Question: The designer of a sample survey stratifies a population into two strata, H and L. H contains 100,000 people, and L contains 500,000. He decides to allocate 100 samples to stratum H and 200 to stratum L, taking a simple random sample in each stratum.
a. How should the designer estimate the population mean?
b. Suppose that the population standard deviation in stratum H is 20 and the standard deviation in stratum L is 10. What will be the standard error of his estimate?
c. Would it be better to allocate 200 samples to stratum H and 100 to stratum L?
d. Would it be better to use proportional allocation?