This preview shows pages 1–3. Sign up to view the full content.
ST 310 Final Exam
Due no later than December 15, 2007 (in
electronic or paper form).
Do 4 problems of your choice.
1.
Adaptive cluster sampling.
Consider the population given in the attached
spreadsheet. A unit (square) “satisfies the condition” if a 1 is present, oth
erwise not. The sampling frame is a
25
×
25
grid; a simple random sample
of
n
=20
of these squares produces the sample coordinates given (i.e., we
sample the corresponding grid squares). For various reasons, it is not eco
nomically feasible in this application to use the sample “geometry” given in
the text; instead, one of the two patterns given in the spreadsheet must be
used. Carry out the adaptive cluster sampling procedure until it terminates,
for
each
of the two patterns (separately). Is either “better” in this case? Would
there be any way to choose one of the patterns
a priori
?
2. A large grocerystore chain wishes to audit its price scanners. A simple ran
dom sample of
n
=50
orders (receipts) is selected and carefully audited, with
results (receipts) given in the attached spreadsheet: “recorded” means the re
ceipt recorded by the computer based on the scanner data (from the cashier’s
scans of the items); ”actual” means the actual receipt based on handchecking
every item against its actual (official) price. The longrun average scanner
based receipt (from database records) is $62.11. Use two different strategies
to estimate the true,
actual
average receipt, and give associated standard er
rors. Comment on the relative precision of these two estimates.
3. In a forest study to determine quantity of a certain kind of timber, the for
est region is subdivided into polygons according to natural and artificial map
boundaries. A random sample of polygons is then selected by PPSWR (prob
ability proportional to size
with
replacement) sampling, the quantity of har
vestable timber in the polygon is measured, and the total timber quantity in
1
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document the forest is estimated. Data from a sample of 10 such polygons, along with
their sizes (expressed as a proportion of the population = probability of se
lection on one draw) is given in the attached spreadsheet. Compute the first
order inclusion probabilities
π
i
for the sample units, and hence compute the
HorvitzThompson estimate of the population total
τ
.(
Hint
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 01/28/2012 for the course STATISTICS 3010 taught by Professor Ooz during the Spring '11 term at Cornell University (Engineering School).
 Spring '11
 Ooz

Click to edit the document details