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Use A χ2\chi ^ { 2 } Test to Test the Claim That in the Given Contingency

question 47

Essay

Use a χ2\chi ^ { 2 } test to test the claim that in the given contingency table, the row variable and the column variable are independent. 160 students who were majoring in either math or English were asked a test question, and the researcher recorded whether they answered the question correctly. The sample results are given below. At the 0.10 significance level, test the claim that response and major are independent.
 Correct  Incorrect  Math 2753 English 4337\begin{array} { r | c c } & \text { Correct } & \text { Incorrect } \\\hline \text { Math } & 27 & 53 \\\text { English } & 43 & 37\end{array}

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Definitions:

Nucleus

a membrane-bound organelle found in eukaryotic cells that contains most of the cell's genetic material.

Yellowstone National Park

A national park located primarily in Wyoming, extending into Montana and Idaho, known for its wildlife and geothermal features such as geysers and hot springs.

Prokaryotic

Referring to organisms, such as bacteria and archaea, that lack a nucleus and other membrane-bound organelles.

Archaea

A category of unicellular microorganisms that are genetically different from both bacteria and eukaryotes, frequently located in harsh environments.

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