The government is attempting to determine whether travelers should be tested for contagious disease. Let’s assume that the decision will be made on a financial basis. Assume that each traveler who enters and does not have the disease will contribute $10,000 to the national economy. On the other hand, the travelers who is allowed into country and has a disease does not contribute to GDP and costs the United States $100,000. Based on the data, it is assumed that 10% of all travelers have the disease. The government has three options: admit all travelers, ban all flights, or test travelers for disease before determining whether they should be admitted to country or not. It costs $100 to test a person for the disease. Recent studies suggest that the false negative rate of the test is 20% (i.e. ℙ{−|sick}=0.20); whereas the false positive rate is 5% (i.e. ℙ{+|healthy}=0.05). The government’s goal is to maximize ( per traveler ) expected benefits minus expected costs.i. Draw the decision tree and find the optimal policy together with its expectedoutcome (i.e. EMV of the optimal policy).ii. Find EVSI and EVPI.iii. What is the minimum level of false negative at the test for which the government would reject the travelers even though they have negative test result. (Assuming the rest of the probabilities stay the same). (Hint: you can consider the tree below.)
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