Large Sample Theory

All of the estimates mentioned in the preceeding section ($\bar{X}$, $\widehat{P}$, $X{\mkern -13.5 mu}\overline{\phantom{\text{X}}}_1 - X{\mkern -13.5 mu}\overline{\phantom{\text{X}}}_2$, and $\widehat{P}_1 - \widehat{P}_2$) have approximately normal distributions for large enough sample sizes ($n$ for one sample, $n_1$ and $n_2$ for two samples).