on the chi square example, I understand where X^2 = 0.04 but I don't understand how X^2 critical = 3.841.

Chi-Square Test: Males and Females = Male = 50 Female = 50, so the total will be 100 Male / O (Observed Value) = 51, E (Expected Value) = 50 0-E =1 (0 - E)^2 = 1 (0 -E )^2 / E = 1/50 = 0.02 Female / 0 = 49 , E = 50 O-E=-1 (0- E)^2 = 1 (0- E)^2 / E = 1/50 = 0.02 So X^2 observed ^2 = 0.04 Deg of freedom (F) = 2-1 =1 =(meaning number of categories - 1) X^2 critical = 3.841 X^2 critical > X^2 observed 3.841 > 0.04