Ecologists sometimes find rather strange relationships in our environment. For example, do beavers benefit beetles? Researchers laid out 23 circular plots, each four meters in diameter, in an area where beavers were cutting down cotton wood trees. In each plot, they counted the number of stumps from trees cut by beavers and the number of clusters of beetle larvae. Ecologists think that the new sprouts from stumps are more tender than other cottonwood growth, so that beetles prefer them. If so, more stumps should produce more beetle larvae. Here are the data.
Stumps Beetle larvae
12 2
31 1
12 3
24 3
36 4
42 3
42 1
10 2
26 5
55 1
18 3
41 2
Stumps Beetle larvae
25 1
7 2
20 2
16 1
17 1
7 4
53 1
9 2
13 1
14 4
52 2
Analyze these data to see if they support the "beavers benefit beetles" idea. Follow the four-step process in reporting your work.
State: Select the appropriate practical question.
What is the relationship between beaver stumps and beetle larvae?What is the highest value of beetle larvae? Do more beavers lead to more beetles?What is the maximum number of beaver stumps found?
Formulate: Select from the statistical operations listed below ones that are appropriate for this problem. (Select all that apply.)
histogramregression linescatterplotcorrelationfive-number summarymean and standard deviation
Solve: Choose the best numerical summary for this problem.
five-number summaryx and s correlation and regression linerange
Calculate your chosen numerical summary. (Enter "0" if the selection is not part of your chosen summary.)
x s
Minimum Maximum
r Intercept Slope
Min Q1 M Q3 Max
Conclude: Select the appropriate conclusion that answers the question stated in step one.
The strong negative association does not support the idea that beavers benefit beetles.
The weak correlation value does not support the idea that beavers benefit beetles.
The strong positive association supports the idea that beavers benefit beetles.
The largest number of beetle larvae was 55 and the largest number of stumps was 5.