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ANOVA: Is the omnibus null hypothesis rejected or retained?

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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?

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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.

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#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 provided by:
Changping Wang, MA
Education
  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
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