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(d) Use the known information on the estimate the true average age of the trees. Construct the 95% confidence inte true average age of all the trees in the stand based on the regression estimator. (e) Which interval estimate is better and why? appropriate? Why? umbst of

(d) Use the known information on the estimate the true average age of the trees. Construct the 95% confidence inte true average age of all the trees in the stand based on the regression estimator. (e) Which interval estimate is better and why? appropriate? Why? umbst of

Algebra: Structure And Method, Book 1
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 8P
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2.1 Last 3 parts Provide solution for d,e,f parts
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 3141
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 3141
Upulation: State wise total number marriages during 2001 and total population during 2002. (Source: Statistical Abstracts of the United States--2003). No. State Marriages 1 AL 2 AK 3 4 5 6 7 8 9 10 SHAREE 11 12 13 14 15 16 17 18 HERRERIES 19 20 21 22 23 24 25 AZ AR CA CO CT DE DC FL GA НІ ID IL IN IA KS KY LA ME MD ΜΑ MI MN MS 42.2 5.1 40.4 38.4 224.2 36.5 18.6 5.2 3.5 Population 151.3 51.3 24.0 14.7 89.8 34.1 20.9 20.3 36.6 37.5 11.4 37.5 40.0 66.5 33.0 18.7 Continued... 4487 644 5456 2710 35116 4507 3461 807 571 16713 8560 1245 1341 12601 6159 2937 2716 4093 4483 1294 5458 6428 10050 5020 2872 6 26 27 38 29 301 32 33 34 35 363738 39 40 41 2 3 44 45 46 48 49 50 51 No. 28 42 43 47 State Marriage Population MO MT NE NV NH NJ NM NY NC ND OH OK OR PA RI SC SD TN TX UT VT VA WA WV WI WY 42.2 6.4 13.6 146.1 10.6 54.1 13.9 145.5 61.1 4.1 82.3 16.6 26.0 71.4 7.4 36.8 6.7 77.7 194.9 23.2 6.0 63.4 42.2 14.2 34.9 5.0 5673 909 1729 2173 1275 8590 1855 19158 8320 634 11421 3494 3522 12335 1070 4107 761 5797 21780 2316 617 7294 6069 1802 5441 499
Transcribed Image Text:Upulation: State wise total number marriages during 2001 and total population during 2002. (Source: Statistical Abstracts of the United States--2003). No. State Marriages 1 AL 2 AK 3 4 5 6 7 8 9 10 SHAREE 11 12 13 14 15 16 17 18 HERRERIES 19 20 21 22 23 24 25 AZ AR CA CO CT DE DC FL GA НІ ID IL IN IA KS KY LA ME MD ΜΑ MI MN MS 42.2 5.1 40.4 38.4 224.2 36.5 18.6 5.2 3.5 Population 151.3 51.3 24.0 14.7 89.8 34.1 20.9 20.3 36.6 37.5 11.4 37.5 40.0 66.5 33.0 18.7 Continued... 4487 644 5456 2710 35116 4507 3461 807 571 16713 8560 1245 1341 12601 6159 2937 2716 4093 4483 1294 5458 6428 10050 5020 2872 6 26 27 38 29 301 32 33 34 35 363738 39 40 41 2 3 44 45 46 48 49 50 51 No. 28 42 43 47 State Marriage Population MO MT NE NV NH NJ NM NY NC ND OH OK OR PA RI SC SD TN TX UT VT VA WA WV WI WY 42.2 6.4 13.6 146.1 10.6 54.1 13.9 145.5 61.1 4.1 82.3 16.6 26.0 71.4 7.4 36.8 6.7 77.7 194.9 23.2 6.0 63.4 42.2 14.2 34.9 5.0 5673 909 1729 2173 1275 8590 1855 19158 8320 634 11421 3494 3522 12335 1070 4107 761 5797 21780 2316 617 7294 6069 1802 5441 499
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