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: Diameter Age Tree No. 1 2 3 4 5 6 7 8 9 10 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 5.7 8.0 10.3 12.0 9.2 8.5 7.0 10.7 9.3 8.2 Age 61 80 147 122 106 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. of the trees to apply regression estimator to timate of the
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: Diameter Age Tree No. 1 2 3 4 5 6 7 8 9 10 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 5.7 8.0 10.3 12.0 9.2 8.5 7.0 10.7 9.3 8.2 Age 61 80 147 122 106 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. of the trees to apply regression estimator to timate of the
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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2.1
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
S
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
5.7
8.0
10.3
12.0
9.2
8.5
7.0
10.7
9.3
8.2
Age
Lerca
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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