Question

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 dead cicadas under 39 randomly selected plants in a natural plot of American bellflowers 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 boxplots and summary statistics of seed mass (in milligrams) for 39 cicada plants and 33 undisturbed (control) plants:

a. Write a few sentences comparing the distributions of seed mass for the two groups of plants.

b. Based on the graphical displays, which distribution likely has the larger mean? Justify your answer.

c. Explain the purpose of the random assignment in this study.

d. Name one benefit and one drawback of only using American bellflowers in the study

Short answer

a. Cicada plants are skewed, with the same centre and a wider dispersion.

b. The graphical representations larger Cicada plant group is most likely responsible for the dispersion.

c. In experiments, researchers modify an independent variable while controlling for other variables to see how it affects a dependent variable.

d. 39 Plants in a natural plot of American bellflowers on the forest floor were chosen at random.

Step-by-step solution

Part (a) Step 1: Given Information

The given graph is

Part (a) Step 2: According to the question

The cicada plant distribution appears to be sloped to the right, whereas the control plant distribution appears to be tilted to the left.

For both distributions, the median would be the same, but the mean for Cicada Plants would be substantially higher.

The box plot is narrower than the cicada plants, which have a wider spread.

Because neither distribution appears to feature outliers, there are no 'x's in the box plots.

Part (b) Step 1: Given information

The given table is and the graph is

Part (b) Step 2: Calculation

In component (a), it was determined that the control plants group comprised more biassed. The mean in the control plants distribution is too much influenced by the left-skewed, and because a left-skewed distribution contains abnormally small values, these small values will decrease the mean, resulting in the control plants group's mean being lower than the cicada plants group's mean.

Part (c) Step 1: Given Information

The given table and graph is

Part (c) Step 2: According to question

The random group assignments ensure that the two groups are as similar as possible before to the experiment, as well as that the findings of the experiment are due to the treatments.

Part (d) Step 1: Given Information

The given table and the given graph is

Part (d) Step 2: According to the given question

Because all flowers will be of the same type, the variations between the treatment and control groups will be minimal.

One disadvantage is that you will only have data for one type of flower, so the experiment results will not be applicable to other flowers.