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a. Given the following Information obtained from three normally distributed populations, construct an ANOVA table. (Round Intermediate calculations to at least 4 decimal places. Round "SS" to 2 decimal places, "MS" to 4 decimal places, and "F' to 3 decimal places.) SSTR = 173.9; SSE = 2,616.8; C = 3; n₁ = n₂ = n3 = 6 ANOVA Source of Variation Between Groups Within Groups Total SS df MS F Do not reject He: we cannot conclude that some means differ. Reject He: we can conclude that some means differ. Do not reject He: we can conclude that some means differ. O Reject He: we cannot conclude that some means differ. p-value 0.617 b. At the 10% significance level, what is the conclusion to the ANOVA test of mean differences?

a. Given the following Information obtained from three normally distributed populations, construct an ANOVA table. (Round Intermediate calculations to at least 4 decimal places. Round "SS" to 2 decimal places, "MS" to 4 decimal places, and "F' to 3 decimal places.) SSTR = 173.9; SSE = 2,616.8; C = 3; n₁ = n₂ = n3 = 6 ANOVA Source of Variation Between Groups Within Groups Total SS df MS F Do not reject He: we cannot conclude that some means differ. Reject He: we can conclude that some means differ. Do not reject He: we can conclude that some means differ. O Reject He: we cannot conclude that some means differ. p-value 0.617 b. At the 10% significance level, what is the conclusion to the ANOVA test of mean differences?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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**a. Analysis of Variance (ANOVA) Table Construction** Given the following information obtained from three normally distributed populations, construct an ANOVA table. *Round intermediate calculations to at least 4 decimal places. Round "SS" to 2 decimal places, "MS" to 4 decimal places, and "F" to 3 decimal places.* - SSTR = 173.9 - SSE = 2,616.8 - c = 3 (Number of groups) - n₁ = n₂ = n₃ = 6 (Sample size per group) **ANOVA Table:** | Source of Variation | SS | df | MS | F | p-value | |---------------------|--------|-----|------|-------|---------| | Between Groups | | | | | 0.617 | | Within Groups | | | | | | | Total | | | | | | **b. Conclusion at the 10% Significance Level** What is the conclusion to the ANOVA test of mean differences? - ○ Do not reject H₀; we cannot conclude that some means differ. - ○ Reject H₀; we can conclude that some means differ. - ○ Do not reject H₀; we can conclude that some means differ. - ○ Reject H₀; we cannot conclude that some means differ. **Explanation:** The ANOVA table helps identify whether there are any statistically significant differences between the means of the groups. The p-value provided (0.617) suggests that at the 10% significance level, we fail to reject the null hypothesis (H₀). Therefore, we cannot conclude that there are differences among the group means at this significance level.
Transcribed Image Text:**a. Analysis of Variance (ANOVA) Table Construction** Given the following information obtained from three normally distributed populations, construct an ANOVA table. *Round intermediate calculations to at least 4 decimal places. Round "SS" to 2 decimal places, "MS" to 4 decimal places, and "F" to 3 decimal places.* - SSTR = 173.9 - SSE = 2,616.8 - c = 3 (Number of groups) - n₁ = n₂ = n₃ = 6 (Sample size per group) **ANOVA Table:** | Source of Variation | SS | df | MS | F | p-value | |---------------------|--------|-----|------|-------|---------| | Between Groups | | | | | 0.617 | | Within Groups | | | | | | | Total | | | | | | **b. Conclusion at the 10% Significance Level** What is the conclusion to the ANOVA test of mean differences? - ○ Do not reject H₀; we cannot conclude that some means differ. - ○ Reject H₀; we can conclude that some means differ. - ○ Do not reject H₀; we can conclude that some means differ. - ○ Reject H₀; we cannot conclude that some means differ. **Explanation:** The ANOVA table helps identify whether there are any statistically significant differences between the means of the groups. The p-value provided (0.617) suggests that at the 10% significance level, we fail to reject the null hypothesis (H₀). Therefore, we cannot conclude that there are differences among the group means at this significance level.
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