Which ONE of the following options is the CORRECT formula for Chi-Square $\left(\chi^{2}\right)$ test?
Given, $O_{1}, O_{2}, \ldots . O_{n}$ are the observed values, $E_{1}, E_{2}, \ldots . E_{n}$ are the corresponding expected values, $\bar{O}$ is the mean of observed values, $n$ is the number of observations, $\mu$ is the mean of $E_{i}, i=1, \ldots, n, \sigma_{o}$ is the standard deviation of observed values, and $\sigma_{E}$ is the standard deviation of expected values $E_{i}, i=1, \ldots, n$.
- $\chi^{2}=\sum_{\mathrm{i}=1}^{\mathrm{n}} \frac{\left(O_{i}-E_{i}\right)^{2}}{E_{i}}$
- $\chi^{2}=\sqrt{\frac{\sum_{i=1}^{n}\left(O_{i}-\bar{O}\right)}{n-1}}$
- $\chi^{2}=\dfrac{\bar{O}-\mu}{\sigma_{o} \sqrt{n}}$
- $\chi^{2}=\dfrac{\left(\sigma_{o}\right)^{2}}{\left(\sigma_{E}\right)^{2}}$
