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Use the Following Set of Observed Frequencies to Test the Independence

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Use the following set of observed frequencies to test the independence of the two variables.Variable one has values of 'A' and 'B'; variable two has values of 'C', 'D', and 'E'. CDEA12108B202426\begin{array} { | l | l | l | l | } \hline & \mathrm { C } & \mathrm { D } & \mathrm { E } \\\hline \mathrm { A } & 12 & 10 & 8 \\\hline \mathrm { B } & 20 & 24 & 26 \\\hline\end{array} Using α\alpha = 0.05, the critical chi-square value is _______.


Definitions:

Indirect Material Cost

Indirect material costs are costs related to materials that do not directly become part of the final product but are necessary for the manufacturing process.

Direct Material Cost

The expense of basic materials and parts directly utilized in manufacturing a product.

Period Cost

Costs that are not directly tied to the production process and are expensed in the period in which they are incurred, such as selling, general, and administrative expenses.

Opportunity Cost

The cost of forgone alternatives when one option is chosen over another.

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