Editing Z-test (section)

==Procedure==
How to perform a ''Z''-test when ''T'' is a statistic that is approximately normally distributed under the null hypothesis is as follows: 

First, estimate the [[expected value]] μ of ''T'' under the null hypothesis and obtain an estimate ''s'' of the [[standard deviation]] of ''T''.

Second, determine the properties of ''T'': one-tailed or two-tailed.

For null hypothesis '''''H''<sub>0</sub>''': '''''μ'' ≥ ''μ''<sub>0</sub>''' vs [[alternative hypothesis]] '''''H''<sub>1</sub>''': '''''μ'' < ''μ''<sub>0</sub>''', it is lower/left-tailed (one-tailed).

For null hypothesis '''''H''<sub>0</sub>''': '''''μ'' ≤ ''μ''<sub>0</sub>''' vs alternative hypothesis '''''H''<sub>1</sub>''': '''''μ'' > ''μ''<sub>0</sub>''', it is upper/right-tailed (one-tailed). 

For null hypothesis '''''H''<sub>0</sub>''': '''''μ'' = ''μ''<sub>0</sub>''' vs alternative hypothesis '''''H''<sub>1</sub>''': '''''μ'' ≠ ''μ''<sub>0</sub>''', it is two-tailed. 

Third, calculate the [[standard score]]:
<math display="block">
 Z = \frac{\bar{X} - \mu_0}{s},
</math> which [[one- and two-tailed tests|one-tailed and two-tailed]] [[p-values|''p''-values]] can be calculated as Φ(''Z'') (for lower/left-tailed tests), Φ(&minus;''Z'') (for upper/right-tailed tests) and 2Φ(&minus;|''Z''|) (for two-tailed tests), where Φ is the standard [[normal distribution|normal]] [[cumulative distribution function]].