digital zyBooks to transform their STEM education.

### zyBooks benefit both students and instructors:

- Instructor benefits
- Customize your course by reorganizing existing content, or adding your own content
- Continuous publication model updates your course with the latest content and technologies
- Robust reporting gives you insight into students’ progress, reading and participation
- Save time with auto-graded labs and challenge activities that seamlessly integrate with your LMS gradebook
- Build quizzes and exams with hundreds of included test questions

- Student benefits
- Learning questions and other content serve as an interactive form of reading
- Instant feedback on labs and homework
- Concepts come to life through extensive animations embedded into the interactive content
- Review learning content before exams with different questions and challenge activities
- Save chapters as PDFs to reference the material at any time

## Authors

Nathan Tintle / Professor, Statistics / University of Illinois Chicago

Beth Chance / Professor, Statistics / California Polytechnic University

George Cobb / Robert L. Rooke Professor Emeritus, Statistics / Mount Holyoke College

Allan Rossman / Professor and Department Chair, Statistics / California Polytechnic University

Soma Roy / Professor, Statistics / California Polytechnic University

Todd Swanson / Associate Professor, Mathematics and Statistics / Hope College

Jill VanderStoep / Assistant Professor, Mathematics and Statistics / Hope College

## zyBooks Authors

Julia Schedler / PhD in Statistics / Rice University

Ayla Sánchez / Senior Content Developer, Statistics / zyBooks / PhD in Mathematics / Tufts University