How large a sample do I need?

I want to test a postcard. I have a list of 15,000 names, 4,000 of whom have already signed up for information. I want to mail an offer to some statistically significant sample of the remaining 11,000. How many do I need to mail?
Additional information needed

In order to help you with your quetion we need some additional information, such as what it is you are testing. If you are conducting a survey what type of information are you going to get (dichotomous vs polytomous). Also expected response rates etc.