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# hw8 - The forester decides to take a simple random...

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Unformatted text preview: The forester decides to take a simple random sampie'of n = 12 from the N ~_— 250 trees marked for sale. Let x denote basal area and y the cubic—foot volume for a tree. The total basal area for all 250 trees, rx , is 75 square feet. Use the data in the acCornpany/ing table to estimate 7:), , the total cubic—foot volume for those trees marked for sale, and place . a bound on the error of estimation. ' Tree ‘ Cubic—foot ‘ sampled basal area, J: Volume, 3: Tree Cubic-foot sampled basal area, x Volume, 3: 6.2 Use the data in Exercise 6.1 to compute an estimate of r}. , using N 33'. Place a bound on the error of estimation. Compare your results with those obtained in Exercise 6.1. Why is the estimate N 37, which does not use any basal-area data, much larger than the ratio estimate? (Look at M audit“. Soeculate about the reason for this discrepancy.) 6.3 A consumer survey was conducted to determine the ratio of the money spent on food to the total income per year for households in a small community. A simple random sample of 14 households was selected from 150 in the community. Sample data are given in the accompanying table. Estimate R, the population ratio, and place a bound on the error of estimation. Which points have greatest inﬂuence on the estimate? Total Amount spent Total Amount spent Household income, I on food, y Household income, 2: ' on food, y 6.4 A corporation is interested in estimating the total earnings from sales of color television sets at the end of a 3wmonth period. The total earnings figures are available for all dis- tricts Within the corporation for the conesgonding 3-month period of the previous year. A simple random sample of 13 district ofﬁces is selected from the 123 ofﬁces within the corporation. Using a ratio-estimator, estimate ry and place a bound on the error of esti- mation. Use the data in the accompanying tabie and take 13; m 128, 200. Three-month - Threewmonth Three-month Threemonth ‘ data from data from data from data from Ofﬁce previous year, xi current year, y, Ofﬁce previous year, x1- current year, y‘- 1 550 610 s 1200 1440 2 720 730 9 1350 1570 3 1500 1600 10 1750 2210 4 1020 1030 11 670 900 5 620 600 12 729 865 6 980 1050 13 1530 1710 7 928 977 6.5 Use the data in Exercise 6.4 to estimate the mean earnings for ofﬁces within the corpo— ration. Place a bound on the error of estimation. 6.6 An investigator has a colony of N m 763 rats that have been subjected to a standard drug. The average Iength of time to thread a maze oorreetty under inﬂuence of the standard drug was found to be or = 17.2 seconds. The investigator now would like to subject a random sample of 11 rats to a aew drug. Estimate the average time required to thread the maze while trader the inﬂuence of the new drug. (The data are sheets in the accompanying table.) Place a bound on the error of estimation. [Hint Empioyiag a ratio estimator for [Ly is reasonabie if we assume that the rats will react to the new drug in much the same way as they reacted to the standard drug] What is the most unusual feature of the scatter plot for these data? ...
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