The Excel CONFIDENCE.NORM Function

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Related Function:

CONFIDENCE.T

Confidence Interval

In statistics, the confidence interval is the range that a population parameter is likely to fall into, for a given probability.

Eg. For given population and a probability of 95%, the confidence interval is the range, in which a population parameter is 95% likely to fall.

Note that the accuracy of the confidence interval relies on the population having a normal distribution.

The Confidence Interval is discussed further on the Wikipedia Confidence Interval Page

Basic Description

The Excel CONFIDENCE.NORM function uses a Normal Distribution to calculate a confidence value that can be used to construct the confidence interval for a population mean, for a supplied probablity and sample size. It is assumed that the standard deviation of the population is known.

The Confidence.Norm function is new to Excel 2010. However, this is simply a renamed version of the Confidence function, which is available in earlier versions of Excel.

The format of the function is :

CONFIDENCE.NORM( alpha, standard_dev, size )

where the arguments are as follows :

alpha	-	The significance level (=1-confidence level) - eg. a significance level of 0.05 equates to a confidence level of 95%
standard_dev	-	The standard deviation of the population
size	-	The population sample size

To calculate the confidence interval for a population mean, the returned CONFIDENCE value must then be added to, and subtracted from, the sample mean. ie. for the sample mean x :

Confidence Interval = x ± CONFIDENCE

Confidence.Norm Function Example

In the spreadsheet below, the Excel Confidence.Norm Function is used to calculate the confidence interval, with a significance of 0.05 (ie. a confidence level of 95%), for the mean of a sample of heights of 100 men. The sample mean is 1.8 meters and the standard deviation is 0.07 meters.