# 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.

Syntax

ZTEST(array,μ0,sigma)

Array     is the array or range of data against which to test μ0

μ0    is the value to test.

Sigma     is 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.

• Create a blank workbook or worksheet.
• Select the example in the Help topic.

Note   Do not select the row or column headers.

Selecting an example from Help
• Press CTRL+C.
• In the worksheet, select cell A1, and press CTRL+V.
• 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.
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 2007