# Z.TEST Function

Calculates the one-tailed P-value of a Z-test

Calculates the one-tailed P-value of a Z-test

The Z TEST Excel formula is categorized under Statistical functions. It will calculate the one-tailed P-value of a Z-test.

As a financial analyst, the Z.TEST function is useful for various analysis. For example, we can decide if we should invest in a particular stock when it provides a specific average daily return.

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

The Z.TEST function uses the following arguments:

**Array**(required argument) – It is the array or range of data against which we need to test x. Array is a set of values against which the hypothesized sample mean is to be tested.**X**(optional argument) – It is the hypothesized sample. It is the value to test.**Sigma**(optional argument) – It represents the population standard deviation if this is known. If omitted, the function uses the sample standard deviation.

To understand the uses of the Z.TEST function, let us consider an example:

Suppose we are given the following data:

To calculate the one-tailed probability-value of a z-test for the data with a hypothesized population mean of 4, we will use the following formula:

We get the result below:

For calculating the two-tailed probability-value of a z-test for the above data with a hypothesized population mean of 4, we will use the following formula:

We get the result below:

** **

- Z.TEST represents the probability that the sample mean would be higher 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.
- #VALUE! error – Occurs when the value of x or the value of sigma is non-numeric.
- #NUM! error – Occurs when the sigma argument provided is equal to zero.
- #N/A error – Occurs when the provided array is empty.
- #DIV/0! error – Occurs when:
- The sigma is not provided and the standard deviation of the supplied array is zero.
- The given array contains just one value.

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