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

question 88

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.

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Definitions:

Ecological Footprints

A metric that calculates the environmental impact of an individual, community, or activity in terms of the amount of land and water area required to support their consumption and absorb their wastes.

Conservation

The practice of protecting and preserving natural resources and the environment.

Environmental Justice

The movement aimed at ensuring that no community suffers from disproportionate exposure to pollution, environmental hazards, and lack of access to natural resources, emphasizing fairness and equity.

Anthropocentric

Viewing and interpreting everything in terms of human values and experiences.