For df values beyond the range of Appendix Table A.3, chi square cutoffs can be approximated by

Question:

For df values beyond the range of Appendix Table A.3, chi square cutoffs can be approximated by using a formula based on cutoffs from the standard normal pdf, f_Z(z). Define χ²_p,n and z^∗_p so that P (χ²_n ≤ χ²_p,n) = p and P(Z ≤ z^∗_p) = p, respectively. Then

χ²_p,n= n(1− 2/9n +z^∗_p,√2/9n)³

Approximate the 95th percentile of the chi square distribution with 200 df. That is, find the value of y for which

P(χ²₂₀₀≤ y) = 0.95

Distribution
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