Pitcher plants of the genus Nepenthes are typically carnivorous, obtaining a gre
ID: 3205231 • Letter: P
Question
Pitcher plants of the genus Nepenthes are typically carnivorous, obtaining a great deal of their nutrition from insects that become trapped in the pitcher, die, and decay. N. lowii, a pitcher plant from Borneo, produces a second type of pitcher that attracts tree shrews (Tupaia montana), which provide nutrients by defacating into the pitcher while they feed on a substance secreted by the plant. Based on measurements of 20 plants, Clarke et al. (2009) calculated 95% confidence interval for the mean fraction of total leaf nitrogen in the plant species derived from tree shrews: 0.57 < u < 1.0.
a. Does this result imply that individual plants receive 57% and 100% of their leaf nitrogen from tree shrews? Explain.
b. Is the confidence interval meant to bracket the sample mean or the population mean? Explain.
c. Identify two values for the mean shrew fraction of total leaf nitrogen that the analysis suggests are among the most plausible.
d. Identify two values for the mean shrew fraction of total leaf nitrogen that the analysis suggests are less plausible. Explain.
Explanation / Answer
a. Does this result imply that individual plants receive 57% and 100% of their leaf nitrogen from tree shrews? Explain.
Answer:
This result does not imply that individual plants receive 57% and 100% of their leaf nitrogen from tree shrews because the confidence interval represent the interval values for the population mean and not any value for individual observation.
b. Is the confidence interval meant to bracket the sample mean or the population mean? Explain.
Answer:
The confidence interval is meant to bracket the population mean. We use the sample mean to find out the confidence interval for the population mean. We always infer population mean by using the sample mean.
c. Identify two values for the mean shrew fraction of total leaf nitrogen that the analysis suggests are among the most plausible.
Answer:
The values at the middle of interval or near to point estimates are most plausible. For the given confidence interval, the point estimate would be (0.57 + 1)/2 = 1.57/2 = 0.785. So, values near to 0.785, e.g. 0.78 and 0.79 would be most plausible.
d. Identify two values for the mean shrew fraction of total leaf nitrogen that the analysis suggests are less plausible. Explain.
Answer:
The extreme values of the confidence interval are less plausible. For example, the values 0.57 and 1.0 are less plausible because these are the lower limit and upper limit for the given confidence interval.