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

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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:enter image description here


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