National income from manufacturing industries is to be estimated for 1989 from a sample of 6 of the 19 industry categories that reported figures early for that year. Incomes from all 19 industries are known for 1980 and the total is $674 billion. From the data provided, estimate the total national income from manufacturing in 1989, with a bound on the error. All figures are in billions of constant (1982) dollars. Industry 1980 1989 Lumber and wood products Electrie and electronie 21 63 26 91 equipment Motor vehicles and 91 47 equipment Food and kindred products Textile mill products 60 70 70 70 Chemicals and allied 50 50 products a. Find a ratio estimator of the 1989 total income, and place a bound on the eror of estimation. Interpret the results. b. Find a regression estimator of the 1989 total income, and place a bound on the error of estimation. Interpret the results. c. Find a difference estimator of the 1989 total income, and place a bound on the error of estimation. d. Which of the three methods, parts (a), (b), or (c), is most appropriate in this case? Why?

National income from manufacturing industries is to be estimated for 1989 from a sample of 6 of the 19 industry categories that reported figures early for that year. Incomes from all 19 industries are known for 1980 and the total is $674 billion. From the data provided, estimate the total national income from manufacturing in 1989, with a bound on the error. All figures are in billions of constant (1982) dollars. Industry 1980 1989 Lumber and wood products Electrie and electronie 21 63 26 91 equipment Motor vehicles and 91 47 equipment Food and kindred products Textile mill products 60 70 70 70 Chemicals and allied 50 50 products a. Find a ratio estimator of the 1989 total income, and place a bound on the eror of estimation. Interpret the results. b. Find a regression estimator of the 1989 total income, and place a bound on the error of estimation. Interpret the results. c. Find a difference estimator of the 1989 total income, and place a bound on the error of estimation. d. Which of the three methods, parts (a), (b), or (c), is most appropriate in this case? Why?

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MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

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Concept explainers

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.

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Question

National income from manufacturing industries is to be estimated for 1989 from a sample
of 6 of the 19 industry categories that reported figures early for that year. Incomes from all 19
industries are known for 1980 and the total is $674 billion. From the data provided, estimate the
total national income from manufacturing in 1989, with a bound on the error. All figures are in
billions of constant (1982) dollars.
Industry
1980
1989
Lumber and wood products
Electrie and electronie
21
63
26
91
equipment
Motor vehicles and
91
47
equipment
Food and kindred products
Textile mill products
70
70
60
70
Chemicals and allied
50
50
products
a. Find a ratio estimator of the 1989 total income, and place a bound on the error of
estimation. Interpret the results.
b. Find a regression estimator of the 1989 total income, and place a bound on the error of
estimation. Interpret the results.
c. Find a difference estimator of the 1989 total income, and place a bound on the error of
estimation.
d. Which of the three methods, parts (a), (b), or (c), is most appropriate in this case? Why?

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