# WorksheetFunction.Z_Test Method (Excel)

Returns the one-tailed probability-value of a z-test. For a given hypothesized population mean, 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

expression. `Z_Test`( `_Arg1_` , `_Arg2_` , `_Arg3_` )

expression A variable that represents a 'WorksheetFunction' object.

### Parameters

Name Required/Optional Data Type Description
Arg1 Required Variant Array is the array or range of data against which to test the hypothesized population mean.
Arg2 Required Double The value to test.
Arg3 Optional Variant Sigma - The population (known) standard deviation. If omitted, the sample standard deviation is used.

Double

## Remarks

• If array is empty, Z_TEST returns the #N/A error value.

• Z_TEST 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_S(array); and n is the number of observations in the sample 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 ? 0 . From the symmetry of the Normal distribution, if AVERAGE(array) < ?0 , 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 ? 0 (in either direction) than AVERAGE(array), when the underlying population mean is ?0 : =2 * MIN(Z_TEST(array,?0 ,sigma), 1 - Z_TEST(array,?0 ,sigma)).