Exercise 2.1. Foresters want to estimate the average age of trees in a stand. Determining age is cumbersome because one needs to count the tree rings on a core taken from the tree. In general, though, the older the tree, the larger the diameter, and diameter is easy to measure. The foresters measure the diameter of all 1132 trees and find that the population mean equals 10.3 inches. They then randomly select 20 trees for age measurements: Age Tree No. 1 2 3 4 56789 10 Diameter 12.0 11.4 7.9 9.0 10.5 7.9 7.3 10.2 11.7 11.3 125 119 83 85 99 117 69 133 154 168 Tree Diameter No. 11 12 13 14 15 16 67 17 18 19 20 5.7 8.0 10.3 12.0 9.2 8.5 7.0 10.7 9.3 8.2 Age 3815281858 61 80 147 122 106 97 99 (a) Plot the data, and guess the sign of correlation. (b) Estimate the population mean age of trees in the stand by using the usual estimator of the population mean and give an appropriate standard error for your estimate. Construct the 95% confidence interval estimate of the true average age of all trees in the stand. (c) Use the known information on the diameters of the trees to apply ratio estimator to estimate the true average age of the trees. Construct the 95% confidence interval estimate of the true average age of all the trees in the stand based on the ratio estimator. (d) Use the known information on the diameters of the trees to apply regression estimator to estimate the true average age of the trees. Construct the 95% confidence interval estimate of the true average age of all the trees in the stand based on the regression estimator. (e) Which interval estimate is better and why? (f) Is applying product estimator appropriate? Why? ation, number of