Arnold gathers samples of Zodfish from each of the four oceans, the Atlantic, the Pacific, the Indian and the Arctic ...

  

Arnold gathers samples of Zodfish from each of the four oceans, the Atlantic, the Pacific, the Indian and the Arctic. He measures the lengths of the fish in his samples.

1. If he is conducting an ANOVA test as described in Section 12.2 what would be his null hypothesis?

2. What two concerns might you immediately have about the requirements that need to be met for the test? You can assume that different unrelated researchers did the gathering in each ocean and that they took random samples.

3. If he ultimately decides for the alternative hypothesis what exactly would that mean about the fish? He finds that SS Treatment is 46.604 and that SS Error is 81.509. They used 12 Pacific, 10 Atlantic, 9 Indian and 8 Arctic Zodfish in the study.

4. What is SS Total?

5. What is MS Treatment?

6. What is MS Error?

7. What is the F score?

8. They find a p-value of .0011. What does this mean and what conclusion would they draw about the fish?

9. What does this mean about the relationship between the “variance between samples” and the “variance within samples”?

10. Is it possible that one of the types (say Arctic) is significantly different in size than the other 3 and that could be causing the results we are seeing?