## confidence limits (about the mean)

https://doi.org/10.1351/goldbook.C01247
Symmetric confidence limits ($$\pm C$$) about the estimated mean, which cover the population mean with @P04855@ $$1 - \alpha$$. 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 @C01246@ $$1 - \alpha$$ and @D01572@ $$v$$. 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 @C01246@ is $$1 - \alpha$$. The confidence interval is given as $$\overline{x}\ \pm \ C$$.
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@ $$t_{p,\infty}$$, is the limiting value of the $$t$$-distribution function for $$\nu = \infty$$ at @C01246@ $$1 - \alpha$$. This is identical to $$z_{\text{p}}$$, the $$p$$th 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 [Terms] [Paper]