# 7

# CONFIDENCE INTERVALS

In this chapter, we take the simulation procedures that we have been working on and put them in a more formal (traditional) statistics framework. After completing this chapter, you should be able to:

- distinguish between the appropriate uses of point estimates and interval estimates,
- calculate confidence intervals (via resampling or formulas),
- explain the relationship between the Central Limit Theorem and the applicability of Normal approximations for confidence intervals,
- calculate standard error and explain the difference between it and standard deviation,
- calculate the confidence interval for a mean or proportion,
- calculate the confidence interval for a difference in means or proportions.

This material, particularly the vocabulary and definitions, is most relevant for the *research* community. *Data scientists*, however, will encounter confidence intervals in their work and will benefit from a solid understanding, via resampling, of how they work.

## 7.1 POINT ESTIMATES

The procedures we have discussed all involve establishing the possible error that occurs when we measure some parameter in a population by taking a sample from that population. The technical term for this procedure of establishing the possible error is a confidence interval. It is one way to measure the accuracy of a measurement. The statistic or the measurement itself is often called a *point estimate.*

*Definition:* Point estimate

A point estimate is a statistic, such as a mean, median, and percentile ...