A corporation is interested in estimating the total earnings from sales of color television sets at the end of a three-month period. The total earnings figures are available for all districts within the corporation for the corresponding three-month period of the previous year. A simple random sample of 13 district offices is selected from the 123 offices within the corporation. a) Using a ratio estimator, estimate ty and place a bound on the error of estimation. Use the data in the accompanying table and take t = 128,200. b) Also estimate the mean earnings for office within the corporation and place a bound on the error of estimation.

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A corporation is interested in estimating the total earnings from sales of color television
sets at the end of a three-month period. The total earnings figures are available for all
districts within the corporation for the corresponding three-month period of the previous
year. A simple random sample of 13 district offices is selected from the 123 offices within
the corporation.
a) Using a ratio estimator, estimate ty and place a bound on the error of estimation.
Use the data in the accompanying table and take tx = 128,200.
b) Also estimate the mean earnings for office within the corporation and place a bound on
the error of estimation.
Three-month
data from
Three-month
Three-month
Three-month
data from
data from
data from
Office
previous year, X;
current year, y;
Office
previous year, X;
current year, y;
1
550
610
1200
1440
2
720
780
1350
1570
3
1500
1600
10
1750
2210
1020
1030
11
670
980
620
600
12
729
865
980
1050
13
1530
1710
7
928
977
Transcribed Image Text:A corporation is interested in estimating the total earnings from sales of color television sets at the end of a three-month period. The total earnings figures are available for all districts within the corporation for the corresponding three-month period of the previous year. A simple random sample of 13 district offices is selected from the 123 offices within the corporation. a) Using a ratio estimator, estimate ty and place a bound on the error of estimation. Use the data in the accompanying table and take tx = 128,200. b) Also estimate the mean earnings for office within the corporation and place a bound on the error of estimation. Three-month data from Three-month Three-month Three-month data from data from data from Office previous year, X; current year, y; Office previous year, X; current year, y; 1 550 610 1200 1440 2 720 780 1350 1570 3 1500 1600 10 1750 2210 1020 1030 11 670 980 620 600 12 729 865 980 1050 13 1530 1710 7 928 977
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