t to estimate the average age of trees in a stand. Determining some because one needs to count the tree rings on a core e tree. In general, though, the older the tree, the larger and diameter is easy to measure. The foresters measure of all 1132 trees and find that the population mean equals ien randomly select 120 trees for age measurement. meter, x Age, y Tree No. Diameter, x Age, y 12.0 125 11 5.7 61 11.4 119 12 8.0 80 7.9 83 13 10.3 114 9.0 85 14 12.0 147 10.5 99 15 9.2 122 7.9 117 16 8.5 106 7.3 69 17 7.0 82 10.2 133 18 10.7 88 11.7 154 19 9.3 97 11.3 168 20 8.2 99 scatterplot of y vs. I. e the populationm mean age of trees in the stand using imation and give an approximate standard error for your (b) using regression estimation. our estimates on your graph. How do they compare?

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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 form 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. They then randomly select 120 trees for age measurement.
Tree No. Diameter, x Age, y Tree No. Diameter, x Age, y
1
12.0
125
11
5.7
61
11.4
119
12
8.0
80
3
7.9
83
13
10.3
114
4
9.0
85
14
12.0
147
5
10.5
99
15
9.2
122
7.9
117
16
8.5
106
7
7.3
69
17
7.0
82
10.2
133
18
10.7
88
9.
11.7
154
19
9.3
97
10
11.3
168
20
8.2
99
(a) Draw a scatterplot of y vs. r.
(b) Estimate the population mean age of trees in the stand using
ratio estimation and give an approximate standard error for your
estimate.
(c) Repeat (b) using regression estimation.
(d) Label your estimates on your graph. How do they compare?
Transcribed Image Text: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 form 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. They then randomly select 120 trees for age measurement. Tree No. Diameter, x Age, y Tree No. Diameter, x Age, y 1 12.0 125 11 5.7 61 11.4 119 12 8.0 80 3 7.9 83 13 10.3 114 4 9.0 85 14 12.0 147 5 10.5 99 15 9.2 122 7.9 117 16 8.5 106 7 7.3 69 17 7.0 82 10.2 133 18 10.7 88 9. 11.7 154 19 9.3 97 10 11.3 168 20 8.2 99 (a) Draw a scatterplot of y vs. r. (b) Estimate the population mean age of trees in the stand using ratio estimation and give an approximate standard error for your estimate. (c) Repeat (b) using regression estimation. (d) Label your estimates on your graph. How do they compare?
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