A hypothesis test, using a sample of n independent observations, of the null hypothesis that a normal distribution with variance σ2, has mean μ. Writing the sample mean as x̄, the test statistic is z, given by In the case where the alternative hypothesis is that the mean is not μ, then, if |z| > 1.96, there is evidence to reject the null hypothesis at the 5% significance level in favour of the alternative hypothesis.