I have a very large number of true/false questions. I want to take a sample of these questions and use them to test a subject. I would like to infer the proportion of questions out of the larger set that the subject will answer correctly, based on the number the subject answered correctly in the sample.
Would it be a valid approach to model the subject's answers on a sample of questions from the full set as a Binomial experiment, assuming that the sample questions are selected randomly? If so, what assumptions am I making in using this model?
It seems to me that I would be required to assume that the subject's answers to each question is in some way fixed, so that, for a particular question, she would choose the same answer regardless of when she was asked.