I create 3 different tests each with 10 questions and then assign the tests to students at random. Not all students sit the same test but they will have some questions in common.

If I find that 40 students answered a question and scored 70% then I would I work out the margin of error around that 70%. I want to have an idea what the populate proportion is (say 95% CI).

Q.

* Do I treat each individual question as the sample proportion and then do 1.96 * sqrt(0.5*0.5/40) for the margin of error?

* Do I somehow take into account the number of questions in the test of the total number of question

* A combination of both.

I think that the individual questions will effectively be assigned randomly to students, despite the fact it's the tests that are randomly handed out. Another way to think about it is that once the test is assigned there is no choice.

Any advice would be gratefully received!