Formular Number 
Name 
Formular 
Formular with R


5.3.1 
ztransformation for sample mean 
$Z={\frac {{\bar {X}}\mu _{x}}{\sigma /{\sqrt {n}}}}$ 
Example

5.4.1 
ztransformation for difference between two means 
$Z={\frac {({\bar {X}}_{1}{\bar {X}}_{2})(\mu _{1}\mu _{2})}{\sqrt {{\frac {\sigma _{1}^{2}}{n_{1}}}+{\frac {\sigma _{2}^{2}}{n_{2}}}}}}$ 
Example

5.5.1 
ztransformation for sample proportion 
$Z={\frac {{\bar {p}}p}{\sqrt {\frac {p(1p)}{n}}}}$ 
Example

5.5.2 
Continuity correction when x < np 
$Z_{c}={\frac {{\frac {x+.5}{n}}p}{\sqrt {pq/n}}}$ 
Example

5.5.3 
Continuity correction when x > np 
$Z_{c}={\frac {{\frac {X+.5}{n}}p}{\sqrt {pq/n}}}$ 
Example

5.6.1 
ztransformation for difference between two proportions 

Example

Symbol Key 
