$$\sqrt{\frac{\left(N-1\right)s^2}{{\chi }_{\left(\frac{\alpha }{\mathrm{2,}}N-1\right)}^2}}\le \sigma \le \sqrt{\frac{\left(N-1\right)s^2}{{\chi }_{\left(1-\frac{\alpha }{\mathrm{2,}}N-1\right)}^2}}$$