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. This function is still available for compatibility with earlier versions of Excel. However, if backward compatibility is not required, you should consider using the new functions from now on, because they more accurately describe their functionality.

For more information about the new function, see Z.TEST function.

Syntax

ZTEST(array,x,[sigma])

The ZTEST function syntax has the following arguments:

  • 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:

    Formula

    or when sigma is omitted:

    formula

    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.

How do I copy an example?

  1. Select the example in this article.

    Important   Do not select the row or column headers.

    selecting an example from help

    Selecting an example from Help

  2. Press CTRL+C.

  3. In Excel, create a blank workbook or worksheet.

  4. In the worksheet, select cell A1, and press CTRL+V.

    Important   For the example to work properly, you must paste it into cell A1 of the worksheet.

  5. 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.

1

2

3

4

5

6

7

8

9

10

11

12



13



14



15



16

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 Starter, Excel Online, SharePoint Online



Was this information helpful?

Yes No

How can we improve it?

255 characters remaining

To protect your privacy, please do not include contact information in your feedback. Review our privacy policy.

Thank you for your feedback!

Support resources

Change language