SOLUTION: A Two-Way ANOVA Summary Table is shown below. Source SS d.f. MS F Factor A 9.42 2 4.71 2.77 Factor B 15.10 2 7.55 4.44 Interaction A x B 10.34 4 2.58 1.52 Within (error) 45

Question 1193824: A Two-Way ANOVA Summary Table is shown below.
Source
SS d.f. MS F
Factor A 9.42 2 4.71 2.77
Factor B 15.10 2 7.55 4.44
Interaction A x B 10.34 4 2.58 1.52
Within (error) 45.90 27 1.7
Total 80.75 35
The critical value for the F test using = 0.05, d.f.N. = 2, and d.f.D = 27 is 3.35. Then,
A. only the null hypothesis concerning Factor A should be rejected.
B.only the null hypothesis concerning Factor B should be rejected.
C. only the null hypothesis concerning Factor A and the Interaction (AxB) effect should be rejected.
D. all of the null hypotheses should be accepted.
Answer by parmen(42) (Show Source): You can put this solution on YOUR website!
**1. Understand the Null Hypotheses**
* **Factor A:** There is no significant main effect of Factor A on the dependent variable.
* **Factor B:** There is no significant main effect of Factor B on the dependent variable.
* **Interaction (A x B):** There is no significant interaction effect between Factor A and Factor B on the dependent variable.
**2. Compare F-statistics to Critical Value**
* **Factor A:** F = 2.77
* **Factor B:** F = 4.44
* **Interaction (A x B):** F = 1.52
* **Critical Value:** F = 3.35
* **Decision Rule:** Reject the null hypothesis if the calculated F-statistic is greater than the critical value.
**3. Make Decisions**
* **Factor A:** 2.77 < 3.35. **Do not reject the null hypothesis.**
* **Factor B:** 4.44 > 3.35. **Reject the null hypothesis.**
* **Interaction (A x B):** 1.52 < 3.35. **Do not reject the null hypothesis.**
**Conclusion:**
* **Only the null hypothesis concerning Factor B should be rejected.**
**Therefore, the correct answer is B.**
This means there is sufficient evidence to suggest that Factor B has a significant main effect on the dependent variable, while the main effect of Factor A and the interaction effect between A and B are not statistically significant at the 0.05 level.

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