APFIVE In a study comparing job satisfaction among three groups (A, B, and C), the table above displays the number of individuals who are satisfied or not satisfied, with 80 respondents per group. Assuming the overall proportion of satisfaction is the same across groups, perform a chi-square test for homogeneity. What is the approximate chi-square statistic and the conclusion at the 0.05 significance level? (Hint: Calculate the overall satisfaction proportion, then the expected counts for each group.)
| Group | Satisfied | Not Satisfied | Total |
|---|---|---|---|
| A | 60 | 20 | 80 |
| B | 55 | 25 | 80 |
| C | 50 | 30 | 80 |
| Total | 165 | 75 | 240 |
Approximately $$7.50$$; though high, it is not sufficient evidence to conclude a difference.
Approximately $$7.50$$; this value exceeds the critical value, leading to rejection of the null hypothesis.
Approximately $$2.91$$; because the statistic is near 3, it indicates a significant difference among the groups.
Approximately $$2.91$$; since this value is less than the critical value of approximately $$5.991$$ (for df = 2), there is insufficient evidence to reject the null hypothesis.
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