1. A wood trader would like to estimate the total weight (in gram) of woods in the forest that he is going to acquire. Suppose the forest has N = 1000 trees, let z; be the diameter (in cm) of the trees and y; be the weight (in gram) of the trees in a simple random sample of n = 10 trees. The sum of the square of the diameters of all trees in the forest is T2 = 28,000,000. Using the information below, answer the following questions: i 1 12.00 2 35.00 3 37.00 4 40.00 5 44.00 6 54.00 7 57.00 8 58.00 9 66.00 10 73.00 Yi 300.00 2500.00 2700.00 3200.00 3900.00 5800.00 6500.00 6700.00 8700.00 10700.00 a.) Estimate the total weights of the tree in the forest using ratio estimation and place a bound on the error of estimation. b.) Estimate the total weights of the tree in the forest using regression estimation and place a bound on the error of estimation. c.) Do you think the regression estimates would be better than the one obtained from the ratio estimation? Without detailed calculation, provide a valid reason why your claim holds.

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1. A wood trader would like to estimate the total weight (in gram) of woods in the
forest that he is going to acquire. Suppose the forest has N = 1000 trees, let z; be the
diameter (in cm) of the trees and y; be the weight (in gram) of the trees in a simple
random sample of n = 10 trees. The sum of the square of the diameters of all trees
in the forest is T2 = 28,000,000. Using the information below, answer the following
questions:
i
Xi
1
12.00
2
35.00
3
37.00
4
40.00
5
44.00
6 54.00
7
57.00
8
58.00
9
66.00
10 73.00
Yi
300.00
2500.00
2700.00
3200.00
3900.00
5800.00
6500.00
6700.00
8700.00
10700.00
a.) Estimate the total weights of the tree in the forest using ratio estimation and place
a bound on the error of estimation.
b.) Estimate the total weights of the tree in the forest using regression estimation and
place a bound on the error of estimation.
c.) Do you think the regression estimates would be better than the one obtained from
the ratio estimation? Without detailed calculation, provide a valid reason why
your claim holds. "'
Transcribed Image Text:1. A wood trader would like to estimate the total weight (in gram) of woods in the forest that he is going to acquire. Suppose the forest has N = 1000 trees, let z; be the diameter (in cm) of the trees and y; be the weight (in gram) of the trees in a simple random sample of n = 10 trees. The sum of the square of the diameters of all trees in the forest is T2 = 28,000,000. Using the information below, answer the following questions: i Xi 1 12.00 2 35.00 3 37.00 4 40.00 5 44.00 6 54.00 7 57.00 8 58.00 9 66.00 10 73.00 Yi 300.00 2500.00 2700.00 3200.00 3900.00 5800.00 6500.00 6700.00 8700.00 10700.00 a.) Estimate the total weights of the tree in the forest using ratio estimation and place a bound on the error of estimation. b.) Estimate the total weights of the tree in the forest using regression estimation and place a bound on the error of estimation. c.) Do you think the regression estimates would be better than the one obtained from the ratio estimation? Without detailed calculation, provide a valid reason why your claim holds. "'
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