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Full solution: Section II: Free Response Show all your work. Indicate clearly the

Chapter 7, Problem AP2.24

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QUESTION:

Section II: Free Response Show all your work. Indicate clearly the methods you use, because you will be graded on the correctness of your methods as well as on the accuracy and completeness of your results and explanations. 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: 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) Write a few sentences comparing the distributions of seed mass for the two groups of plants. (b) Based on the graphical displays, which distribution 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.

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QUESTION:

Section II: Free Response Show all your work. Indicate clearly the methods you use, because you will be graded on the correctness of your methods as well as on the accuracy and completeness of your results and explanations. 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: 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) Write a few sentences comparing the distributions of seed mass for the two groups of plants. (b) Based on the graphical displays, which distribution 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.

ANSWER:

Step 1 of 4

(a)

Distribution: The distribution of the cicada plants is slightly skewed to the right (as the box in the boxplot is slightly to the left), while the distribution of the control plants is skewed to the left (as the box of the boxplot and the vertical line in the box of the boxplot (median) lies to the right).

Centre: The median is the same for both distributions, while the mean is slightly higher for Cicada plants.

Spread: The Cicada plants have a slightly larger spread, since the boxplot is wider.

Outliers: Neither distribution appears to contain outliers as there are no "  's in the boxplots.

 

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