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

question 31

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.
$\begin{array}{c|ccc} & \text { Rock } & \text { Pop } & \text { Classical } \\\hline \mathbf{1 5 - 2 5} & 50 & 85 & 73 \\\mathbf{2 5 - 3 5} & 68 & 91 & 60 \\\text { 35-45 } & 90 & 74 & 77\end{array}$
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:

Hemocytoblasts

Hemocytoblasts are stem cells in the bone marrow that can develop into different types of blood cells, playing a crucial role in hematopoiesis.

Yellow Bone Marrow

Yellow bone marrow is a type of bone marrow primarily composed of fat cells, found in the long bones of adults and functions as storage for fats.

Formed Elements

Cellular components of blood, including red blood cells, white blood cells, and platelets.

White Blood Cell

Immune system cells responsible for defending the body against infectious diseases and foreign substances.