8.44.* A chi-squared variable with degrees of freedom equal to df has representation z21 + · · · + z2 df, where z1, . . . , zdf are independent standard normal variates.

(a) If z is a test statistic that has a standard normal distribution, what distribution does z2 have?

(b) Explain how to get the chi-squared values for df = 1 from z-scores in the standard normal table (Table A).
Illustrate for the chi-squared value of 6.63 having P-value 0.01.

(c) The chi-squared statistic for testing H0: independence between belief in an afterlife (yes, no) and happiness (not too happy, pretty happy, very happy) is X2m in a 2×3 table for men and X2w in a 2 × 3 table for women. If H0 is true for each gender, then what is the probability distribution of X2m + X2w ?