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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 Cubicfoot
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 basalarea 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 3month period of the previous year.
A simple random sample of 13 district ofﬁces is selected from the 123 ofﬁces within the
corporation. Using a ratioestimator, 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. Threemonth  Threewmonth Threemonth 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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 Spring '11
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