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Preferred Label : confidence limits (about the mean);

IUPAC definition : 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: \[C \frac{t_{{p},v {S}}}{\sqrt{n}}\] 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.;

Scope note : if the population standard deviation s is known, confidence limits about a single result may be calculated with the formula:c tp,sthe coefficient t p,, is the limiting value of the t-distribution function for v at confidence level 1a. this is identical to zp, the pth percentage point of the standard normal variate.;

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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: \[C \frac{t_{{p},v {S}}}{\sqrt{n}}\] 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.

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06/05/2025


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