Test the Null Hypothesis of Independence of the Two Classifications $A$

Essay

Test the null hypothesis of independence of the two classifications, $A$ and $B$ , of the $3 \times 3$ contingency table shown below. Test using $\alpha = .025$ .
$\begin{array} { l l | l l l } & &{ \quad\mathrm { B } } \\& & \mathrm { B } _ { 1 } & \mathrm {~B} _ { 2 } & \mathrm {~B} _ { 3 } \\\hline & \mathrm { A } _ { 1 } & 19 & 40 & 60 \\\mathrm {~A} & \mathrm {~A} _ { 2 } & 55 & 23 & 22 \\& \mathrm {~A} _ { 3 } & 31 & 42 & 47\end{array}$