1. Farmers in a river valley would like to estimate the average number of bushels of
grain per plot of land. Each plot is 1/4 of an acre of land. The data set bushels.txt
contains the population of values of bushels of grain for all N = 1400 plots of land.
The observations are sorted by distance from the river.
(a) Take a systematic sample of size n = 50, with starting the 12th observation.
Report the estimated average number of bushels of grain per plot of land, and
compute a bound for the error of estimation.
(b) Take a repeated systematic sample, with 5 samples of size ten. The ve starting
points are 2, 13, 26, 47, and 83. Report the estimated average number of bushels
of grain per plot of land, and compute a bound for the error of estimation.
2. A manufacturing company buys glass optical bers to make cables. They currently
have a shipment of 250 boxes of bers, with 12 bers per box. If the bers have
too many aws, they can not be used. The company wants to determine the average
number of aws per cable in the shipment. They take a random sample of 10 boxes,
and count the numbers of aws in the 12 bers in each box. These are shown in the
table below. Estimate the average number of aws per cable in the shipment, and
compute a bound on the error of estimation.
Box # # aws Box # # aws
9 32 67 27
12 28 72 25
43 18 109 24
44 27 184 17
56 30 215 28
3. (similar to exercise 8.17.) To emphasize safety, a taxicab company wants to estimate
the proportion of unsafe tires on their 175 cabs. (Ignore spare tires.) Selecting a
simple random sample of tires is impractical, so cluster sampling is used with each
cab as a cluster. A random sample of 15 cabs gives the following numbers of unsafe
tires per cab:
2;0;1;2;4;0;2;2;0;0;1;0;3;1;1
Estimate the proportion of unsafe tires being used on the company’s cabs and place
a bound on the error of estimation.
4. Exercise 8.10 in the text, using only the rst 10 sampled wards (and pretending a
simple random sample of only 10 wards was taken).