# mid1soln - Midterm One Solutions General Comments Overall I...

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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 make the observed row counts sum correctly. It was not necessary to explain your reasoning for any of these entries. In fact there was an even easier approach! I gave you the STATA command which
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