# CONFIDENCE.NORM function

## Description

Returns the confidence interval of a sample mean.

DAX CONFIDENCE.NORM function is new in Excel 2016.

## Syntax

CONFIDENCE.NORM (alpha, standard_dev, size)


## Parameters

Sr.No. Parameter & Description
1

alpha

The significance level used to compute the confidence level.

The confidence level equals 100 * (1 - alpha) %. For example, if alpha is 0.05, then confidence level is 95%.

2

standard_dev

The population standard deviation for the data range and is assumed to be known.

3

size

The sample size.

## Return Value

A range of values.

## Remarks

The confidence interval is a range of values. The sample mean $\bar{x}$ is at the center of this range and the range is $\bar{x}$ ± CONFIDENCE.NORM.

For example, if x is the sample mean of delivery times for products ordered through the mail, x ± CONFIDENCE.NORM is a range of population means.

For any population mean, μ0, in this range, the probability of obtaining a sample mean further from μ0 than x is greater than alpha; for any population mean, μ0, not in this range, the probability of obtaining a sample mean further from μ0 than x is less than alpha. In other words, assume that we use x, standard_dev, and size to construct a twotailed test at significance level alpha of the hypothesis that the population mean is μ0.

Then, we will not reject that hypothesis, where μ0 is in the confidence interval, and will reject that hypothesis, where μ0 is not in the confidence interval.

• If any parameter is non-numeric, CONFIDENCE.NORM returns the #VALUE! error value.

• If alpha ≤ 0 or alpha ≥ 1, CONFIDENCE.NORM returns the #NUM! error value.

• If standard_dev ≤ 0, CONFIDENCE.NORM returns the #NUM! error value.

• If size is not an integer, it is truncated.

• If size < 1, CONFIDENCE.NORM returns the #NUM! error value.

• If we assume alpha equals 0.05, we need to calculate the area under the standard normal curve that equals (1 - alpha), or 95 percent. This value is ± 1.96. The confidence interval is therefore −

$$\bar{x}\:\pm\:1.96\lgroup\frac{\sigma}{\sqrt{n}}\rgroup$$

## Example

= CONFIDENCE.NORM (0.05,2.5,50) returns 0.692951912174839.

dax_functions_statistical.htm