Question

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.

Answer 1

Answer:

The appropriate conclusion that answers the question stated in step one is:

• The weak correlation value does not support the idea that beavers benefit beetles.

• The largest number of beetle larvae was 55 and the largest number of stumps was 5.

Step-by-step explanation:

1) Select the appropriate practical question.

The appropriate practical question is:

"How does the number of beaver-caused stumps influences the number of beetle larvae clusters?"

2) Make a scatter plot.

The scatter plot is attached below.

From the scatter plot it can be seen that there exists a negative relationship between beaver stumps and beetle larvae. That is as the number of stumps increases the number of beetle larvae decreases.

The maximum number of beaver stumps found is 5.

3)

The best numerical summary for this problem are,

Correlation and regression line

The least square regression line for predicting the number of beetle larvae from the number of stumps is:

y = 31.594 - 2.8365 x.

Use the Excel function "=CORREL(array1,array2)" to compute the correlation.

The correlation value is, r = -0.219.

Both the correlation coefficient and regression line explains a negative relationship between the number of beetle larvae and the number of stumps.

Values amid 0 and 0.3 (0 and -0.3) implies a weak positive (negative) linear relationship amid the variables.

Thus, a correlation coefficient, r = -0.219, indicates a weak negative correlation between two variables.

Thus, the appropriate conclusion that answers the question stated in step one is:

• The weak correlation value does not support the idea that beavers benefit beetles.

• The largest number of beetle larvae was 55 and the largest number of stumps was 5.