Using Fieller’s theorem to calculate the confidence interval of a ratio (paired measurements)

If you have two means (with their own confidence intervals) and want to represent them as a ratio, how do calculate the confidence interval for the ratio?

An answer that was given to me, mentions Fieller’s theorem, which enables you to compute a confidence interval for a ratio quite easily (see calculator here).

Unfortunately, I cannot use this tool as my measurements are paired. Is there any way around this?

I might have been clearer in the following image:
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Answer

The problem of calculating confidence/likelihood intervals for the ratio of two means is addressed in Chapter 7 of the book Statistical Inference in Science, and in Chapter 10 of Empirical Bayes and Likelihood Inference.

Note also that (i) the ratio of the means is different to the [mean of the ratio] (http://www.hindawi.com/journals/ads/2006/078375/abs/), (ii) the distribution of the ratio of two normal variables [is not normal] (http://link.springer.com/article/10.1007%2Fs00362-012-0429-2#page-1).

Attribution
Source : Link , Question Author : Marc , Answer Author : Laikon

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