Question

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 400 stude

nts. 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 interpret.

c)

Make a decision about H0, using α = .05. Based on this decision, what can you conclude

about the parameter?

Answer 1

Let p denotes the true proportion of correct answers.

Conclusion in problem context :

There is sufficient evidence to support the claim that more people answer the question correctly than would be expected just due to chance.