Before I get called out as -ist, let me explain. Psychology is one of the few "default" subjects - i.e. something you pick when you don't know what do you want to major in. It's also a stereotypical feminine subject, hence huge gender gap. The other popular "default" choice is economics, which tend to draw those proficient at maths.
The point being, psychology students are a very particular subset of the population, and thus it's difficult to generalize results from them to everyone.
In general you can't say whether a sample size of 2000 will get you within a specific margin of error without additional information. It very much depends e.g. on what the hypothesis you're testing is or what you're trying to estimate.
> In the Journal of Personality and Social Psychology, the premier journal in social psychology – the subdiscipline of psychology that should (arguably) be the most attentive to questions about the subjects’ backgrounds – 67% of the American samples (and 80% of the samples from other countries) were composed solely of undergraduates in psychology courses (Arnett 2008). In other words, a randomly selected American undergraduate is more than 4,000 times more likely to be a research participant than is a randomly selected person from outside of the West.
Source: http://hci.ucsd.edu/102b/readings/WeirdestPeople.pdf