*8.44. A chi-squared variable with degrees of freedom equal to df has representation z\ + ... + z 2

df, where z i,...,Zdf are independentstandard normal variates.

(a) If z is a test statistic that has a standard normal distribution, what distribution does z 2

have?

(b) Explain how to get the chi-squarcd values for df = 1 in Table C 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 Hq: independence between belief in an afterlife (yes, no) and happiness (not too happy, pretty happy, very happy) is ^

2 in a 2 X 3 table for men and ^ m a

2 x 3 table for women.

If Hq is true for each gender, then what is the probability distribution of X\ + X^-