A search of statistical power in the built-in Help (version 10), and at this site didnt turn up anything. But a web search led me to an application called GPower see here for a video of this in action:
G*Power tutorial (t-tests)
Does Mathematica have a statistical power function, or series of functions ?
If not, is this something that could be added in a future version ?
Further searching shows that Matlab has this capability: sampsizepwr
As well as Minitab: Minitab's Power and Sample Size Tools
And SAS: Introduction to Power and Sample Size Analysis
And StatSoft: Designing an Experiment, Power Analysis
I also would find it very useful to have more capability in this direction. There are add-ons to do some of this (or there used to be), but it really seems like core functionality for stats, data science, and so on.