STAT 410 96-2 Assignment 7 Solutions


  1. To estimate Total Government Transfer Payments to households in this population you use the estimate in Theorem 5.4 and estimate the standard error by using 5.12 and multiplying by N=1024.
  2. To estimate the Percentage of dwellings which are owner-occupied you use 5.52 with standard errors estimated by 5.53 or 5.58 with the variance estimated as in the sentence below 5.59.
  3. To estimate the Mean household income of owner occupied houses you use the methods of section 5A.14 with estimates given by 5A.70 and variance estimates using 5A.73.
  • Then find the optimal allocation of a sample of 36 units among these three strata for measuring total government transfer payments to households in this population. This uses 5.26 to get values of n_h. However you have to plug in estimates of the population standard deviations from your sample. Moreover you will not get integers as solutions in general. You should examine all of the possible sets of integers which add up to 36 and are within 1 of the values given by 5.26. The correct answer will depend on the sample you actually got in the first part of this homework set.
  • Does stratification and optimal allocation produce a big variance reduction over simple random sampling for estimating Total Government Transfer Payments to households in this population? To answer you must take the variance you will achieve with the integer allocation you decide on and compare it to the variance of the mean of a simple random sample of 36. That is, you compare 5.12 with 2.20. To use 2.20 you must either use the srs you drew for an earlier assignment or you must use 5.32 to compute an estimate of the overall population variance from the stratum sample variances and stratum means. (In 5.32 you would have to replace the population values by estimates.)
  • Bonus question Give an estimate and standard error for Average Employment Income of Employed persons in these households using the stratified sample. This bonus question was really rather similar to question 2 about owner occupied houses. You must get stratified random sampling estimates of both total employment income and of total number of employed persons. Then your estimate is a combined ratio estimate and you must use 6.51 with estimates plugged in to estimate the standard error.

    • The questions.