Power of a test The power of a test can be calculated with the following formula: β ( μ ) = P μ ( x ¯ − μ σ 0 / n < μ 0 − μ σ 0 / n − z 1 − a 2 ) + P μ ( x ¯ − μ σ 0 / n > μ 0 − μ σ 0 / n + z 1 − a 2 ) = 1 − ϕ ( μ 0 − μ σ 0 / n − z 1 − a 2 ) + ϕ ( μ 0 − μ σ 0 / n + z 1 − a 2 ) {\displaystyle {\begin{aligned}\beta _{(}\mu )&=P_{\mu }({{{\bar {x}}-\mu } \over {\sigma _{0}{/}{\sqrt {n}}}}<{{\mu _{0}-\mu } \over {\sigma _{0}{/}{\sqrt {n}}}}-{z}_{1-{{a} \over {2}}})+P_{\mu }({{{\bar {x}}-\mu } \over {\sigma _{0}{/}{\sqrt {n}}}}>{{\mu _{0}-\mu } \over {\sigma _{0}{/}{\sqrt {n}}}}+{z}_{1-{{a} \over {2}}})\\&=1-\phi ({{\mu _{0}-\mu } \over {\sigma _{0}{/}{\sqrt {n}}}}-{z}_{1-{{a} \over {2}}})+\phi ({{\mu _{0}-\mu } \over {\sigma _{0}{/}{\sqrt {n}}}}+{z}_{1-{{a} \over {2}}})\\\end{aligned}}}