Question

The data set cherry.csv, from Hand et al. (1994), contains measurements of diameter (inches), height (feet), and timber volume (cubic feet) for a sample of 31 black cherry trees. Diameter and height of trees are easily measured, but volume is more difficult to measure.

(i) Suppose that these trees are a SRS from a forest of N = 2967 trees and that the sum of the diameters for all trees in the forest is tx = 41835 inches. Use ratio estimation to estimate the total volume for all trees in the forest. Give a 95% CI.

(ii) Estimate the average timber volume and construct the 95% CI.

"Diam","Height","Volume"
8.3,70,10.3
8.6,65,10.3
8.8,63,10.2
10.5,72,16.4
10.7,81,18.8
10.8,83,19.7
11,66,15.6
11,75,18.2
11.1,80,22.6
11.2,75,19.9
11.3,79,24.2
11.4,76,21
11.4,76,21.4
11.7,69,21.3
12,75,19.1
12.9,74,22.2
12.9,85,33.8
13.3,86,27.4
13.7,71,25.7
13.8,64,24.9
14,78,34.5
14.2,80,31.7
14.5,74,36.3
16,72,38.3
16.3,77,42.6
17.3,81,55.4
17.5,82,55.7
17.9,80,58.3
18,80,51.5
18,80,51
20.6,87,77

Answer 1