Symmetric confidence limits ($\pm C$) about the estimated mean, which cover the population mean with probability $1-\alpha$. The quantity $C$ is calculated by the formula: $$C=\frac{t_{\text{p},v^S}}{\sqrt{n}}$$ Here $t_{\text{p},v}$, is the critical value from the $t$- (or Student) distribution function corresponding to the confidence level $1-\alpha$ and degrees of freedom $v$. The symbol $p$ represents the percentile (or percentage point) of the $t$-distribution. For 1-sided intervals, $p=1-\alpha$; for 2-sided intervals, $p=1-\frac{\alpha }{2}$. In each case, the confidence level is $1-\alpha$. The confidence interval is given as $\bar{x}\pm C$.