Multiple-choice questions on Advanced Placement exams have five options: A, B, C, D, and E.
A random sample of the correct choice on 400 multiple-choice questions on a variety of AP exams shows that B was the most common correct choice, with 90 of the 400 questions having B as the answer.
Does this provide evidence that B is more likely than 20% to be the correct choice?
a. Define the parameter, state hypotheses, and calculate the sample statistic.
b. Is a Normal distribution appropriate for this test, based on the values of n and Po? Explain.
c. Calculate the standard error and z-test statistic, assuming a Normal distribution is appropriate.
d. Find the p-value and draw a Normal curve with appropriate shaded region. You may give either a precise p-value from Stat key or bounds on a p-value from Table A.
e. State the conclusion of the test in context f. Find a 95% confidence interval for the proportion of questions on all AP exams having B as the correct choice using the normal distribution and the formula for standard error. Show your calculations