# ZTEST function

Returns the one-tailed probability-value of a z-test. For a given hypothesized population mean, μ0, ZTEST returns the probability that the sample mean would be greater than the average of observations in the data set (array) — that is, the observed sample mean.

To see how ZTEST can be used in a formula to compute a two-tailed probability value, see "Remarks" below.

Important   This function has been replaced with one or more new functions that may provide improved accuracy and whose names better reflect their usage. Although this function is still available for backward compatibility, you should consider using the new functions from now on, because this function may not be available in future versions of Excel.

## Syntax

`ZTEST(array,x,[sigma])`

The ZTEST function syntax has the following arguments (argument: A value that provides information to an action, an event, a method, a property, a function, or a procedure.):

• Array     Required. The array or range of data against which to test x.
• X     Required. The value to test.
• Sigma     Optional. The population (known) standard deviation. If omitted, the sample standard deviation is used.

## Remarks

• If array is empty, ZTEST returns the #N/A error value.
• ZTEST is calculated as follows when sigma is not omitted:

or when sigma is omitted:

where x is the sample mean AVERAGE(array); s is the sample standard deviation STDEV(array); and n is the number of observations in the sample COUNT(array).

• ZTEST represents the probability that the sample mean would be greater than the observed value AVERAGE(array), when the underlying population mean is μ0. From the symmetry of the Normal distribution, if AVERAGE(array) < μ0, ZTEST will return a value greater than 0.5.
• The following Excel formula can be used to calculate the two-tailed probability that the sample mean would be further from μ0 (in either direction) than AVERAGE(array), when the underlying population mean is μ0:

=2 * MIN(ZTEST(array,μ0,sigma), 1 - ZTEST(array,μ0,sigma)).

## Example

The example may be easier to understand if you copy it to a blank worksheet.

1. Select the example in this article. If you are copying the example in Excel Online, copy and paste one cell at a time.
Important: Do not select the row or column headers.

Selecting an example from Help

1. Press CTRL+C.
2. Create a blank workbook or worksheet.
3. In the worksheet, select cell A1, and press CTRL+V. If you are working in Excel Online, repeat copying and pasting for each cell in the example.
Important: For the example to work properly, you must paste it into cell A1 of the worksheet.
4. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

After you copy the example to a blank worksheet, you can adapt it to suit your needs.

A
Data
3
6
7
8
6
5
4
2
1
9
Formula Description (Result)
=ZTEST(A2:A11,4) One-tailed probability-value of a z-test for the data set above, at the hypothesized population mean of 4 (0.090574)
=2 * MIN(ZTEST(A2:A11,4), 1 - ZTEST(A2:A11,4)) Two-tailed probability-value of a z-test for the data set above, at the hypothesized population mean of 4 (0.181148)
=ZTEST(A2:A11,6) One-tailed probability-value of a z-test for the data set above, at the hypothesized population mean of 6 (0.863043)
=2 * MIN(ZTEST(A2:A11,6), 1 - ZTEST(A2:A11,6)) Two-tailed probability-value of a z-test for the data set above, at the hypothesized population mean of 6 (0.273913)

Applies to:
Excel 2010, Excel Web App, SharePoint Online for enterprises, SharePoint Online for professionals and small businesses