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(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 a = 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 x2 = 82.292 obtained by using Statdisk and Minitab?

Transcribed Image Text:

=1/2(2+ \\ + 2) = 2x - (z+V2k 1)2