The data set cherry.csv, from Hand et al. (1994), contains measurements of diameter (inches), height (feet),...

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

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

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

"Diam","Height","Volume"8.3,70,10.38.6,65,10.38.8,63,10.210.5,72,16.410.7,81,18.810.8,83,19.711,66,15.611,75,18.211.1,80,22.611.2,75,19.911.3,79,24.211.4,76,2111.4,76,21.411.7,69,21.312,75,19.112.9,74,22.212.9,85,33.813.3,86,27.413.7,71,25.713.8,64,24.914,78,34.514.2,80,31.714.5,74,36.316,72,38.316.3,77,42.617.3,81,55.417.5,82,55.717.9,80,58.318,80,51.518,80,5120.6,87,77

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