A multiple-choice test question has four possible responses. The question is designed to be very difficult, with none of the four responses being obviously wrong, yet with only one correct answer. It first occurs on an exam taken by 500 students. The designers test whether more people answer the question correctly than would be expected just due to chance (i. e., if everyone randomly guessed the correct answer).

In order to have full credit, you need to show all asked parts.

1. Set up the hypotheses for the test.
2. Of the 500 students, 200 correctly answer the question. Find the P-value, and interpret.