AP2.24. Every $17$years, swarms of cicadas emerge from the ground in the eastern United States, live for about six weeks, and then die. (There are several different “broods,” so we experience cicada eruptions more often than every $17$years.) There are so many cicadas that their dead bodies can serve as fertilizer and increase plant growth. In a study, a researcher added $10$cicadas under $39$randomly selected plants in a natural plot of American bell flowers on the forest floor, leaving other plants undisturbed. One of the response variables measured was the size of seeds produced by the plants. Here are the box plots and summary statistics of seed mass (in milligrams) for $39$cicada plants and $33$undisturbed (control) plants:

Variable: n Minimum Q1 Median Q3 Maximum

Cicada plants: 39 0.17 0.22 0.25 0.28 0.35
Control plants: 33 0.14 0.19 0.25 0.26 0.29
(a) Is this an observational study or an experiment? Explain.
(b) Based on the graphical displays, which distribution has
the larger mean? Justify your answer.
(c) Do the data support the idea that dead cicadas can
serve as fertilizer? Give graphical and numerical evidence
to support your conclusion.

In a study, a researcher added $10$cicadas under $39$ randomly selected plants in a natural plot of American bell flowers on the forest floor, leaving other plants undisturbed.

A study in which an experimenter or researcher handles the situation is understood as an experimental study.
The experimental study has full control over, which proceeding into the plot of the land.
Hence, the given study is an experimental study.

The box plots and summary statistics of seed mass (in milligrams) for $39$cicada plants and $33$ undisturbed (control) plants.

The mean is strongly influenced by skewness, the mean is more influenced by the left-skewness in the control plants distribution.

Since a left-skewed distribution containing the smaller value thus it would reduce the mean .

So, it could be concluded that the mean of the cicada plants is larger.

To conclude the data is supporting the belief that dead cicadas could be served as fertilizer.

From the given figure and numerical summaries of , it is known that the the median for cicada and control groups are same, that is $0.25$.

The data is not supporting the belief that dead cicadas could be served as fertilizer. Because, the median for both the groups is same.