Practice exam question #2 for Bayesian Decision

Question 2 A new drug is being tested on a group people with a particular ailment. We wish to establish whether there is a link between taking the drug and recovery from an ailment. During the drug trial 250 peoples were given the drug and 350 were given a placebo. The results in Table 1 show that, of the 250 given the drug, 1 10 recovered from the ailment; this compares favourably with just 125 out of the 350 given the placebo who recovered. Table 1 (Question 2) Drug trial results Recovered Drug Taken Number of subjects No No 225 No Yes 140 Yes No 125 Yes Yes 110 The data is subsequently broken down by nationality into English and Scottish subjects and the results shown in Table 2. Table 2 (Question 2) Stratified drug trial results with nationality of patient included Nationality | Recovered Drug Taken Number of subjects English No No 15 English No Yes 60 English Yes No 35 English Yes Yes 90 Scottish No No 210 Scottish No Yes 80 Scottish Yes No 90 Scottish Yes Yes 20 a) Derive the recovery percentages for Table 1 and determine whether the drug is effective. b) Derive the recovery percentages for English and Scottish people from Table 2 and determine whether the drug is effective given a person's nationality. c) What is Simpson's paradox and explain whether it applies to this drug trial? d) Identify causal or confounding factors that might have influenced the drug testing study results. e) Draw one or more BNs to represent how the confounding factors identified in Question 2 e) might have influenced the results