## confidence limits (about the mean)

https://doi.org/10.1351/goldbook.C01247
Symmetric confidence limits (±C) about the estimated mean, which cover the population mean with probability 1- α. The quantity C is calculated by the formula: $C = \frac{t_{\text{p},v^{S}}}{\sqrt{n}}$ Here t p , v, is the critical value from the t- (or Student) distribution function corresponding to the confidence level 1- α and degrees of freedom v. The symbol p represents the percentile (or percentage point) of the t-distribution. For 1-sided intervals, p = 1- α; for 2-sided intervals, p = 1- α 2. In each case, the confidence level is 1- α. The confidence interval is given as x _ ± C.
Note:
If the population @S05911@ σ is known, confidence limits about a single result may be calculated with the formula: $C = t_{\text{p},\infty}\sigma$ The @C01124@ t p , ∞, is the limiting value of the t-distribution function for v = ∞ at @C01246@ 1- α. This is identical to z p, the pth percentage point of the standard normal variate.
Source:
PAC, 1994, 66, 595. 'Nomenclature for the presentation of results of chemical analysis (IUPAC Recommendations 1994)' on page 601 (https://doi.org/10.1351/pac199466030595)