Use A $x ^ { 2 }$ Test to Test the Claim That in the Given Contingency

Essay

Use a $x ^ { 2 }$ test to test the claim that in the given contingency table, the row variable and the column variable are
independent. The table below shows the age and favorite type of music of 668 randomly selected people. $$\begin{array} { c | c c c } & \text { Rock } & \text { Pop } & \text { Classical } \\\hline \mathbf { 1 5 } - \mathbf { 2 5 } & 50 & 85 & 73 \\\mathbf { 2 5 } - \mathbf { 3 5 } & 68 & 91 & 60 \\\mathbf { 3 5 } - \mathbf { 4 5 } & 90 & 74 & 77\end{array}$$ Use a 5 percent level of significance to test the null hypothesis that age and preferred music type are independent.