Suppose That You Wish to Perform a Chi-Square Test of Independence

Essay

Suppose that you wish to perform a chi-square test of independence. True or false, if the two variables are not associated, then the test statistic $\chi ^ { 2 } = \Sigma \frac { ( \mathrm { O } - \mathrm { E } ) ^ { 2 } } { \mathrm { E } }$ has approximately a chi-square distribution with rc - 1 degrees of freedom, where $r$ and $c$ are the number of possible values for the two variables under consideration? If the statement is false, explain why.