I don't know who told you not to worry because your house is new - Radon levels seem to run higher in new construction because newer homes are more air-tight, so radon gets trapped in longer.
But unless you spend a lot of time in your basement, you are probably OK.
In MA radon testing is not mandatory. However, buyers frequently have the house tested as part of the inspection process, and if the results fall above 4 pCi/L then they might request remediation. The seller will usually comply. The remediation is not much more than a pipe to let the air circulate, and it costs around $1500-$2000, as others have said.
Unfortunately the test kits you buy (or that the inspector uses) will only tell you the level the days you test. And since radon is a naturally occurring gas produced by the breakdown of uranium in soil, rock, and water, the level isn't constant. It changes from season to season and even from week to week, depending on the weather.
The better solution is to get a radon reading device that tracks your average radon over time. It's much more reliable than the short term test that only reads for a couple of days.
The best site I've found for info on Radon is the EPA's site:
http://www.epa.gov/radon/pubs/consguid.html
I'm a Realtor so I try to keep up on these issues.
Hope this helps!