# Appropriate test for proportion data

I have two independent groups A and B. Each participant is given 5 questions to solve and his/her answer is evaluated as correct or incorrect.

However, participants can skip questions, so the number of attempted questions for each participant varies.

So, I end up with the data below:

     Group   # of correct answers  # of attempted answers   Correct Ratio
p1    A            3                       5                    0.6
p2    A            2                       4                    0.5
p3    B            1                       1                    1.0
p4    B            1                       3                    0.33
......


I want to test the whether the answers' correctness is different between group A and B. Which statistical test should I use?

Currently I simply count the total # of attempted answers and # of correct answers for all people from group A and B, say 90/100 vs 75/90, and use proportion test (in R as prop.test). But I don't know whether it is appropriate?