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Performing Cchi Square Tests for Independence of Two Groups

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Are teacher evaluations independent of grades? After midterms, a random sample of 284 students was asked to evaluate teacher performance. The students were also asked to supply their midterm grade in the course being evaluated. In this study, only students with a grade of A, B, or C were included in the summary table. Use a 5% level of significance to test the claim that teacher evaluations are independent of midterm grades. (40 pts) Mid

Term Grade
Evaluation A B C Row Total
Positive 53 33 18 104
Neutral 25 46 29 100
Negative 14 22 44 80
Column Total 92 101 91 284

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The solution gives detailed steps on performing two chi square tests for testing independence of two groups.

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1. We need to calculate expected value for each cell, the result is

Evaluation A B C
Positive 92*104/284 101*104/284 91*104/284
Neutral 92*100/284 101*100/284 91*100/284
Negative 92*80/284 ...

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