Objective

The objective is to compute a confidence interval for the mean $\mu$ of a population whose standard deviation is $\sigma$ using a random sample from that population.

We choose a level of confidence that the interval contains the (unknown) population mean $\mu$ , which we denote by $100\cdot(1-\alpha)$ .

This means that if we repeated the process of drawing the sample and calculating the confidence interval many times, we expect the interval to actually contain $\mu$ $100(1-\alpha$ percent of the time.