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. They then randomly select 20 trees for age measurement. Tree No. Diameter, x Age, y Tree No. Diameter, x Age, y
1 12.0 125 11 5.7 61
2 11.4 119 12 8.0 80
3 7.9 83 13 10.3 114
4 9.0 85 14 12.0 147
5 10.5 99 15 9.2 122
6 7.9 117 16 8.5 106
7 7.3 69 17 7.0 82
8 10.2 133 18 10.7 88
9 11.7 154 19 9.3 97
10 11.3 168 20 8.2 99
a. Draw a scatter plot of y vs. x.
b. Estimate the population mean age of trees in the stand using ratio estimation and give an approximate standard error for your estimate.
c. Repeat (b) using regression estimation.
d. Label your estimates on your graph. How do they compare?