The question cannot be answered.
What does 'best' mean?
The statistical most profound?
The cheapest for the university?
The optimized combination of both?
...
And no, assuming that the 'best' is clearly defined, because it is a statistics test, is not valid.
Apart from this, the statistical best method is to include 'did not respond' in the model, as (an)other commenter(s) has (have) already mentioned. Bayes rules, btw!
Reselecting 130 students is not different from going with the 90, if the not-/responding is a confounding variable, as you just select more from the responder group.
> What does 'best' mean? The statistical most profound? The cheapest for the university?
It means the method producing the sample most representative of the population. It's fairly obvious they're not asking about (say) budget/cost minimization on a statistics test.
I may be a little bit picky, but if someone cannot formulate a clear question in such a simple case, he will fail more badly in more complicated cases.
Apart from this, the statistical best method is to include 'did not respond' in the model, as (an)other commenter(s) has (have) already mentioned. Bayes rules, btw!
Reselecting 130 students is not different from going with the 90, if the not-/responding is a confounding variable, as you just select more from the responder group.