## Excel Office

Excel How Tos, Tutorials, Tips & Tricks, Shortcuts

# What is Z.TEST function in Excel?

Z.TEST  is one of Statistical functions in Microsoft Excel that returns the one-tailed P-value of a z-test.Go to the explanation section below to see how Z.TEST can be used in a formula to compute a two-tailed probability value.
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.

## Syntax of Z.TEST function

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

The Z.TEST function syntax has the following arguments:

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

## Explanation of Z.TEST function

• 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 of Z.TEST function

Steps to follow:

1. Open a new Excel worksheet.

2. Copy data in the following table below and paste it in cell A1

Note: For formulas to show results, select them, press F2 key on your keyboard and then press Enter.

You can adjust the column widths to see all the data, if need be.

 Data 3 6 7 8 6 5 4 2 1 9 Formula Description (Result) 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) 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) 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) 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) 0.273913