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In a random sample of n subjects with n being very large, let X be the number of successes. Now I want to create the confidence interval for the natural log of the proportion of successes. Can I simply log the confidence interval I would get from applying CLT on the proportion estimate? This should be possible as quantiles are preserved under monotonically increasing transformations.
Or should I just use the standard error obtained from the Delta method and calculate a confidence interval from that?

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