Subjects statistics

Anova Conclusion 1E1464

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1. **State the problem:** We are analyzing an ANOVA test comparing the mean Burnout Scores among three groups of Serbian teachers based on Marital Status: Married, Divorced, and Single. 2. **Hypotheses:** - Null hypothesis ($H_0$): $\mu_1 = \mu_2 = \mu_3$ (all group means are equal) - Alternative hypothesis ($H_a$): At least one group mean differs 3. **ANOVA table values given:** - Degrees of Freedom (Between groups): $2.0$ - Degrees of Freedom (Within groups): $769.0$ - Sum of Squares Between (Adj SS): $22881.8$ - Sum of Squares Within (Residual): $233769.8$ - Mean Square Between (Adj MS): $\frac{22881.8}{2} = 11440.9$ - Mean Square Within (Adj MS): $304.3$ (calculated as $\frac{233769.8}{769}$) - F-Value: $\frac{11440.9}{304.3} \approx 37.61$ - P-Value: $0.000$ (very small) 4. **Interpretation:** Because the p-value is so small, we reject the null hypothesis and conclude that at least one marital status group has a different average Burnout Score. 5. **Best conclusion:** Option D: "Because the p-value is so small, we have overwhelming evidence that in the population of Serbian teachers at least one Marital Status group has an average Burnout Score that differs from the other average Burnout Scores." 6. **Pairwise comparisons:** The Tukey interval for Divorced-Married is (-0.921, 2.308), which includes zero, so no significant difference between Divorced and Married groups. **Final answer:** $$\boxed{\text{D}}$$