Assignment 3:  STRATIFICATION
Due: February 27, 1996

     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
 
1. Stratify Lockhart City into 5 strata.  Using ADDGEN generate a
stratified random sample of size 200 from Lockhart City with proportional 
allocation.  Find the responses using the program SURVEY.  Estimate, using
sample mean estimates in each stratum, the average price a household in
Lockhart City is willing to pay for cable service and the average number of
TV's per household in Lockhart City.  Don't forget to include standard
errors everywhere.

2. Use ratio estimates within each stratum and repeat problem 1.

3. We have now estimated the same quantities with two designs and
two estimators (4 possible combinations):
   (i) Simple random sampling and sample mean estimates
   (ii) Simple random sampling and ratio estimates
   (iii) Stratified random sampling and sample mean estimates
   (iv) Stratified random sampling and ratio estimaes
Using the results and samples from assignments 1 and 2, estimate the
relative efficiencies of (ii), (iii), and (iv) relative to (i) for
estimating the average price a household is willing to pay for cable
TV and the mean number of TV's.
   Discuss, in terms of the SURVEY program assumptions, the efficiency
of stratification relative to simple random sampling in estimating the
average price and the number of TV's.  How do these results compare with
simple random sampling and the ratio estimate.
   Suppose we can use the same information to make strata or in a ratio
estimate.  When do you think the supplementary information should be used
for stratification and when should it be used for ratio estimation.