confidence limits (about the mean)

Symmetric confidence limits (± C) about the estimated mean, which cover the population mean with probability1 − α. The quantity C is calculated by the formula:
C = t p , v S n
Here t p , v, is the critical value from the t- (or Student) distribution function corresponding to the confidence level1 − α and degrees of freedomv. 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.
If the population standard deviationσ is known, confidence limits about a single result may be calculated with the formula:
C = t p , ∞ σ
The coefficientt p , ∞, is the limiting value of the t-distribution function for v = ∞ at confidence level1 − α. This is identical to z p, the pth percentage point of the standard normal variate.
PAC, 1994, 66, 595 (Nomenclature for the presentation of results of chemical analysis (IUPAC Recommendations 1994)) on page 601