# Confidence interval of the weighted mean

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