# ANOVA: Is the omnibus null hypothesis rejected or retained?

Scenario:

Five individual groups

G1 = mean 11.6, variance 9.6, n 10

G2 = mean 13.6, variance 9.6 n 10

G3 = mean 16.6, variance 11.6. n 10

G4 = mean 15.6. variance 13.6, n 10

G5 = mean 18.2, variance 10.4. n 10

Source of variation Sum of Squares Degrees of Freedom Mean Square F

Treatments 266.08 4 66.52 6.07

within 493.20 45 10.96

TOTAL 759.28 49

1) Is the omnibus null hypothesis rejected or retained? - explain & give critical value used.

2) What is the size of the pooled variance, the individual variance, what assumption is being made in the pooled variance? Is it justifiable given the data?

3) What is the SEM between group 2 & group 5?

4) What is the value of t? Is the result significant?

https://brainmass.com/statistics/analysis-of-variance/anova-is-the-omnibus-null-hypothesis-rejected-or-retained-42063

#### Solution Preview

The solution is provided in the attached Word document.

#1) Is the omnibus null hypothesis rejected or retained? - explain & give critical value used.

If we use 5% significance level, then by looking up the website ...

#### Solution Summary

This complete solution provides calculations, answers and explanation. Formulas and calculations for (2) through (4) are formatted and included in an attached Word document. 330 words.