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I want to obtain a confidence interval for the ratio of means of two samples. The samples are of uneven size. They don't come from normal distributions. Is there anything methodologically wrong about using bootstrapping to estimate the confidence interval?

The algorithm would be similar to the approach in the first example here:

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    $\begingroup$ I would say to maintain the uneven sample size when you do your bootstrap samples. The point of bootstrap is to mimic the original data collection by drawing from the next-best distribution if you don’t have the population: the empirical distribution. $\endgroup$
    – Dave
    Commented Feb 16, 2020 at 3:55

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Seems fine, assuming A is independent of B. You can just compute the 2.5th and 97.5th percentiles of the ratios, and there's your 95% confidence interval.

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