Every 17 years, swarms of cicadas emerge from the ground in the eastern United S

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 so many cicadas that their dead bodies can serve as fertilizer.
In an experiment, a researcher added cicadas under some plants in a natural plot of bellflowers on the forest floor, leaving other plants undisturbed. In this experiment, cicada-supplemented bellflowers from a natural field population produced foliage with 12% greater nitrogen content relative to controls (P = 0.031).

A colleague who knows no statistics says that an increase of 12% isn't a lot - maybe it's just an accident due to natural variation among the plants. Explain in simple language how P = 0.031 answers this objection. The observed difference between cicada-supplemented bellflowers and controls accounts for all but 3.1% of the samples. Assuming no difference in nitrogen content, the probability that the increase in nitrogen content for cicada-supplemented bellflowers relative to controls is at least 12%, is less than 0.031. This small value is good evidence that the null Hypothesis is true. The maximum difference in nitrogen content between cicada-supplemented bellflowers and controls is 0.031. This small value is good evidence that the null Hypothesis is true. Assuming no difference in nitrogen content, the probability that the increase in nitrogen content for cicada-supplemented bellflowers relative to controls is at least 12%, is less than 0.031. This small value is good evidence that the null Hypothesis should be rejected. eBook

Explanation / Answer

Answer

Assuming no difference in nitrogen content, the probability that the increase in nitrogen content for cicada-supplemented bellflowers relative to controls is at least 12%, is less than 0.031. This small value is good evidence that the null Hypothesis should be rejected.

Explanation:

Assuming the null hypothesis is true, the p-value is the probability of a test statistic being as extreme or more extreme than the one that was found. Vlaues that are more extreme than the value of the test statistic are further from the mean than the test statistic.

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