13. Statistical Inference

Chapter Learning Objectives

1. Draw inferences and each conclusions using data corrupted by (measurement) uncertainty

2. Choose the statistical inference technique for common science and engineering applications

Main Idea behind Statistical Inference

Idea 1: How to infer a quantity about a population using samples?

Example: How to estimate height of ND engineering students using our class as a sample?

• The average height in our class approximates or estimates the mean height of the student body.

• How to quantify the uncertainty in our estimate?

We will do this using confidence intervals confidence intervals.

Idea 2: How to test a scientific or engineering hypothesis?

Example: We receive a shipment of 1000 widgets and select only 10 of them to weigh. We wish to infer is the entire batch is within manufacturing specifications.

We will do this using hypothesis testing.

Class Activity

Which partner can generate the longest list of statistic inference examples? Consider inference problem you would encounter as a student, a citizen, and a practicing chemical engineer.

We will see throughout this lecture that confidence intervals and hypothesis testing have the same mathematical basis and are closely related.

Sections

• 13.1. Central Limit Theorem
• 13.2. Standard Normal Distribution
• 13.3. Confidence Intervals
• 13.4. Student’s t-Distribution
• 13.5. Hypothesis Testing Basics
• 13.6. Flavors of Hypothesis Testing
• 13.7. Type I and Type II Errors
• 13.8. Statistical Power Basics
• 13.9. Statistical Power in Python
• 13.10. Statistical Power Practice Problems
• 13.11. Bootstrap Confidence Intervals