A) Using one or more of the following variables: age, sex, race, or marstat, divide the population into strata. Explain how you decided upon your stratification variable and how you chose the number of strata to use. (Note: It is NOT FAIR to use the values of inctot in the population to choose your strata! However, you may draw a pilot sample of size 200 using an SRS to aid you in constructing your strata.)
B) Using the strata you constructed, draw a stratified random sample using proportional allocation. Explain how you calculated the sample size to be drawn from each stratum.
C) Using the stratified sample you selected with proportional allocation, estimate the total income for the population, along with a 95% CI.
D) Using the pilot sample of size 200 to estimate thewithin-stratum variances, use optimal allocation to determinesample stratum sizes. Use the same value of n as in part B. Draw astratified ramdom sample from the population along with a 95%CI.
E) Under what conditions can optimal allocation be expected to perform much better than proportional allocation? Do these conditions exist for this population? Comment on the relative performance you observed between these two allocations.
F) Overall, do you think your stratification was worth while for sampling from this population? if you were to start over on the stratification, what would you do differently?