= Normal-mean sample size calculation
{title2=$n=\left\lceil\sigma^2(z_{1-\alpha}+z_{1-\beta})^2/(\delta^*)^2\right\rceil$}
For a one-sided normal-mean test of size $\alpha$ with known standard deviation $\sigma$, a positive alternative $\delta^*$ and target <statistical power> $1-\beta>\alpha$, the required <sample size> is the ceiling of $\sigma^2(z_{1-\alpha}+z_{1-\beta})^2/(\delta^*)^2$. This follows by shifting the <standard normal quantile> in the alternative rejection <probability>.
Back to article page
