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

question 9

Essay

Use a $\chi ^ { 2 }$ 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.
Use a 5 percent level of significance to test the null hypothesis that age and preferred music type are independent.
$\begin{array} { c | c c c } & \text { Rock } & \text { Pop } & \text { Classical } \\\hline \mathbf { 1 5 } - \mathbf { 2 5 } & 50 & 85 & 73 \\\mathbf { 2 5 - 3 5 } & 68 & 91 & 60 \\\mathbf { 3 5 } - 45 & 90 & 74 & 77\end{array}$

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Definitions:

Numbered List

A list organized with items denoted by numbers, typically used for step-by-step guidance, ranking, or to show sequence.

Rational Appeals

Marketing strategies that use logical arguments or factual evidence to persuade consumers of the value or benefits of a product or service.

Emotional Appeals

Emotional appeals are persuasive techniques that aim to evoke an emotional response from the audience to influence their thoughts or actions.

Claim Letter

A formal letter sent to a company or individual, asserting one's right to request a correction, refund, or compensation for unsatisfactory goods or services.