## Elementary Statistics (12th Edition)

$\alpha=1-0.9=0.1.$ Then we find the critival chi-square values by the given formula:$X_{L}^2=\frac{1}{2}(-z_{\alpha/2}+\sqrt{2k-1})^2=\frac{1}{2}(-1.645+\sqrt{2\cdot105-1})^2=82.072.$ $X_{R}^2=\frac{1}{2}(z_{\alpha/2}+\sqrt{2k-1})^2=\frac{1}{2}(1.645+\sqrt{2\cdot105-1})^2=129.635.$ These values are really close to the actual values.