A study of the effects of acid rain on trees in the Hopkins Forest shows that of 100 trees sampled, 25 of them exhibited some sort of damage from acid rain. Test at the 5% level of significance to determine if this rate is higher than the 15% quoted in a recent Environmetrics article on the average proportion of damaged trees in the Northeast.

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Mathematics

9 May, 18:24

A study of the effects of acid rain on trees in the Hopkins Forest shows that of 100 trees sampled, 25 of them exhibited some sort of damage from acid rain. Test at the 5% level of significance to determine if this rate is higher than the 15% quoted in a recent Environmetrics article on the average proportion of damaged trees in the Northeast.

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Sarahi Pratt · Answer 1

H0: p = 0.15; HA: p > 0.15. ˆ p = 0.25; z = 2.80; Pvalue = 0.0026. The 95% confidence interval is (0.165, 0.335).

We must assume the trees sampled are a simple random sample of the trees in the area and are less than 10% of all trees in the forest. The results are generalizable only to the Hopkins forest (or nearby if the forest is viewed as representative). Because the P-value is so low, we reject H0. There is strong evidence that the proportion of trees damaged by acid rain in the Hopkins forest is higher than the 15% average for the Northeast.