## Excel Z.TEST Function

### Description

The Excel Z.TEST function returns the one-tailed P-value of a z-test which is useful for various analyses. Based on the given hypothesized population mean, x, Z.TEST function returns the probability that the sample mean would be greater than the observed sample mean.

Formula syntax

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

Arguments

 array: Required, the array or range of the data against which to test x. x: Required, the value used to test. sigma: Optional, represents to use the population’s standard deviation if this is known. If it is omitted, the sample standard deviation is used.

### Returns

Z.TEST function returns a numeric value.

### Remarks

1. Z.TEST represents the probability that the sample mean would be greater than the observed mean AVERAGE(array), when the underlying population mean is μ0. From the symmetry of the normal distribution, if AVERAGE(array) < x, Z.TEST returns a value greater than 0.5.

2. Z.TEST is calculated as follows

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

### Errors

1. #VALUE! error – Occurs when the x or sigma is not a numeric value.

2. #NUM! error – Occurs when sigma = 0.

3. #N/A! error – Occurs when array is empty.

4. #DIV/0! error – Occurs when array contains only one value, or sigma is omitted and the standard deviation of the supplied array is 0.

### Version

Excel 2010 and later versions

### Usage and Examples

Basic usage

To get the one-tailed probability value of a z-test for the data in range B3:B9 with a hypothesized population mean of 6, please use the formula as this:

=Z.TEST(B3:B9,6)

Press Enter key to get the result.

#### Other Functions:

• Excel POISSON Function
The Excel POISSON function returns the Poisson distribution which is used to predict the number of events occurring over a specific time.

• Excel WEIBULL Function
The Excel WEIBULL function returns the Weibull probability density function or Weibull cumulative distribution for a supplied set of parameters.

• Excel EXPON.DIST Function
EXPON.DIST function used in Excel 2010, returns the exponential distribution based on the given x value and the parameter of the distribution.

• Excel F.DIST Function
The Excel F.DIST function returns the F probability distribution which is usually used to measure the degree of diversity between two data sets.

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