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Exercise 2.4. A private organization PQR was interested in estimating the average amount of real estate farm loans (in $000) during 1997in the United States. The organization collected information from 15 states, the real estate (y) and non-real estate (x) farm loans, included in an SRSWOR sample taken from a list of 50 states and observed the following results: n i=1 n = 18867.089, ₁ = 12525.246, i=1 n n n [x² = 48780336.98, y = 18001501.38 and Exy₁ = 2659171056. i=1 i=1 i=1 The average amount of non-real estate farm loans is $878.16 (in $000) for the year 1997 is known. (a)Obtain a ratio estimate for the average amount of the real estate farm loans (in $000) during 1997. Develop an estimator of the mean squared error of the ratio estimator and hence deduce the 95% confidence interval.

Exercise 2.4. A private organization PQR was interested in estimating the average amount of real estate farm loans (in $000) during 1997in the United States. The organization collected information from 15 states, the real estate (y) and non-real estate (x) farm loans, included in an SRSWOR sample taken from a list of 50 states and observed the following results: n i=1 n = 18867.089, ₁ = 12525.246, i=1 n n n [x² = 48780336.98, y = 18001501.38 and Exy₁ = 2659171056. i=1 i=1 i=1 The average amount of non-real estate farm loans is $878.16 (in $000) for the year 1997 is known. (a)Obtain a ratio estimate for the average amount of the real estate farm loans (in $000) during 1997. Develop an estimator of the mean squared error of the ratio estimator and hence deduce the 95% confidence interval.

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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2.4
Exercise 2.4. A private organization PQR was interested in estimating the average amount of real estate farm loans (in $000) during 1997in the United States. The organization collected information from 15 states, the real estate (y) and non-real estate (x) farm loans, included in an SRSWOR sample taken from a list of 50 states and observed the following results: 12 11 n Σ x = 18867.089, Σ = 12525.246, x² = 48780336.98, y = 18001501.38 and i=1 i=1 i=1 11 Σ xixi = 2659171056. The average amount of non-real estate farm loans is $878.16 (in $000) for the year 1997 is known. 2 (a)Obtain a ratio estimate for the average amount of the real estate farm loans (in S000) during 1997. Develop an estimator of the mean squared error of the ratio estimator and hence deduce the 95% confidence interval.
Transcribed Image Text:Exercise 2.4. A private organization PQR was interested in estimating the average amount of real estate farm loans (in $000) during 1997in the United States. The organization collected information from 15 states, the real estate (y) and non-real estate (x) farm loans, included in an SRSWOR sample taken from a list of 50 states and observed the following results: 12 11 n Σ x = 18867.089, Σ = 12525.246, x² = 48780336.98, y = 18001501.38 and i=1 i=1 i=1 11 Σ xixi = 2659171056. The average amount of non-real estate farm loans is $878.16 (in $000) for the year 1997 is known. 2 (a)Obtain a ratio estimate for the average amount of the real estate farm loans (in S000) during 1997. Develop an estimator of the mean squared error of the ratio estimator and hence deduce the 95% confidence interval.
(b) Obtain a regression estimate for the average amount of the real estate farm loans during 1997. Develop an estimator of the mean squared error of the regression esti- hence deduce the 95% confidence interval. (c) Comment on the interval estimates. la with their weekly inco
Transcribed Image Text:(b) Obtain a regression estimate for the average amount of the real estate farm loans during 1997. Develop an estimator of the mean squared error of the regression esti- hence deduce the 95% confidence interval. (c) Comment on the interval estimates. la with their weekly inco
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