Related Function:

The CONFIDENCE.T function returns the confidence interval for a population mean, using a Student’s T-distribution.

• This function was introduced in Excel 2010 and so is not available in earlier versions.
• CONFIDENCE.T and CONFIDENCE.NORM functions replace the CONFIDENCE function included in earlier versions of Excel.

### Syntax

=CONFIDENCE.T(alpha,standard_dev,size)

#### Arguments

Argument Description
alpha Specifies the name of a parameter

 • The confidence level equals 100*(1 – alpha)%, i.e. an alpha of 0.05 indicates a 95 percent confidence level
standard_dev The standard deviation of the population
size The population sample size

#### Examples

A B C D
1 Data Formula
2 0.05 Significance level
3 2.5 Standard deviation
4 100 Sample size
5
6 Formula Result Notes
7 =CONFIDENCE.T(A2,A3,A4) 0.496054 Confidence interval, based on Student’s T-distribution, for the mean of a population based on a sample size of 100, with a 5% significance level and a standard deviation of 2.5

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

In the example above, the CONFIDENCE.T function is used to calculate the confidence interval, with a significance of 0.05 (confidence level of 95%), for the travel time to work for a sample population of 100 people. The sample mean is 30 minutes and the standard deviation is 2.5 minutes.

Therefore, the confidence interval is , which is equal to a drive time of 30 ± 0.496054 minutes, or 29.5 to 30.5 minutes.

#### Common Function Error(s)

Problem What went wrong
#VALUE! Occurs if any of the supplied arguments are non-numeric
#NUM! Occurs if either:

 • the supplied alpha is ≤ 0 or ≥ 1 • the supplied standard_dev is ≤ 0 • the supplied size argument is < 1
#DIV/0! Occurs if the supplied size argument = 1

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

For example, for a 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.