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

question 12

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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Definitions:

Shifts

Changes or transitions in positions, attitudes, conditions, or periods of time, often indicating a departure from previous states or norms.

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Organizations that collect funds from members and donate those funds to campaign for or against political candidates, legislation, or policies.

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Term used to describe large-scale corporate operations, often with significant influence on society and the economy.

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Activities aimed at influencing the decision making process within specific groups. Usually refers to efforts made to win elections or promote specific policies.

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