confidence limits (about the mean)

Symmetric confidence limits ( $Math - text$ ) about the estimated mean, which cover the population mean with probability $Math - ei$ . The quantity $Math - text$ is calculated by the formula:

$Math - e$

Here $Math - text$ , is the critical value from the $Math - text$ - (or Student) distribution function corresponding to the confidence level $Math - ei$ and degrees of freedom $Math - text$ . The symbol $Math - text$ represents the percentile (or percentage point) of the $Math - text$ -distribution. For 1-sided intervals, $Math - ei$ ; for 2-sided intervals, $Math - ei$ . In each case, the confidence level is $Math - ei$ . The confidence interval is given as $Math - ei$ .

Note:

If the population standard deviation $Math - note$ is known, confidence limits about a single result may be calculated with the formula:

$Math - e$

The coefficient $Math - note$ , is the limiting value of the $Math - note$ -distribution function for $Math - ei$ at confidence level $Math - ei$ . This is identical to $Math - note$ , the $Math - note$ 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