. National income from manufacturing industries is to be estimated for 1999 from a sample of 6 of the 19 industry categories that reported figures early or that year. Incomes from all 19 industries are known for 1990 and the total is $674 billion. From the summary data provided, we wish to estimate the total national income from manufacturing in 1999, with bound on the error. All figures are in billions of constant dollars. Industry 1990 (x,) 1999 (y,)

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 91E
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. National income from manufacturing industries is to be estimated for
1999 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 1990 and the total is
$674 billion. From the summary data provided, we wish to estimate the total
national income from manufacturing in 1999, with bound on the error. All figures
are in billions of constant dollars.
Industry
1990 (x,)
1999 (y,)
Lumber products
Electronic products
Motor vehicles products
Food products
Textile products
Chemical products
21
26
63
91
35
47
60
70
16
17
50
76
Ex, = 245, y, = 327,
Σx-11991, ΣΥ-2131,
2x,y, = 16196
d, = (y, -x,), d; =1730, Ed, = 82
,Find a ratio estimator of the 1999 total income, and place a bound on
the error of estimation.
'I Find a regression estimator of the 1999 total income, and place a
bound on the error of estimation.
, Find a difference estimator of the 1999 total income, and place a bound
on the error of estimation.
Which of the three methods would you recommend as the most
efficient estimator? Why?
Transcribed Image Text:. National income from manufacturing industries is to be estimated for 1999 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 1990 and the total is $674 billion. From the summary data provided, we wish to estimate the total national income from manufacturing in 1999, with bound on the error. All figures are in billions of constant dollars. Industry 1990 (x,) 1999 (y,) Lumber products Electronic products Motor vehicles products Food products Textile products Chemical products 21 26 63 91 35 47 60 70 16 17 50 76 Ex, = 245, y, = 327, Σx-11991, ΣΥ-2131, 2x,y, = 16196 d, = (y, -x,), d; =1730, Ed, = 82 ,Find a ratio estimator of the 1999 total income, and place a bound on the error of estimation. 'I Find a regression estimator of the 1999 total income, and place a bound on the error of estimation. , Find a difference estimator of the 1999 total income, and place a bound on the error of estimation. Which of the three methods would you recommend as the most efficient estimator? Why?
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