Assignment 3:  STRATIFICATION
Due: October 9, 1997

     The objectives of stratification are to control the error in 
estimation by ensuring that samples are representative of the population; 
to ease administration of a survey by partitioning the task; and to 
provide separate and independant estimates in different parts of the 
population.
     The theory indicates that we will be successful in the first 
objective if our strata differ from each other but have units with little 
variation within each stratum.  This observation leads to the idea of 
using knowledge of our population to group similar units together to for 
strata.  In our case we are rather fortunate to have extensive knowledge 
of the characteristics of Stephens County in the tables and district map 
of Assignment 1.

PROBLEMS

0. Append to this assignment your simulation study for the efficient
stratification of Lockhart City.
 
1. Stratify the rural areas (districts 1-43) of Stephens County into 5
strata.

We consider three designs for these areas:
   i. simple random sample, size 200
   ii. stratified random sample, size 200 allocated proportionally
   iii. stratified random sample, size 200 using Neyman allocation
The variable of interest is the average price a household is willing to
pay for cable TV.

2. Using a process similar to the simulation exercise done in class, take
10 samples from each of designs i and ii.  What is the design effect of
design ii.

3. Compare the design effect for design ii in the rural areas with the
design effect for the efficient stratification in Lockhart City.  How are
the effects of stratification in the two areas related to the SURVEY
program assumptions.  Pay special attention to the differences between
the rural and urban areas of the county.

4. Neyman allocation requires knowledge of the variance of the study
variable (the price a household is willing to pay for cable TV) within
each stratum.  We will use, instead, the assessed value of the household's
living quarters as a surrogate variable to allocate the sample.  The
Stephen's County tax assessor will provide this assessed value for a
charge of $1 per household.  (This is much less than the billing charges
for the rest of the SURVEY program.)  This is done by providing the
SURVEY program a list of addresses with negative district numbers; thus
an address of -38, 112 will provide the assessment for household 112 in
district 38.
   We have a $50 budget for sample design.  Estimate the variance of
household assessment in each of the five strata of problem 1 by using a
sample of 10 households per stratum.  Calculate a Neyman allocation.

5. Take 10 samples from design iii and calculate its design effect.  Is
Neyman allocation a substantial improvement over proportional allocation
in this case?  Under what circumstances can we expect Neyman allocation
to be markedly better than proportional allocation?

6. Problem 3.30 in Sarndal et al.

7. Problem 3.39 in Sarndal et al.