Cattle Are Classified According to Age (Young, Medium, and Old) $\mathrm { P } ($

Cattle are classified according to age (young, medium, and old) and as to carcass quality (grades A, B, and C) . In one study, the animals were classified as :


The chi-square statistic for testing if there is an association between age and grade was calculated. The null hypothesis being tested is:

A) $\mathrm { P } ($ grade and age $) = \mathrm { P } ($ grade $) \mathrm { P } ($ age $)$
B) $\mathrm { P } ($ grade $\mid$ young $) < \mathrm { P } ($ grade $\mid$ medium $) < \mathrm { P }$ (grade $\mid$ old $)$
C) Grade and age classifications are dependent
D) Age depends on grade