# Thread: Optimal allocation problem

1. ## Optimal allocation problem

A population consists of two strata, H and L, of sizes 100,000 and 500,000 and standard deviations 20 and 12, respectively. A stratified sample of size 100 is to be taken.
a. Find the optimal allocation for estimating the population mean.
b. Find the optimal allocation for estimating the difference of the means of the strata,
mu_H - mu_L

Thank you!

2. ## Re: Optimal allocation problem

Originally Posted by ohm713
A population consists of two strata, H and L, of sizes 100,000 and 500,000 and standard deviations 20 and 12, respectively. A stratified sample of size 100 is to be taken.
a. Find the optimal allocation for estimating the population mean.
b. Find the optimal allocation for estimating the difference of the means of the strata,
mu_H - mu_L

Thank you!
Let N denote the sample size from strata H and 100-N the sample size from strata L.

a. Now what is your estimator for the population mean? What is its variance?

b. What is the variance of your estimate of the difference of strata means?

(you find N which minimises these variances)

CB