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28. Acid rain. A study of the effects of acid rain on
Chapter 20, Problem 28(choose chapter or problem)
28. Acid rain. A study of the effects of acid rain on trees in the Hopkins Forest shows that 25 of 100 trees sampled exhibited some sort of damage from acid rain. This rate seemed to be higher than the 15% quoted in a recent Environmetrics article on the average proportion of damaged trees in the Northeast. Does the sample suggest that trees in the Hopkins Forest are more susceptible than trees from the rest of the region? Comment, and write up your own conclusions based on an appropriate confidence interval as well as a hypothesis test. Include any assumptions you made about the data.
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QUESTION:
28. Acid rain. A study of the effects of acid rain on trees in the Hopkins Forest shows that 25 of 100 trees sampled exhibited some sort of damage from acid rain. This rate seemed to be higher than the 15% quoted in a recent Environmetrics article on the average proportion of damaged trees in the Northeast. Does the sample suggest that trees in the Hopkins Forest are more susceptible than trees from the rest of the region? Comment, and write up your own conclusions based on an appropriate confidence interval as well as a hypothesis test. Include any assumptions you made about the data.
ANSWER:Based on the sample, it appears that trees in the Hopkins Forest may be more susceptible to damage from acid rain than trees in the rest of the Northeast.
To test whether this is statistically significant, we should set up a hypothesis test and calculate a confidence interval. We will assume that the sample is randomly drawn and that the Hopkins Forest is being sampled from the same population as the rest of the Northeast, and that the 15% damage rate for the Northeast is an accurate estimate of the true proportion of damaged trees in the popu