Very interesting idea, but not sure Twitter sentiment analysis tells us anything. Most Twitter users don't tweet, and most college-age people are not active Twitter users. Instagram would provide more comprehensive data.

Even then, you have to make a variety of (sometimes shaky) assumptions:

1. The data set is a representative sample

2. Sentiment of social media posts is a good proxy for happiness

3. Machine analysis is sentiment is reliable (i.e. doesn't fail when it encounters sarcasm, which is common on Twitter)