Student's tdistribution  Confidence Intervals
Student's tdistribution
Lessons
Notes:
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 tscores ($t_{\frac{\alpha}{2}})$.
Once we find the tscores for particular values (this is done in a similar way to finding zscores) we have a new formula for the Margin of Error:
$E=Z_\frac{\sigma}{2}*\frac{S}{\sqrt{n}}$

2.
In “Anchiles”, a small madeup town near the equator, 15 random days were sampled and found to have an average temperature of 28°C, with a standard deviation of 4°C. Assume that the average daily temperature of this town is normally distributed.