Sample skew in a known skewed population I have a sample taken from a population that I know to have a highly positive skew, although I know nothing else about the population.  
My sample displays a similar skew.  Sample size is 120.
Is it incorrect to transform (Box-Cox) my sample to normality to perform simple parametric tests like a mean with a confidence interval?
Should I just stick with medians?
 A: This is a difficult issue to answer from the information given.  You might want to read this answer and revise your question.  For example, let's say your lambda for the box-cox was close to -1.  You could then use an inverse transform.  If your measure is time in seconds for an event then you have a new measure, without skew of events/second.  There's no good* reason to pick one over the other because they're arbitrary representations of the same thing and you'd certainly then want to go with the non-skewed measure.  In that case, by all means transform.
On the other hand, you could have something come out that suggests a very arbitrary transformation.  It's difficult to interpret what comes out of that. You could try back transforming if there are only additive effects but then interactions could appear.  Conversely, if there are any interactions they may be completely uninterpretable back transformed.  And then how do you interpret that without a model justifying the kind of transformation?
Medians aren't a panacea either.  Medians are susceptible to samples size effects such that they become more sensitive to the skew as the sample size gets smaller.  So, in comparison of groups, the medians would have to come from equal sample sizes.  Also, just substituting medians for means bypasses the fact that they mean very different things.  You should be saying what you intend, perhaps you need to figure out your intent?
*OK, one could have a very specific model that selected one... but then the transform question would be very different.
