I. For a chi-square test for homogeneity, the null hypothesis states that the distribution of a categorical variable is the same for all populations.

II. The degrees of freedom for a chi-square test for homogeneity are calculated as $$(\text{number of populations} - 1)$$.

III. The chi-square test for homogeneity and the chi-square test for independence use the same test statistic and have identical conditions for use.

Which of these statements are true?