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\subsection*{Formulas for 1-Sample Inferential Statistics}
\begin{equation*}
\begin{array}{|c|c|c|c|c|c|} %col 0,30,180,210,280,350
\hline
                              & \text{Confidence Interval}                                                                                                                          & \text{Hypothesis CV}        & \text{Hypothesis TV}                                                & \text{Sample size}                                                  & \text{d.f.} \\
\hline&&&&& \\
\text{Proportion } p          & \hat{p} - z_{\alpha/2} \sqrt{\displaystyle\frac{pq}{n}} \le p \le \hat{p} + z_{\alpha/2} \sqrt{\displaystyle\frac{pq}{n}}                           & z \text{ chart}             & z = \displaystyle\frac{\hat{p}-p}{\sqrt{pq/n}}                      & n=pq\left( \displaystyle\frac{z_{\alpha/2}}{E} \right)^2            & --- \\
&&&&& \\
z                             & \overline{x} - z_{\alpha/2} \sqrt{\displaystyle\frac{\sigma}{n}} \le \mu \le \overline{x} + z_{\alpha/2} \sqrt{\displaystyle\frac{\sigma}{n}}       & z \text{ chart}             & z = \displaystyle\frac{\overline{x}-\mu}{\sigma / \sqrt{n}}         & n= \left( \displaystyle\frac{z_{\alpha/2} \sigma}{E} \right)^2      & --- \\
&&&&& \\
t                             & \overline{x} - t_{\alpha/2} \sqrt{\displaystyle\frac{s}{n}} \le \mu \le \overline{x} + t_{\alpha/2} \sqrt{\displaystyle\frac{s}{n}}                 & t \text{ chart}             & t = \displaystyle\frac{\overline{x} - \mu}{s/\sqrt{n}}              & ---                                                                 & n-1 \\
&&&&& \\
\text{Variance}               & \displaystyle\frac{(n-1)s^2}{\chi^2_{\alpha/2}} \le \sigma^2 \le \displaystyle\frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}                                  & \chi^2 \text{ chart}        & \chi^2 = \displaystyle\frac{(n-1)s^2}{\sigma^2}                     & ---                                                                 & n-1 \\
&&&&& \\
\text{Standard Deviation}     & \sqrt{\displaystyle\frac{(n-1)s^2}{\chi^2_{\alpha/2}}} \le \sigma \le \sqrt{ \displaystyle\frac{(n-1)s^2}{\chi^2_{1-(\alpha/2)}}}                   & \chi^2 \text{ chart}        & \chi^2 = \displaystyle\frac{(n-1)s^2}{\sigma^2}                     & ---                                                                 & n-1 \\
&&&&& \\          %maybe change chi's subscript spacing
\hline
\end{array}
\end{equation*}


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