Confidence Intervals and Bootstrapping

Confidence Intervals

Required Video: Overview of Confidence Intervals

Required Tutorial: Simulate some confidence intervals

Optional Video: Calculating Confidence Intervals

(Content Note: A recent study on race and Covid is referenced in this video.)

Check-In 1: Confidence Intervals

Educators in California are concerned that high school students do not get enough sleep. They collect data about 300 students, and calculate a 99% confidence interval for the average hours of sleep a night to be (7.0,7.5).

Which of the following is a correct interpretation of the confidence interval?

• 99% of all high school students get between 7 and 7.5 hours of sleep per night.
• 99% of the 300 students surveyed got between 7 and 7.5 hours of sleep per night.
• We are 99% confident that the 300 students surveyed got between 7 and 7.5 hours of sleep on average per night.
• We are 99% confident that California students get between 7 and 7.5 hours of sleep on average per night.
• There is a 99% probability of a student getting between 7 and 7.5 hours of sleep.
• There is a 99% probability that the true mean hours of sleep of California students is between 7 and 7.5 hours of sleep.

Bootstrapping

Required Video: Bootstrapping

Required Reading: Modern Dive Chapter 8: Bootstrapping and Confidence Intervals

You don’t need to carefully read every word in this chapter, but please look over it. In particular, you’ll find some shortcuts from the infer package that make the bootstrapping process even easier and cleaner!

Recommended Reading: Confidence Intervals and Bootstrapping

Fun Fact:

The term “bootstrap” comes from the phrase “pull yourself up by your bootstraps!” meaning, essentially, that you should take responsibility for your own life improvement.

This is kind of a joke - of course, you can’t fly through the air by grabbing your shoelaces and pulling up!

Similarly, the bootstrap procedure in statistics feels a bit like cheating; we’re magically making more samples from our original.

It’s one of my favorite terms in all of statistics!

Check-In 2: Bootstrapping

Use the mtcars dataset to study horsepower of cars (hp).

Make a 95% Confidence Interval for:

• The mean horsepower

• The median horsepower

• The variance of horsepower