Formula Review

The Central Limit Theorem for Sample Means:

$\bar{X}$ ~ N$\left({\mu }_{\bar{x}}\text{, }\frac{\sigma }{\sqrt{n}}\right)$

$Z=\frac{\bar{X}-{\mu }_{\bar{X}}}{{\sigma }_{\bar{X}}}=\frac{\bar{X}-\mu }{\sigma /\sqrt{n}}$

The Mean $\bar{X}:{\mu }_{\overline{x}}$

Central Limit Theorem for Sample Means z-score $z=\frac{\bar{x}-{\mu }_{\overline{x}}}{\left(\frac{\sigma }{\sqrt{n}}\right)}$

Standard Error of the Mean (Standard Deviation ($\bar{X}$)): $\frac{\sigma }{\sqrt{n}}$

Finite Population Correction Factor for the sampling distribution of means: $Z=\frac{\overline{x}-\mu }{\frac{\sigma }{\sqrt{n}}·\sqrt{\frac{N-n}{N-1}}}$

Finite Population Correction Factor for the sampling distribution of proportions: ${\sigma }_{\mathrm{p\text{'}}}=\sqrt{\frac{p(1-p)}{n}}\times \sqrt{\frac{N-n}{N-1}}$