The Question
My Understanding
I know that for a stratified simple random sample, the variance of $\hat{t}_{y,st}$ is
$$V_p(\hat{t}_{y,st})= \sum_{h=1}^L N_h^2(1-\frac{n_h}{N_h})\frac{S_h^2}{n_h}$$
where $S_h^2$ is the true variance, $N_h$ the Total number of units and $n_h$ the Number of units in sample.
If $\frac{n_h}{N_h}$ are negligible I guess it means that $V_p(\hat{t}_{y,st})= \sum_{h=1}^L \frac{N_h^2 S_h^2}{n_h}$
I also saw that under neyman allocation $n_h*= n\frac{N_hS_h}{\sum_{h=1}^LN_hS_h}$
I did all the possible algebra but could not end up with the desired result. Please help me or give me some tips.