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Unformatted text preview: Midterm One Solutions General Comments: • Overall I was quite happy with the performance on this exam. The mean was 84.5, the median was 87, the high score was 100.5 and the low score was 45.5 I have given approximate grade ranges below. However, remember that you get to reduce weight on your lowest midterm and your grade is a combination of many factors so do not interpret these as the score necessary to receive a particular grade for the course overall. They should just give you a sense of where you stood in the class and how I felt about the overall performance. • The definition of the p-value in part (h) of Problem 1 and the comparisons of confidence intervals in parts (b) and (c) of problem 2 caused the most difficulty on this exam. Read those solutions carefully! Grade Score Range Number in Range A 90+ 43 A- 85-89.5 15 B+ 80-84.5 20 B 70-79.5 11 B- 65-69.5 5 C+ 60-64.5 1 C 55-59.5 3 C-/F 45-50 3 THE STORY BEHIND THE EXAM: Pete’s Powerful Pills (PPP) and Martha’s Miracle Medicines (MMM) are rival pharmaceutical companies in the city of Los Seraphim. Recently each has developed a new vaccine which is supposed to prevent Statisticitis, a disease that commonly afflicts statistics students at the local school, the University of Calculationally Learned Adults. During the exam we will try to evaluate which vaccine works better and learn a little more about the disease. 1 Question 1: Cures on Contingency (33 points, 40 minutes) An independent testing agency runs a study to compare the PPP and MMM vaccines to see if they have different rates of effectiveness. They interview a total of 200 students who have taken one of the vaccines and record whether or not they have gotten statisticitis. A STATA printout for their study analysis is given below, although it seems to have some pieces missing. Use the printout to answer the following questions: . tabi 5 15\95 85, exp chi2 e Expected counts are printed below observed counts Took PPP Took MMM Total Got Statisticitis 5 __15_ __20_ 10.00 10.00 Didn’t Get __95_ __85_ _180_ Statisticitis 90.00 90.00 Total _100_ 100.00 _200_ Pearson chi2(1) = 5.5556 Pr = 0.018 Fisher’s exact = 0.032 1-sided Fisher’s exact = 0.016 Part a (7 points) Fill in the missing entries (marked ) in the contingency table above. Note: you will be able to get full credit on following parts of the problem even if you cannot fill all of these in. If you later need a number you have not filled in, simply put in an appropriate symbol. Solution: The completed table is shown above. We were given that a total of 200 students were studied so that is the grand total. The column totals must add to 200 so that tells us the first column total must be 100. Since the entries of the first column must sum to 100 the number of students who took PPP and didn’t get statisticitis must be 95. Finally note that the expected counts must sum to the row and column totals just like the observed counts so the two row totals must be 20 and 180 respectively. This lets us full in the final observed values as 15 and 85 to makemust be 20 and 180 respectively....
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- Winter '07
- Statistics, Null hypothesis, Statistical hypothesis testing, Statistical tests, Fisher's exact test