Finding Critical Values of x2 For large numbers of degrees of freedom, we can approximate critical values of x2 as follows:

Here k is the number of degrees of freedom and z is the critical value, found in Table A-2. For example, if we want to approximate the two critical values of x2 in a twotailed hypothesis test with a 5 0.05 and a sample size of 150, we let k 5 149 with z 5 21.96 followed by k 5 149 and z 5 1.96.

a. Use this approximation to estimate the critical values of x2 in a two-tailed hypothesis test with n 5 101 and a 5 0.05. Compare the results to those found in Table A-4.

b. Use this approximation to estimate the critical values of x2 in a two-tailed hypothesis test with n 5 150 and a 5 0.05.