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) the distribution of the control plants is skewed to the left.

(b) the mean of the control plants group will be lower than the mean of the cicada plants group.

(c)the results of the experiment are due to the treatments.

(d)Advantage: differences between control group and treatment are small

Disadvantage: result of experiment cannot be generalized to other flowers.

Step-by-step solution

Part (a) Step 1: Given Information

Part (a) Step 2: Simplification

By seeing the distribution, it is observed that the distribution of the cicada plants is slightly skewed to the right, where the distribution of the control plants is skewed to the left.

Centre: The median would be the same for both of the distributions, where the mean is slightly higher for Cicada Plants.

Spread: the cicada plants have a large spread, where the box plot is wider.

Outlines: neither distributions appears to contain outliers as there are no " x 's in the box plots.

Part (b) Step 1: Given Information

Part (b) Step 2: Simplification

In the previous part (a), it is concluded that the control plants group contained more skewed. Since the mean is strongly influenced by skewed the mean is too more influenced by the left-skewed in the control plants distribution, since a left-skewed distribution contains unusually small values, these small values will decrease the mean and therefore the mean of the control plants group will be lower than the mean of the cicada plants group.

Part (c) Step 1: Given Information

Part (c) Step 2: Simplification

The random assignments to the groups ensure that the two groups are as similar as possible prior to the experiment and then it also knows that the results of the experiment are due to the treatments.

Part (d) Step 1: Given Information

Part (d) Step 2: Simplification

A benefit is that the differences between the treatment and control group will be very small, because all flowers will be of the same type.

A drawback is that you will only have data for one type of flower and therefore the results of the experiment could not be generalized to other flowers.