STAT 410 96-2 Assignment 11 Solutions

1. For the Stat Village data consider the simple random sample of 6 blocks I used on the midterm. Draw a subsample of size 4 from each block and use the resulting data to estimate and give estimated standard errors for
   
   
   1. Total Government Transfer Payments to households in this population. Evaluate ybarbar and 10.15. You have N=128, n=6, M=8, m=4. The values of both s_1 and s_2 depend on the samples you got.
   
   
   
   2. Average Employment Income of Employed persons in these households. If y is household income and x is number of employed adults we want ybarbar /xbarbar and then need a standard error. As with ratio estimates write
      ybarbar/xbarbar - R = ubarbar/xbarbar
      where u is the variable y-Rx. Then replace xbarbar with Xbarbar and compute the estimated standard error of ubarbar and divide by xbarbar. The estimated standard error of ubarbar depends on s_1^2 and s_2^2 for u and these have R in them -- you have to replace those values by ybarbar/xbarbar.
   
   
   
   3. Percentage of dwellings which are owner-occupied. See 10.24.
   
   
   
2. Question 10.1 Here n=80, N=400, m=5, M=50 and the variance estimate is 362*(1-80/400)/80+ (80/400)*(1-5/50)*805/(5*80) = 5.25 which is to be compared to 362/80=4.53.

The questions.