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 0.05. Steps 1 and 2 of the hypothesis testing procedure are given. Finish the question by doing steps 3 and 4.

Step 1: H0: p = 0.25

Ha: p > 0.25

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