I'm dealing with a question that has given me a peculiar result and I would like someone's opinion on how to deal this:
Say you have a population of $N=550$ objects: $N_1=75$ red and $N_2=475$ blue.
Given their $s_h^2$ 's and a required bound on a characteristic of interest, I was able to calculate the proper total sample size $n$ required, and used the formula to calculate each $n_h$.
The problem is that I ended up with a calculated $n_1>N_1$ because of the large difference in stratum sample variances. I've still used the calculated $n$, set $n_1=N_1$ and set $n_2=n-n_1$, but I don't think this will guarantee the required bound. What do I do?