Amultiple-choice test question has four possible responses.

The question is 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.

Test whether more people answer the question correctly than would be expected just due to chance (that is, if everyone randomly guessed the correct answer).

(a) Set up the hypotheses for the test.

(b) Of the 500 students, 175 correctly answer the question.

Find the P-value, and interpret.