What is the statistical significance test that should be run to see if the results from a smaller group of those surveyed is significant and reflective of the larger group? 

For instance: 
1. Survey 1000 people and out of the 1000 people we also want to look at the group of 300 people that are within a certain demo. Would it be statistically significant to look at these results and assume that they are non-directional at 95% confidence? 
2. And then from that, what should I run in order to see if proportions between the two is significant? Let's say out of the larger group of 1000, 100 answered yes to a questions. And out of those 300, 50 answered yes to a question.