# TOPIC 15

# Central Limit Theorem and Statistical Inference

Kissing couples lean their heads either to the right or to the left. Do they lean their heads to the right more often than to the left? After all, most people are right-handed, and for most people the right eye is dominant. Scientists have suggested that late-stage human embryos even turn their heads to the right in the womb. Perhaps this “right” tendency is reflected in how couples kiss as well. But by studying a sample, even a random sample of kissing couples, you expect that the sample proportion who lean right may not exactly reflect the population proportion. How much do you expect a sample proportion to differ from the population proportion? For example, if 65% of kissing couples in a sample lean their heads to the right, would that convince you that more than half of the population leans their heads to the right?

## Overview

In previous topics, you used hands-on and technology simulations to discover that, although the value of a sample proportion or a sample mean varies from sample to sample, the variation has a predictable long-term pattern. The Central Limit Theorem (CLT), introduced in Topics 13 and 14, specifies that, for large sample sizes, this pattern follows a normal distribution. Therefore, we can calculate probabilities of different outcomes using the appropriate normal model. In this topic, you will continue to practice with these calculations while looking ahead to ideas of statistical inference that you ...