Confidence intervals

A confidence interval estimates an unknown population mean using sample data. Because the population standard deviation is usually unknown, we use the sample standard deviation $s$ and the $t$-distribution instead of the normal distribution. The interval is $\bar{x}\pm t^{\ast }\frac{s}{\sqrt{n}}$, where $\bar{x}$ is the sample mean, $n$ is the sample size, and $t^{\ast }$ is the critical value from the $t$-distribution with $n-1$ degrees of freedom corresponding to the desired confidence level. The margin of error is $t^{\ast }\frac{s}{\sqrt{n}}$. Add and subtract this margin from the sample mean to get the lower and upper bounds of the interval.