Answers to Multiple-Choice Problems: A student nants to see if the correct answers to multiple choice problems are evenly distributed. She heard a rumor that if you don't know the answer, you should always pick C. In a sample of 100 multiple-choice questions from prior tests and quizzes, the distribution of correct answers are given in the table below. In all of these questions, there were four options {A, 8, C, D}. Correct Answers n = 100 Count 12 24 30 34 The Test: Test the claim that correct answers for all multiple-choice questions are not evenly distributed. Test this claim at the 0.05 significance level. (a) The table below is used to calculate the test statistic. Complete the missing cells. Round your answers to the same number of decimal places as other entries for that column. Correct Observed Assumed Expected i Answer Frequency (Q) Probability Frequency 0.25 0.25 0.25 n = 100 (b) What is the value for the degrees of freedom? 25.0 25.0 (0, Ei)2 5.750 0.040 1.000 (c) What is the critical value of 12 ? Use the answer found in the 12 -table or round to 3 decimal places. (d) What is the conclusion regarding the null hypothesis? O reject Ho O fail to reject Ho (e) Choose the appropriate concluding statement. O We have proven that correct answers for all multiple-choice questions are evenly distributed. O The data supports the claim that correct answers for all multiple-choice questions are not evenly distributed. C) There is not enough data to support the claim that correct answers for all multiple-choice questions are not evenly distributed.