In the previous section we discovered how to make a confidence interval for estimating population mean. However we knew what the population standard deviation (

$\sigma$) was. However it is not always the case that

$\sigma$ is known.

If population standard deviation (

$\sigma$) is unknown then to make a confidence interval to estimate population mean we cannot our old formula for error:

$E=Z_\frac{\sigma}{2}*\frac{\sigma}{\sqrt{n}}$ as it requires a knowledge of

$\sigma$. So instead we are required to use a thing called t-scores (

$t_{\frac{\alpha}{2}})$.

Once we find the t-scores for particular values (this is done in a similar way to finding z-scores) we have a new formula for the Margin of Error:

$E=Z_\frac{\sigma}{2}*\frac{S}{\sqrt{n}}$