Is B a Good Choice on a Multiple-Choice Exam? Multiple-choice questions on Advan

Question

Is B a Good Choice on a Multiple-Choice Exam? 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 25 shows that B was the most common correct choice, with 90 of the 400 questions having Bas the answer. Does this provide evidence that B is more likely to be the correct choice than would be expected if all five options were equally likely? a. Verify that the sample size is large enough. b. Define the parameter and state the null and alternative hypotheses c. Determine the standard error. d. Determine the test statistic e. Find the p-value f. Determine the result of the test. g. State the conclusion in the context of the problem.

Explanation / Answer

a) n 400(0.2) 80 n(1-) 400(0.8) 320 As per the rule,the above two should be >5 and they are, which means that the sample size is large enough. b) H0: =0.2 (All outcomes are equally likely) Ha: >0.2 (B is more likely to occur than the rest of them) c) (1-)/n 0.2(0.8)/400 0.02 d) It would be ZSTAT for proportion e) 0.1056 f) p=90/400=0.225 ZSTAT=p-/(1-)/n 0.225-0.2/0.02 0.025/0.02 1.25 g) Since ZSTAT

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