20 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 exain taken by 400 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).

a) Set up the hypotheses for the test

b) Of the 400 students. 125 correctly answer the question. Find the P-value, and inter- piet.

c) Make a decision about Ho, using a = .05 Based on this decision. what can you con- clude about the parameter"

d) As an alternative inference, construct a 95% confidence interval for the parameter Contrast what you learn using these two methods.