Chapter 8, Problem 106CRE

Guessing on a Multiple-Choice Test A multiple-choice test has 50 questions with four possible options for each question. For each question, only one of the four options is correct. A passing grade is 35 or more correct answers.

a. What is the probability that a person will guess correctly on one multiple-choice question?

b. Test the hypothesis that a person who got 35 right out of 50 is not just guessing, using an alpha of $\mathrm{0.05.}$ Steps 1 and 2 of the hypothesis testing procedure are given. Finish the question by doing steps 3 and 4.

Step 1: ${\text{H}}_{\text{0}}:p=0.25$

${\text{H}}_{\text{a}}:p>0.25$

Step 2: Choose the one-proportion $z\text{-test}\text{.}$ $n\text{ times }p$ is 50 times $0.25,$ which is $\mathrm{12.5.}$ This is more than 10, and 50 times $0.75$ is also more than 10. Assume a random sample.