How we change what others think, feel, believe and do
The Z-test compares sample and population means to determine if there is a significant difference.
It requires a simple random sample from a population with a Normal distribution and where where the mean is known.
The z measure is calculated as:
z = (x - m) / SE
where x is the mean sample to be standardized, m (mu) is the population mean and SE is the standard error of the mean.
SE = s / SQRT(n)
where s is the population standard deviation and n is the sample size.
The z value is then looked up in a z-table. A negative z value means it is below the population mean (the sign is ignored in the lookup table).
The Z-test is typically with standardized tests, checking whether the scores from a particular sample are within or outside the standard test performance.
The z value indicates the number of standard deviation units of the sample from the population mean.
Note that the z-test is not the same as the z-score, although they are closely related.