Chapter 8, Problem 22SE

Guessing 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 $z\text{-test}$ statistic will be close to 0.

ii. the $z\text{-test}$ 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.