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Z-test on a mean with known variance

Does a sample come from a population with mean $ \mu_0$ and variance $ \sigma_0$ ?
$\displaystyle H_0:\mu$ $\displaystyle =$ $\displaystyle \mu_0$ (6.2)
$\displaystyle \sigma$ $\displaystyle =$ $\displaystyle \sigma_0$  
$\displaystyle H_1: \mu$ $\displaystyle \neq$ $\displaystyle \mu_0 \nonumber$  

Test using a Z-score test statistic with the sampling distribution
$\displaystyle Z$ $\displaystyle =$ $\displaystyle \frac{\overline{X}-\mu_0}{\sigma_0/\sqrt{n}}\sim N(0,1)$  


David Stephenson 2005-09-30