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STAT 4240 HW8

# STAT 4240 HW8 - Austin Wen SAT 4240 HW8 6.1 A forester is...

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Austin Wen SAT 4240 HW8 6.1 A forester is interested in estimating the total volume of trees in a timber sale. He records the volume for each tree in a simple random sample. In addition, he measures the basal area for each tree marked for sale. He then uses a ratio estimator of total volume. = , = , = , = n 12 N 250 x basal area y cubic foot volume for a tree = τx 75 square feet Use the data in the accompanying table to estimate τy , the total cubic-foot volume for those trees marked for sale, and place a bound on the error of estimation. Tree Basal ar Volume yi-r*xi 1 0.300000012 6 - 0.35821 2 0.5 9 - 1.59701 3 0.400000006 7 - 1.47761 tau-y 1589.55 2 4 0.899999976 19 - 0.07463 5 0.699999988 15 0.16417 9 tau-x 75 6 0.200000003 5 0.76119 4 Mu-x 0.3 7 0.600000024 12 - 0.71642 r 21.1940 3 8 0.5 9 - 1.59701 N 250 9 0.800000012 20 3.04477 6 n 12 10 0.400000006 9 0.52238 8 11 0.800000012 18 1.04477 6 V(tau-y) 8678.56 4 12 0.600000024 13 0.28358 2 B 186.317 6 average 0.558333339 11.8333 3 -1.3E- 15 Varianc e 1.75029 9 = = . . = . τy yxτx 11 8333 558333375 1589 552 =( ) - = . Vτy τx2 N nnN1μx2sr2 8678 564 = = . B 2Vτy 186 31 6.2 Use the data in 6.1 to compute an estimate of τy , using Ny . Place a bound on the error of estimation.

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STAT 4240 HW8 - Austin Wen SAT 4240 HW8 6.1 A forester is...

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