Chi-Square Test for Homogeneity
A study was conducted to compare job satisfaction levels across three groups: A, B, and C. Independent random samples of 80 individuals were taken from each group, and the results are summarized in the table below.
| Group | Satisfied | Not Satisfied | Total |
|---|---|---|---|
| A | 60 | 20 | 80 |
| B | 55 | 25 | 80 |
| C | 50 | 30 | 80 |
| Total | 165 | 75 | 240 |
Based on these data, what are the approximate chi-square test statistic for homogeneity and the correct conclusion at a significance level of α = 0.05?
Approximately ; though high, it is not sufficient evidence to conclude a difference.
Approximately ; because the statistic is near 3, it indicates a significant difference among the groups.
Approximately ; this value exceeds the critical value, leading to rejection of the null hypothesis.
Approximately ; since this value is less than the critical value of approximately (for df = 2), there is insufficient evidence to reject the null hypothesis.
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