Confidence interval considering the division of 2 means with different CIs? Statistics I have the mean and its confidence interval (standard deviation and size of its sample) of 2 different data A and B. I want to divide A/B and get the confidence interval of its division. Is there a formula for that?
For example, I want to divide time (400 s +/- 20s) per size (10 m +/- 3m). What's the result, considering confidence interval?
 A: There is a lot of important information that you do not have.  Are the 2 groups completely independent?  What is the distribution (The Central Limit Theorem helps with confidence intervals on means when the population(s) are not normal, but not so much for looking at ratios).
In some cases the ratio of 2 normal variables is a Cauchy (which does not like to obey other rules).
One option if you are willing to make certain assumptions is to do a simulation or parametric bootstrap:

*

*generate data for group A with the same sample size from a distribution with the desired mean and standard deviation

*do the same for group B.

*calculate the means and their ratio from the above simulated data.

*repeat steps 1-3 a bunch of times and plot the results.

You can calculate an interval from quantiles of the simulated ratios.  It may be best to do some more simulations where you start from a known truth, simulate some data, then go through the whole process above to see how often the given intervals do contain the true value.  Then go back and change the distributions and see if that makes a difference or not.
