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Use A χ2\chi ^ { 2 } Test to Test the Claim That in the Given Contingency

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Essay

Use a χ2\chi ^ { 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.
 Rock  Pop  Classical 152550857325356891603545907477\begin{array}{l|ccc} & \text { Rock } & \text { Pop } & \text { Classical } \\\hline \mathbf{1 5 - 2 5} & 50 & 85 & 73 \\\mathbf{2 5 - 3 5} & 68 & 91 & 60 \\\mathbf{3 5 - 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.

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