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Exercise 2.5. From a population consisting of 100 individuals with their weekly income (y and age ( x ), we have the following information: N N N N N E x₁ = 35,00, £ y₁ = 50,000, £ x = 85,0000, y = 90,000000 and x/y; = 3000000. i=1 i=1 i=1 i=1 i=1 If we consider an SRSWOR sample of n = 20 units, find the following:

Exercise 2.5. From a population consisting of 100 individuals with their weekly income (y and age ( x ), we have the following information: N N N N N E x₁ = 35,00, £ y₁ = 50,000, £ x = 85,0000, y = 90,000000 and x/y; = 3000000. i=1 i=1 i=1 i=1 i=1 If we consider an SRSWOR sample of n = 20 units, find the following:

A First Course in Probability (10th Edition)
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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2.5 last 2 parts Provide solution for d & e parts
Exercise 2.5. From a population consisting of 100 individuals with their weekly income (y) and age ( x ), we have the following information: N N N N £x; = 35,00, £ y₁ = 50,000, £ x² = 85,0000, y = 90,000000 and xy; = 3000000. N i=1 i=1 i=1 i=1 i=1 If we consider an SRSWOR sample of n = 20 units, find the following: (a) Compute the variance of the sample mean estimator. (b) Compute the mean square error of the ratio estimator. (c) Find the relative efficiency of the ratio estimator with respect to usual estimator. (d) Find the mean square error of the regression estimator. (e) Find the relative efficiency of the regression estimator with respect to both ratio and sample mean estimator. 2001
Transcribed Image Text:Exercise 2.5. From a population consisting of 100 individuals with their weekly income (y) and age ( x ), we have the following information: N N N N £x; = 35,00, £ y₁ = 50,000, £ x² = 85,0000, y = 90,000000 and xy; = 3000000. N i=1 i=1 i=1 i=1 i=1 If we consider an SRSWOR sample of n = 20 units, find the following: (a) Compute the variance of the sample mean estimator. (b) Compute the mean square error of the ratio estimator. (c) Find the relative efficiency of the ratio estimator with respect to usual estimator. (d) Find the mean square error of the regression estimator. (e) Find the relative efficiency of the regression estimator with respect to both ratio and sample mean estimator. 2001
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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