One-Sample Problems

In the introduction, we set up a scenario: you’re a pollster trying to estimate what fraction of Georgia’s registered voters will turn out for an election. You survey a sample of 625 people and use their responses to make a prediction.

That’s a one-sample problem. You have one sample from one population, and you want to say something about the population based on what you see in the sample. The chapters in this part develop the ideas you need to do that well.

• How do you summarize your sample? What’s a good estimate, and what makes one estimate better than another?
• How do you quantify your uncertainty? Saying “I think turnout will be 70%” is less useful than “I think it’s between 68% and 72%, and I’m fairly confident about that.”
• How do you calibrate that confidence? What does it mean to say an interval is “95% confident,” and how do you check whether that claim holds up?

We’ll start with the basics—sampling and point estimation—and build up to confidence intervals, the bootstrap, and the normal approximation.