# Z.TEST function

Returns the one-tailed P-value of a z-test.

For a given hypothesized population mean, x, Z.TEST 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 Z.TEST can be used in a formula to compute a two-tailed probability value, see the Remarks section below.

## Syntax

`Z.TEST(array,x,[sigma])`

The Z.TEST 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, Z.TEST returns the #N/A error value.
• Z.TEST is calculated as follows when sigma is not omitted:

Z.TEST(array,x,sigma) = 1- Norm.S.Dist((Average(array)- x) / (sigma/√n),TRUE)

or when sigma is omitted:

Z.TEST(array,x) = 1- Norm.S.Dist((Average(array)- x) / (STDEV(array)/√n),TRUE)

where x is the sample mean AVERAGE(array), and n is COUNT(array).

• Z.TEST 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) < x, Z.TEST 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 x (in either direction) than AVERAGE(array), when the underlying population mean is x:

=2 * MIN(Z.TEST(array,x,sigma), 1 - Z.TEST(array,x,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)
=Z.TEST(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(Z.TEST(A2:A11,4), 1 - Z.TEST(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)
=Z.TEST(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(Z.TEST(A2:A11,6), 1 - Z.TEST(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