# CONFIDENCE

Returns the confidence interval for a population mean. The confidence interval is a range on either side of a sample mean. For example, if you order a product through the mail, you can determine, with a particular level of confidence, the earliest and latest the product will arrive.

**Syntax**

**CONFIDENCE**(**alpha**,**standard_dev**,**size**)

**Alpha** is the significance level used to compute the confidence level. The confidence level equals 100*(1 - alpha)%, or in other words, an alpha of 0.05 indicates a 95 percent confidence level.

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

**Size** is the sample size.

**Remarks**

- If any argument is nonnumeric, CONFIDENCE returns the #VALUE! error value.
- If alpha £ 0 or alpha ³ 1, CONFIDENCE returns the #NUM! error value.
- If standard_dev £ 0, CONFIDENCE returns the #NUM! error value.
- If size is not an integer, it is truncated.
- If size < 1, CONFIDENCE 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:

**Example**

Suppose we observe that, in our sample of 50 commuters, the average length of travel to work is 30 minutes with a population standard deviation of 2.5. We can be 95 percent confident that the population mean is in the interval:

or:

`CONFIDENCE(0.05,2.5,50)`

equals 0.692951. In other words, the average length of travel to work equals 30 ± 0.692951 minutes, or 29.3 to 30.7 minutes.