# Biostatistics with R/Some Important Sampling Distributions

5.3.1 z-transformation for sample mean ${\displaystyle Z={\frac {{\bar {X}}-\mu _{x}}{\sigma /{\sqrt {n}}}}}$ Example
5.4.1 z-transformation for difference between two means ${\displaystyle Z={\frac {({\bar {X}}_{1}-{\bar {X}}_{2})-(\mu _{1}-\mu _{2})}{\sqrt {{\frac {\sigma _{1}^{2}}{n_{1}}}+{\frac {\sigma _{2}^{2}}{n_{2}}}}}}}$ Example
5.5.1 z-transformation for sample proportion ${\displaystyle Z={\frac {{\bar {p}}-p}{\sqrt {\frac {p(1-p)}{n}}}}}$ Example
5.5.2 Continuity correction when x < np ${\displaystyle Z_{c}={\frac {{\frac {x+.5}{n}}-p}{\sqrt {pq/n}}}}$ Example
5.5.3 Continuity correction when x > np ${\displaystyle Z_{c}={\frac {{\frac {X+.5}{n}}-p}{\sqrt {pq/n}}}}$ Example