8. Multiple Choice Strategy: Some students have suggested that if you have to guess on a multiple-choice question, you Correct - should always choose 0. Carl, the student, wants to investigate Answer Frequency this theory. He is able to get a sample of past tests and quizzes 18 from various teachers. In this sample there are 80 multiple- 17 choice questions with four options (A,B,C',D). The distribution 28 of correct answers from this sample is given in the frequency 17 table to the right. (a) If the correct answers for all multiple-choice problems are uniformly distributed across the four options (A,B, C, D), what is the theoretical proportion of those which should have the answer 0? (b) Based on the sample that Carl collected, what is the point estimate for the proportion of all multiple-choice questions with a correct answer of C'? (c) What is the 90% condence interval for the proportion of all multiple-choice questions with a correct answer of C? (d) Can Carl be 90% condent that the correct answer of C shows up more frequently than the theoretical value found in part (a) would suggest? (e) What is the 99% condence interval for the proportion of all multiple-choice questions with a correct answer of O? (f) Can Carl be 99% condent that the correct answer of C shows up more frequently than the theoretical value found in part (a) would suggest