# Z test

The Z-test is a statistical test used in inference which determines if the difference between a sample mean and the population mean is large enough to be statistically significant.

The Z-test is conducted by the following steps:

First the standard error of the mean is calculated:

$\mathrm{SE} = \frac{\sigma}{\sqrt n}$

Then the formula for the Z-score for the Z-test is calculated by the formula:

$z = \frac{x-\mu}{\mathrm{SE}}$

The Z-score is then compared to a Z-table. The Z-table indicates whether the calculated z-score is within the realm of chance or if the z-score is so different that the sample mean is unlikely to have happened by chance.