# Documentation/Calc Functions/ZTEST

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## Function name:

ZTEST

## Category:

Statistical Analysis

## Summary:

Calculates the probability of observing a z-statistic greater than the one computed based on a sample. The function gives the one-tailed probability-value of a z-test. This is the probability of observing a sample mean as large or larger than the mean of the given sample for samples drawn from a normal distribution.

## Syntax:

ZTEST(**Data**; **mu**[;**Sigma**])

## Returns:

Returns a real number which is the one-tailed probability value of a z-test for data sample **Data**, mean value **mu** and standard deviation as **Sigma**. It ranges from 0 to 1, i.e. [0,1].

## Arguments:

**Data** is an array or a reference to a range of cells which is the given sample, drawn from a normally distributed population.

**mu** is a real number or a reference to the cell containing that number which is the known mean of the population.

**Sigma** is a positive real number or a reference to the cell containing that number which is the known standard deviation of the population. If omitted, the standard deviation of the given sample is used.

- If
**Sigma**is negative or zero then the function returns an error value.

## Additional details:

- ZTEST can also be related to NORMSDIST as :

ZTEST(**Data**,**mu**) = 1 - NORMSDIST((Average(**Data**)-**mu**)/(**sigma**/ √n))

or for the case where sigma is omitted and s is the standard deviation of the Data:

ZTEST(**Data**,**mu**) = 1 - NORMSDIST((Average(**Data**)-**mu**)/(**s**/√n))

- With sample being the mean of
**Data**and

The formula for ZTEST is:

- For more details on z-test, visit Wikipedia.

## Examples:

Formula | Description | Returns |
---|---|---|

=ZTEST(A1:A7;8) where A1:A7 contains 5,5.9,4.1,7.3,2.8,1.2,6 | The function calculates the one-tailed probability value of a z-test for data sample. Here Sigma is not mentioned hence standard deviation of the data is used. |
0.999991103497123 |

=ZTEST(A1:A7;8;10) where A1:A7 contains 5,5.9,4.1,7.3,2.8,1.2,6 | The function calculates the one-tailed probability value of a z-test for data sample. | 0.814813741690979 |

=ZTEST(A1:A7;8;0) where A1:A7 contains 5,5.9,4.1,7.3,2.8,1.2,6 | The function returns an error value for Sigma less than equal to zero. |
Err:502 |

## Related LibreOffice functions:

## ODF standard:

## Equivalent Excel functions:

ZTEST