Confidence Interval for the ratio of two means. http://en.wikipedia.org/wiki/Fieller%27s_theorem

fieller.R

fieller = function(x,y) {
  x.mean = mean(x)
  y.mean = mean(y)
  x.sd = sd(x)
  y.sd = sd(y)
  xy.cov = cov(x,y)
  
  print(sprintf("x has mean %s, y has mean %s", x.mean, y.mean))
  print(sprintf("ratio of means is %s", x.mean/y.mean))
  
  g = pt(.05,length(y) - 1)^2*(y.sd^2)/(y.mean^2)
  
  lower = (1 / (1-g)) * ((x.mean/y.mean) - g*xy.cov/(y.sd^2) - pt(.05, length(y) - 1)/y.mean * sqrt (x.sd^2 - 2*x.mean/y.mean*xy.cov + x.mean^2/y.mean^2 * y.sd^2 - g*(x.sd^2 - xy.cov^2/y.sd^2)))
  upper = (1 / (1-g)) * ((x.mean/y.mean) - g*xy.cov/(y.sd^2) + pt(.05, length(y) - 1)/y.mean * sqrt (x.sd^2 - 2*x.mean/y.mean*xy.cov + x.mean^2/y.mean^2 * y.sd^2 - g*(x.sd^2 - xy.cov^2/y.sd^2)))
  list(lower, upper)
}