Conduct an analysis of variance and compute the F test statistic for the difference in the mean number of cavities between the three REGIONS

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Over 50 species of birds and mammals throughout Minnesota depend on cavities (or holes) in trees for countless purposes. These cavities are used for feeding, nesting, roosting, storing food, denning, escaping predators, providing shelter, raising young, and hibernating, and a single tree can contain dozens of suitable cavities. But does the number of these suitable cavities in cavity trees differ across the state, particularly with regard to elevation?

A random sample of 1106 cavity trees from three different REGIONS that represent a range in elevations across Minnesota was conducted and the number of CAVITIES (1-8) and the ELEVATION (in feet) at the base of the tree were recorded. 

Analysis of Variance

Investigate if the mean number of CAVITIES in cavity trees differs by REGION

1. Construct side-by-side boxplots of CAVITIES versus REGION and identify which REGION appears to have the highest mean number of CAVITIES per cavity tree

2.Conduct an analysis of variance and compute the F test statistic for the difference in the mean number of cavities between the three REGIONS

3.Explain if it was appropriate to use a theoretical F distribution to compute the p-value for the F test statistic above (Assumptions).  Do you have any concerns?

4.Interpret the results of the analysis of variance above, in context 

5. Explain if it is appropriate to generalize these results to all cavity trees throughout all REGIONS of Minnesota Linear Regression

Investigate if the number of CAVITIES in cavity trees is influenced by ELEVATION.  Can we predict the number of cavities (y) if we know the elevation (x)?

6.Construct a scatter plot of CAVITIES versus ELEVATION and describe the direction and strength of the relationship (Interpretation)

7. Compute the p-value for a test of the slope for the relationship above

8. Use linear regression to predict the number of cavities for a tree found at an ELEVATION of 1775 feet 

9. Explain if it is appropriate to trust the prediction above.

10. Explain if we can use these data to demonstrate that higher elevation causes trees to develop more cavities.

Putting It All Together

Use the information you've gathered to answer the original question.

11. Briefly describe if these data support the originally proposed question as to whether or the number of suitable cavities in cavity trees differs across the state, particularly with regard to elevation.

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