A researcher has a population split into two strata: Stratum A (N_A = 4000, μ_A = 50, σ_A = 10) and Stratum B (N_B = 6000, μ_B = 60, σ_B = 15). A stratified sample of n = 500 with optimal allocation (Neyman) is drawn. What is the expected standard error of the stratified sample mean?

$SE(\overline{y}_{st}) = \sqrt{\sum_h W_h^2 \frac{\sigma_h^2}{n_h}}$