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Chapter 7: Q. 24 (page 465)

AP2.24. Every 17years, swarms of cicadas emerge from the ground in the eastern United States, live for about six weeks, and then die. (There are several different 鈥渂roods,鈥� so we experience cicada eruptions more often than every 17years.) There are so many cicadas that their dead bodies can serve as fertilizer and increase plant growth. In a study, a researcher added 10cicadas under 39randomly 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 39cicada plants and 33undisturbed (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.

Short Answer

Expert verified

(a) The given study is an experimental study.

(b) The given data concluded that the mean of the cicada plants is larger.

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

Step by step solution

01

Part (a) Step 1: Given information 

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

02

Part (a) Step 2: Explanation

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.

03

Part (b) Step 1: Given information 

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

04

Part (b) Step 2: Explanation 

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.

05

Part (c) Step 1: Given information 

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

06

Part (c) Step 2: Explanation 

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.

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Most popular questions from this chapter

The Harvard College Alcohol Study finds that 67%of college students support efforts to "crack down on underage drinking." The study took a random sample of almost 15,000students, so the population proportion who support a crackdown is close to p=0.67The administration of a local college surveys an SRS of 100students and finds that 62support a crackdown on underage drinking.

(a) Suppose that the proportion of all students attending this college who support a crackdown is 67%, the same as the national proportion. What is the probability that the proportion in an SRS of 100students is as small as or smaller than the result of the administration鈥檚 sample? Follow the four-step process.

(b) A writer in the college鈥檚 student paper says that 鈥渟upport for a crackdown is lower at our school than nationally.鈥� Write a short letter to the editor explaining why the survey does not support this conclusion

The histogram above left shows the intervals (in minutes) between eruptions of the Old Faithful geyser for all 222recorded eruptions during a particular month. For this population, the median is 75minutes. We used Fathom software to take 500SRSs of size 10from the population. The 500values of the sample median are displayed in the histogram above right. The mean of the 500sample median values is 73.5.

Suppose we had taken samples of size 20instead of size 10. Would the spread of the sampling distribution be larger, smaller, or about the same? Justify your answer

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