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Unformatted text preview: Exercises Tara/(.240 m 9 we H/W/m ( . ii 3 ’M‘m/S ‘ '
7 1 Suppose that a home mortgage company has N mortgages numbered serialiy 1n the order
' that they were granted over a period of 20 years. There is a generally increasmg trend 1n the unpaid baiances because of the rising cost of housing over the years. The compapiy
wishes to estimate the total amount of unpaid baiances. Should you employ a systema c , or a simple random sampie? Why? 1
7.2 A corporation lists employees by income brackets {alphabetically within bpackets) 1:13: highest to lowest. If the objective is to estimate the average income per emp opee, sts are systematic, stratiﬁed, or simple random sampling be used? Assume the. cos equivaient for the three methods and that you can stratify on income brackets. Discuss
the advantages and disadvantages of the three methods. 7.3 A retail store with four departments has charge accounts arranged by department, with
pastdue accounts at the top of each dcpartmentai list. Suppose the departments average
around ten accounts each, with approximately 40% past due. On a given day the ac— counts might appear as shown in the accompanying table (with account numbers 1
through 40). The store wishes to estimate the proportion of pastwdue accounts by sys—
tematic sampling. Depamuent Account numbers iwll 12—20 2148 . 29—40
Delinquent accounts 1, 2, 3, 4 12, 13, 14 21, 22, 23, 24, 25 29, 30, 31, 32 a. List ail possibie l—in—lO systematic sampies and compute the exact variance of the
sample proportion. (Note that there are ten possible values, n'ot all distinct; for the
sample proportion, each with probability i/ to of occurring) b. List ali possible 1in—5 systematic samples and compute the exact variance of the
sample proportion. c. Compare the result in part (a) with an approximate variance obtained in a simple ran~
dorn sample of size n = 4 from this population. Simiiarly, compare the result in part (b) with that obtained from a simple random sample with n a 8. What general
conclusions can you make? 7.4 The management of a particuiar company is interested in estimating the proportion of
employees favoring'a new investment policy. A 1in~ 10 systematic sample is obtained
from employees leaving the building at the end of a particular workday. Use the data in the accompanying table to estimate 13, the proportion in favor of the new policy and place
a bound on the error of estimation. Assume N m 2000. ' "“hnm—WMWM Employee sampled Response
W
3 1
13
23 1
i 993 l
200
E: y, m 132
i=1 ’7 .5 For the situation outlined in Exercise 7.4, determine the sample size reguired to estimate
p to within 0.01 unit. What type of systematic sample should he run? 7 .6 The quality control section of an industrial ﬁrm uses systematic sampling to estimate the '
average amount of ﬁll in iZ—ounce cans comiag off an assembly line. The data in 1the
accompanying table rearesent a l~in~50 systematic sample of the production in 1 day. 138*
timate y, and place a bound on the error of estimation. Assume N t 1800. W Amount ofﬁll (in ounces) W
12.00 11.97 12.01 12.03 12.01 11.80
11.91 11.98 12.03 11.98 12.00 11.83
11.87 12.01 11.98 11.87 11.90 11.88
12.05 11.87 11.91 ' 11.93 11.94 11.89
11.75 11.93 11.95 11.97 11.93 12.05
11.85 11.98 11.87 12.05 12.02 12.04 W 7.7 Use the data in Exercise 7 .6 to determine the sample size required to estimate it to within
0.03 unit. ’7 .8 Soil experts want to determine the amount of exchangeable calcium (in parts per miilion)
in a plot of ground. 80 that the sampling scheme is simpliﬁed, a rectangular grid is su
perimposed on the ﬁeld. Soil samples are taken at each point of intersection 0:1 the grid
(see the diagram). Use the following data to determine the average amount of exchange—
ablecalcium on the plot of ground. Piace a bound on the error of estimation. inﬁll5 2 y; m 90,320 ppm
s z 250 ppm ...
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 Spring '11
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