Using the Following Data, Test for the Independence of the Variables.(Note

question 34

Essay

Using the following data, test for the independence of the variables.(Note: Assume a significance level of 0.05 wherever necessary.)
$$\begin{array} { | c | c | c | } \hline \text { Respondent } & \text { Gender } & \text { Breakfast Preference } \\\hline 1 & \text { Female } & \text { Fruits } \\\hline 2 & \text { Male } & \text { Cereal } \\\hline 3 & \text { Male } & \text { Milk } \\\hline 4 & \text { Female } & \text { Fruits } \\\hline 5 & \text { Female } & \text { Milk } \\\hline 6 & \text { Male } & \text { Cereal } \\\hline 7 & \text { Male } & \text { Milk } \\\hline 8 & \text { Male } & \text { Milk } \\\hline 9 & \text { Female } & \text { Fruits } \\\hline 10 & \text { Male } & \text { Fruits } \\\hline 11 & \text { Male } & \text { Cereal } \\\hline 12 & \text { Female } & \text { Cereal } \\\hline 13 & \text { Female } & \text { Milk } \\\hline 14 & \text { Male } & \text { Fruits } \\\hline 15 & \text { Female } & \text { Fruits } \\\hline\end{array}$$

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Definitions:

Progressive Reformers

Activists and thinkers in the late 19th and early 20th centuries who advocated for wide-ranging changes in society, including government and industry reforms, to address social injustices.

State Intervention

Governmental involvement in economic, social, or personal affairs, usually with the goal of achieving a specific outcome or rectifying a perceived issue.

Political Reforms

Actions taken to improve governance, enhance democratic processes, reduce corruption, and ensure the fair representation of citizens in political institutions.

Progressives

Reformers in the late 19th and early 20th centuries who sought to address social problems caused by industrialization and urbanization, advocating for social justice and government involvement.