If you choose to answer this question, all the following questions (a) and (b) must be...
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If you choose to answer this question, all the following questions (a) and (b) must be answered. (a) Assume that during a preliminary drug test of a young person in the Netherlands, the result comes back positive (indicating drug use). Most people (98%) do not use drugs. The police officer orders a more sensitive follow-up test. In these more sensitive tests, the results are positive 82.6% of the time and negative 17.4% of the time when the person has actually used drugs. In cases where the person has not used any drugs, these sensitive tests show a positive result 12.4% of the time and a negative result 87.6% of the time. Important: round all numbers to three decimal places. (i) [11 marks] The more sensitive test comes back positive. What is the probability that the person has used drugs? Denote by P(D) the probability of using drugs and by P(-ND) the conditional probability of having a negative result when the person has not used drugs (and all other probabilities accordingly). • [numerical entry, 1 mark per correct number] Insert the numbers that corre- sponds to P(D), P(ND), P(+|D), P(-|D), P(+ND), P(-IND) respectively. • [numerical entry, 5 marks] What is the probability that the person has used drugs? (ii) [11 marks] Assume that the police officer who evaluates the sensitive test result suffers from base rate neglect. He wrongly assumes that half of the people use drugs. Which probability does the police officer assign to the person having used drugs? [numerical entry, 1 mark per correct number] Insert the numbers that corre- sponds to P(D), P(ND), P(+|D), P(-|D), P(+ND), P(-ND) respectively. • [numerical entry, 5 marks] Which probability does the police officer assign to the person having used drugs? (b) [12 marks] Which bias(es) can the following behavior be explained by? (i) You meet your friend who is applying to master programs in the US. They already have a favorite program: "Only 2% of applicants make it into this program, but I'm sure I'll be accepted!" • [multiple choice, 2 mark for correct, -2 for incorrect; ] 1. Loss aversion 2. Overconfidence 3. Sunk cost fallacy 4. Base rate neglect 5. Present bias 6. Over-weighting of small probabilities 7. Failure to consider opportunity costs (ii) You go to a restaurant that has an all-you-can-eat buffet. You choose the buffet and eat so much that you feel bad afterwards. • [multiple choice, 3 mark for correct, -3 for incorrect; 1. Risk aversion 2. Conjunction effect 3. Sunk cost fallacy 4. Base rate neglect 5. Present bias 6. Over-weighting of small probabilities If you choose to answer this question, all the following questions (a) and (b) must be answered. (a) Assume that during a preliminary drug test of a young person in the Netherlands, the result comes back positive (indicating drug use). Most people (98%) do not use drugs. The police officer orders a more sensitive follow-up test. In these more sensitive tests, the results are positive 82.6% of the time and negative 17.4% of the time when the person has actually used drugs. In cases where the person has not used any drugs, these sensitive tests show a positive result 12.4% of the time and a negative result 87.6% of the time. Important: round all numbers to three decimal places. (i) [11 marks] The more sensitive test comes back positive. What is the probability that the person has used drugs? Denote by P(D) the probability of using drugs and by P(-ND) the conditional probability of having a negative result when the person has not used drugs (and all other probabilities accordingly). • [numerical entry, 1 mark per correct number] Insert the numbers that corre- sponds to P(D), P(ND), P(+|D), P(-|D), P(+ND), P(-IND) respectively. • [numerical entry, 5 marks] What is the probability that the person has used drugs? (ii) [11 marks] Assume that the police officer who evaluates the sensitive test result suffers from base rate neglect. He wrongly assumes that half of the people use drugs. Which probability does the police officer assign to the person having used drugs? [numerical entry, 1 mark per correct number] Insert the numbers that corre- sponds to P(D), P(ND), P(+|D), P(-|D), P(+ND), P(-ND) respectively. • [numerical entry, 5 marks] Which probability does the police officer assign to the person having used drugs? (b) [12 marks] Which bias(es) can the following behavior be explained by? (i) You meet your friend who is applying to master programs in the US. They already have a favorite program: "Only 2% of applicants make it into this program, but I'm sure I'll be accepted!" • [multiple choice, 2 mark for correct, -2 for incorrect; ] 1. Loss aversion 2. Overconfidence 3. Sunk cost fallacy 4. Base rate neglect 5. Present bias 6. Over-weighting of small probabilities 7. Failure to consider opportunity costs (ii) You go to a restaurant that has an all-you-can-eat buffet. You choose the buffet and eat so much that you feel bad afterwards. • [multiple choice, 3 mark for correct, -3 for incorrect; 1. Risk aversion 2. Conjunction effect 3. Sunk cost fallacy 4. Base rate neglect 5. Present bias 6. Over-weighting of small probabilities
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a i Lets assign the following probabilities PD Probability of using drugs 002 2 of people use drugs PND Probability of not using drugs 098 98 of people do not use drugs PD Probability of a positive te... View the full answer
Related Book For
Income Tax Fundamentals 2013
ISBN: 9781285586618
31st Edition
Authors: Gerald E. Whittenburg, Martha Altus Buller, Steven L Gill
Posted Date:
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