Merg. There are contradictory assumptions here. For the approximation on the standard deviation you assume duration is a Poisson random variable. To use the t-test you assume duration is a normally distributed r.v. There are ways to unify the two assumptions, but they can't be used without direct access to the data. At that point, we could just calculate s.d.
I'd stick with assuming duration time is normally distributed. This leads to another class of adhociness: http://www.statit.com/support/quality_practice_tips/estimati...