Chapter B.2, Problem 17AYU

Critical Values Sir R. A. Fisher, a famous statistician, showed that the critical values of a chi-square distribution can be approximated by the standard normal distribution

  ${\chi }_k^2=\frac{{(z_k+\sqrt{2\nu -1})}^2}{2}$

where v is the degrees of freedom and z_k is the z-score such that the area under the standard normal curve to the right of z_k is k. Use Fisher’s approximation to find ${\chi }_{0.975}^2$ and ${\chi }_{0.025}^2$ with 100 degrees of freedom. Compare the results with those found in Table VIII.