Name: Elementary Statistics Written Homework No software output is required for this assignment. Sections 6.1 & 6.3 1. 6.58 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 State hypotheses, and calculate the sample statistic. Ho: P=0.2 Ha p>0.2 90/400=0.225 P=0.225 b. Is a Normal distribution appropriate for this test, based on the values of n and p? Explain. n=400 Normalv P=0.225 ne 40 (0.20)=80 np= 80>s c. Calculate the standard error and z-test statistic, assuming a Normal distribution is appropriate. 225-2 (2x (17.2) = 1.2 S 400 d. Find the p-value and draw a Normal curve with appropriate shaded region. You may give either a precise p-value from software or bounds on a p-value from Table A. P-value = 0.106 e. State the conclusion of the test in context, using nontechnical language. f. Find a 90% 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.