A multiple-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 400 students.

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).

(a) Set up the hypotheses for the test.

(b) Of the 400 students, 125 correctly answer the question.

Find the P-value, and interpret.