SOLUTION: Application of the analysis of variance to a particular problem has resulted in the following ANOVA table. Complete the test at a significance level of 5%. ----------- -----------

Question 1177142: Application of the analysis of variance to a particular problem has resulted in the following ANOVA table. Complete the test at a significance level of 5%.
-----------------------------------------------------------
Source | DF | SS | MS | F |
-----------------------------------------------------------
Between | 2 | 457.1241 | 228.5621 | 52.74 |
within | 17 | 117.0165 | 4.3339 | |
-----------------------------------------------------------
Answer by CPhill(1959) (Show Source): You can put this solution on YOUR website!
**1. Hypotheses**
* **Null Hypothesis (H0):** The means of all the groups are equal.
* **Alternative Hypothesis (H1):** At least one group mean is different from the others.
**2. Significance Level**
* α = 0.05
**3. Degrees of Freedom**
* df(between) = 2 (from the ANOVA table)
* df(within) = 17 (from the ANOVA table)
**4. F-statistic**
* F = 52.74 (from the ANOVA table)
**5. Critical F-value**
* Using an F-distribution table or calculator with α = 0.05, df1 = 2, and df2 = 17, we find the critical F-value to be approximately 3.59.
**6. Decision**
* Since the calculated F-statistic (52.74) is greater than the critical F-value (3.59), we reject the null hypothesis.
**7. Conclusion**
At a 5% significance level, there is enough evidence to conclude that there is a statistically significant difference between the means of at least two of the groups.
**In simpler terms:** The ANOVA test shows that it's very unlikely that the observed differences between the group means are just due to random chance. Therefore, we can confidently say that there's a real difference in the average values of those groups.
**Further Analysis**
While ANOVA tells us that there's a difference, it doesn't tell us *which* groups are different. To find that out, you would need to perform post-hoc tests (like Tukey's HSD or Bonferroni correction) to compare specific pairs of group means.
RELATED QUESTIONS
An experiment was designed to study the performance of 4 different detergents for... (answered by ikleyn)

Assignment 2: ANOVA Summary Table A psychologist believes that the kind of feedback a... (answered by stanbon)

1. An analysis of variance (ANOVA) differs from t- test for independent means in that an (answered by stanbon)

I need assitance on this problem... Answer the following questions, inserting values... (answered by stanbon)

An experiment was designed to study the performance of 4 different detergents for... (answered by ikleyn)

This problem will introduce the learner into a technique called Analysis of Variance.... (answered by lamboak)

A psychologist believes that the kind of feedback a person receives about their work... (answered by stanbon)

18) An analysis of variance (ANOVA) tests population variance. A. True B.... (answered by drk)

18) An analysis of variance (ANOVA) tests population variance. A. True B.... (answered by stanbon)