Assignment 2: Ratio sampling
Due date: February 15, 1996

SURVEY PROGRAM ASSUMPTIONS:  To make as realistic a simulation as 
possible, certain assumptions have been programmed into SURVEY.  These 
assumptions should be used in efficient design. Some of the assumptions 
of SURVEY are quite obvious.  For example each (occupied) address has at 
least one adult and anyone who does not have a TV will not be willing to 
subscribe to cable service.  Some of the other SURVEY program assumptions 
are:
 
1. All other factors being equal, a household with a higher income will 
tend to have a more expensive house.
2. Assessed valuation is a reasonably accurate estimate of house price.
3. All other factors being equal, a household with a higher income will 
tend to be willing to pay more for cable service.
4. All other factors being equal, a household with a higher income will 
tend to own more television sets.  This tendency is much weaker than that 
of assumption 3 because of the low cost and longevity of most TV sets.  
In addition cable service involves a monthly (as opposed to one time) 
payment for a service much of which can be obtained at low cost by using 
an antenna.
5. Due to zoning and development practices, urban neighborhoods tend to 
be more homogeneous than rural neighborhoods.
6. Within a neighborhood, larger families will tend to have larger houses 
and these houses will tend to have higher assessed values.
7. Larger families tend to watch more TV (not per person, but in total), 
have more TV's, and be more willing to subscribe to cable TV.
8. All other factors being equal, a family's willingness to subscribe to 
cable TV decreases as the other entertainment options available to it 
increase.  These options decrease the further one moves from the 
population concentrations in Stephens County.

PROBLEMS

1. Using the same sample that you used in Assignment 1 and a ratio
estimator constructed from a suitable auxiliary variable, find
a. The average price a household in Lockhart City is willing to pay 
for cable TV service.
b. The average number of TV's per household.
   Given two estimates ybar1 and ybar2 of YBAR derived from the same
sample, the relative precision of ybar1 to ybar2 is Var(ybar2)/Var(ybar1).  
Equivalently, if sample sizes n1 and n2 are required to achieve the same 
standard error using ybar1 and ybar2, respectively, the relative 
precision is n2/n1.  Estimate from your sample the relative precision of 
of the ratio estimate (in assignment 2) to the sample mean estimate (in 
assigment 1) for both the average number of TV's in a household in Lockhart
City and the average price a household is willing to pay for cable TV.
   IMPORTANT: How are your results related to the survey program assumptions.

2. Do you think bias is a problem for the ratio estimates calculated here?
Why or why not.

3. Please do problem 3, page 54, using both the Hansen-Hurwitz and the
Horvitz-Thompson estimators.