The Z-test is a statistical test used in inference.

The test requires the following to be known:

• σ (the standard deviation of the population)
• μ (the mean of the population)
• x (the mean of the sample)

Other conditions to be met include knowing that your sample mean from a simple random sample of the population. If the sample came from a different sampling method, a different formula must be used. It must also be known that the population varies normally (i.e., the sampling disribution of the probabilities of possible values fits a standard normal curve). If it is not known that the population varies normally, if suffices to have a sufficently large sample, generally agreed to be ≥ 30 or 40.

In actuallity, knowing the true σ of a population is unrealistic, as it is impossible to measure every member of a population. It is more realistic to use a t-test, which uses the standard error obtained from the sample along with the t-distribution.

The formula is as follows:

External link

• Code/pseudo-code for Z-test at Google Groups

Z test formula is actually as follows:

z = (x - mu)/sigma