07: Sampling a Population

"The things directly observed are, almost always, only samples." - Alfred Whitehead."The tendency of the casual mind is to pick out or stumble upon a sample which supports or defies its prejudices, and then to make it the representative of a whole class. — Walter Lippmann. "It doesn’t depend on size, or a cow would catch a rabbit" - Pennsylvania German Proverb.Lecture outline: How observing some things tells us a lot about all things?

1. Sampling basics

Sample vs. Population; Statistic vs. Parameter;

Estimating parameters from statistics;

How to choose a sample (how to avoid bias)?

2. Sampling distribution

Law of Large Numbers; Central Limit Theorem;

Standard error; Sample size and Standard error.

Normal distribution; z distribution; t distribution

3. Estimation with a single sample.

Estimating parameters given a single sample.

Introduction to interval estimates and confidence intervals.

Primary reference for this lecture:

Secondary references for this lecture:

1. “How to Measure Anything: Finding the Value of "Intangibles" in Business” by Douglas Hubbard; Chapter 9: “Sampling Reality: How Observing Some Things Tells Us about All Things”

2. "Probability and Statistics with Reliability, Queueing and Computer Science Applications", Kishor Trivedi, Chapter 10: Statistical Inference

3. “Cartoon Guide to Statistics” by Larry Gonick; Chapter 6: “Sampling” and Chapter 9: “Comparing Two Populations”