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).
