This is from Hollander's nonparametric inference, chapter 2:
- A multiple-choice quiz contains ten questions. For each question there are one correct answer and four incorrect answers. A student gets three correct answers on the quiz. Test the hypothesis that the student is guessing.
What is bugging me in this exercise is: how one would decide what the critical region should be? In R, of course, you could write:
And you get a p-value of 0.4296. But what is the critical region behind this p-value and why is R deciding it?
I ran the following:
pbinom(0:10,10,0.2)  0.1073742 0.3758096 0.6777995 0.8791261 0.9672065 0.9936306  0.9991356 0.9999221 0.9999958 0.9999999 1.0000000 dbinom(3,10,0.2)  0.2013266
So I thought a good critical region would be a two-sided one: if B=0 or B >= 4, reject the hypothesis that the student is guessing. The thing is, this doesn't seem to be a correct solution.