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.

a. Find a ratio estimator of the 1989 total income, and place a bound on the error of estimation.

b. Find a regression estimator of the 1989 total income, and place a bound on the error of estimation.

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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Industry 1980 1989 Lumber and wood products 21 26 Electric and electronic 63 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 SOURCE: U.S. Bureau of the Census, Statistical Abstract of the United States, 1993–94, Washington, D.C., 199. Industry 1980 1989 Lumber and wood products 21 26 Electric and electronic 63 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 SOURCE: U.S. Bureau of the Census, Statistical Abstract of the United States, 1993–94, Washington, D.C., 199.