A 20-question multiple choice quiz has five choices for each question. Suppose that a student just guesses, hoping to get a high score. The teacher carries out a hypothesis test to determine whether the student was just guessing. The null hypothesis is p = 0.20, where p is the probability of a correct answer.

a. Which of the following describes the value of the z-test statistic that is likely to result? Explain your choice.

(i) The z-test statistic will be close to 0.

(ii) The z-test statistic will be far from 0.

b. Which of the following describes the p-value that is likely to result? Explain your choice.

(i) The p-value will be small.

(ii) The p-value will not be small.