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In a sampling survey, I get $N$ cases about whether to support a policy and get $x_i(i=1,2,..,N)$, $x_i$ is binary, support $x_i=1$, and $x_i=0$ otherwise, give a weight $w_i(i=1,2,..,N)$to every case, finally I get the odds of support $$O = \frac{ \sum_{i=1}^N w_i \cdot x_i}{\sum_{i=1}^N w_i}$$ I confused with how to get the 95% confidence interval of $O$,and $\delta-method$ (1) can be used to solve the question?
Thanks

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