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
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
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter9: Systems Of Linear Equations
Section9.6: Wind And Water Current Problems
Problem 10P
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Question
Q2.1
Please provide justified answer asap for all parts
Transcribed Image Text: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
5
6
7
8
9
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
No.
11
12
13
14
15
16
17
18
19
20
Diameter
8:27
5.7
8.0
10.3
12.0
9.2
8.5
7.0
10.7
9.3
8.2
Age
61
80
114
147
122
106
82
88
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?
population, number of
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