Finding Critical Values of X2 For large numbers of degrees of freedom, we can approximate critical values of as follows:

Here K is the number of degrees of freedom and z is the critical value(s) found from technology or Table A-2. In Exercise 12 “Spoken Words” we have df = 55, so Table A-4 does not list an exact critical value. If we want to approximate a critical value of X2 in the right-tailed hypothesis test with α = 0.01 and a sample size of 56, we let k = 55 with z = 2.33 (or the more accurate value of z = 2.326348 found from technology). Use this approximation to estimate the critical value of X2 for Exercise 12. How close is it to the critical value of = 82.292 obtained by using Statdisk and Minitab?

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