Confidence intervals/samples/hypothesis testing

Abstract

Take many samples, size n, from a population and find their means. The Central Limit Theorem proves that these means form a Normal distribution with mean μ (that of the population) and standard deviation $\frac{\sigma }{{\sqrt n }}$ (called the standard error):

$$\bar X \sim N\left( {\mu ,\frac{{{\sigma ^2}}}{n}} \right)$$

For small samples (n < 30) see Chapter 19.