Question

Piper generated data by guessing on a test. Hear data was 252 incorrect 128 correct. Which of the following was piper most likely simulating. A: multi choice tests with 5 choices. B: multiple choice test with 4 answers. C: a multiple choice test with 3 answers or D a true or false test

Answer 1

Explanation:

To determine which test Piper was most likely simulating, we can use the formula for the expected number of correct answers on a multiple-choice test:

Expected number of correct answers = (total number of questions) * (probability of getting a question correct)

For a multiple-choice test with 5 choices, the probability of getting a question correct by guessing is 1/5 = 0.2. Therefore, the expected number of correct answers for 380 questions would be:

Expected number of correct answers = 380 * 0.2 = 76

For a multiple-choice test with 4 choices, the probability of getting a question correct by guessing is 1/4 = 0.25. Therefore, the expected number of correct answers for 380 questions would be:

Expected number of correct answers = 380 * 0.25 = 95

For a multiple-choice test with 3 choices, the probability of getting a question correct by guessing is 1/3 = 0.3333. Therefore, the expected number of correct answers for 380 questions would be:

Expected number of correct answers = 380 * 0.3333 = 126.63

For a true or false test, the probability of getting a question correct by guessing is 1/2 = 0.5. Therefore, the expected number of correct answers for 380 questions would be:

Expected number of correct answers = 380 * 0.5 = 190

Comparing the expected number of correct answers for each test to Piper's actual number of correct answers (128), we can see that Piper's performance is closest to what would be expected on a multiple-choice test with 3 answers. Therefore, it is most likely that Piper was simulating a multiple-choice test with 3 answers.