Biostatistics with R/Some Important Sampling Distributions

Summary of Formulars with R

Formular Number	Name	Formular	Formular with R
5.3.1	z-transformation for sample mean	$Z=\frac{\overline{X}-{\mu }_x}{\sigma /\sqrt{n}}$	Example
5.4.1	z-transformation for difference between two means	$Z=\frac{({\overline{X}}_1-{\overline{X}}_2)-({\mu }_1-{\mu }_2)}{\sqrt{\frac{{\sigma }_1^2}{n_1}+\frac{{\sigma }_2^2}{n_2}}}$	Example
5.5.1	z-transformation for sample proportion	$Z=\frac{\overline{p}-p}{\sqrt{\frac{p(1-p)}{n}}}$	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	z-transformation for difference between two proportions	${\displaystyle }$	Example
Symbol Key