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Butterfly Occurrences
Display 10.19 summarizes results from the regression of the log of the number of butterfly species observed on the log of the size of the reserve and the number of days of observations, from 16 reserves in the Amazon River Basin.
(a) What is the two-sided p-value for the test of whether size of reserve has any effect on number of species, after accounting for the days of observation? What is the one-sided p-value if the alternative is that size has a positive effect? Does this imply that there is no evidence that the median number of species is related to reserve size? The researchers tended to spend more days searching for butterflies in the larger reserves. How might this affect the interpretation of the results?
(b) What is a two-sided p-value for the test that the coefficient of lsize is 1? (This is simply a computational exercise; there is no obvious reason to conduct this test with these data.)
(c) What is a 95% confidence interval for the coefficient of lsize?
(d) What proportion of the variation in log number of species remains unexplained by log size and days of observations?
Construct a 95 percent confidence interval for the true mean.
What assumption about the population distribution is needed in order to conduct the t test in (a)?
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