Finding Critical Values In constructing confidence intervals for s or s2, Table A-4 can be used to find the critical values x2 L and x2 R only for select values of n up to 101, so the number of degrees of freedom is 100 or smaller. For larger numbers of degrees of freedom, we can approximate x2 L and x2 R by using

where k is the number of degrees of freedom and za>2 is the critical z score described in Section 7-1. Use this approximation to find the 95% critical values x2 L and x2 R for the acupuncture treatment group in Exercise 16 “Acupuncture for Migraines” where n = 142.

How do the results compare to the actual critical values of x2 L = 110.020 and x2 R = 175.765?

x = 1/1 [ Za/2 + +Za/2 + 2k - 1]