Test the Null Hypothesis of Independence of the Two Classifications $\quad$

Essay

Test the null hypothesis of independence of the two classifications, A and B, of the 3 × 3 contingency table shown below. Test using α = .10. $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$$\mathrm { B }$
$\begin{array} { l l | l l l } & & \mathrm { B } _ { 1 } & \mathrm {~B} _ { 2 } & \mathrm {~B} _ { 3 } \\\hline & \mathrm { A } _ { 1 } & 19 & 40 & 60 \\\mathrm {~A} & \mathrm {~A} _ { 2 } & 55 & 23 & 22 \\& \mathrm {~A} _ { 3 } & 31 & 42 & 47\end{array}$