ECON30019 Assignment 2
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ECON30019 Assignment 2
Due at 11:59 pm on Aug 31, 2023
Question 1. (20 points)
suppose you are in charge of enforcing safe drinking rules in a restaurant, which caters to young and old. The restaurant must abide by the law, which says: If gou aTe dTinking alcohol’ then gou must be 18 oT oldeT. suppose it is too costly for you to hire additional staf to check every single customer. so you are constrained to a few random checks.
1. (1o points) Among the four groups of people below, checking which two groups would help you to conirm that the rule is being followed？ Explain.
(1) people who are drinking alcohol
(2) people who look 18 or older
(3) people who are not drinking alcohol
(4) people who look younger than 18
2. (1o points) If a person tells you to check groups (1) and (2), is he or she correct？If not, which behavioural bias might this person be committing？ Explain.
Question 2. (35 points)
suppose that, in the course of a regular check-up, a doctor discovers that the patient has a potentially cancerous lesion. Most lesions are non-cancerous, say 99%. The doctor orders an x-ray just in case. In laboratory tests on cancerous lesions, the x-ray returns positive (cancer- a伍rming) results 69.6% of the time and negative results 3o.4% of the time. In laboratory tests on non-cancerous lesions, the x-ray returns positive results only 19.3% of the time and negative results 8o.7% of the time.
1. (15 points) The patient,s x-ray comes back positive. what is the probability that the patient has cancer？
2. (15 points) suppose that the doctor calculates the probability that the patient has cancer without regard to the base rate of cancer in the population. That is, the doctor uses Bayes, rule but assumes that cancerous and non-cancerous lesions are equally likely. what mistaken conclusion will the doctor draw from the test？
3. (5 points) Explain why it is important in these situations to have hospital procedures
that require additional tests to be performed before a patient undergoes treatment.
Question 3. (45 points)
Aaron is new to a city. According to his experience in his hometown, Aaron initially believes that september is spring. so he believes that for a day in september, the probability it is warm is 9o% and the probability it is cold is 1o%. Assume the weather of each day is independent.
1. (1o points) what does Aaron initially believe is the probability of having 5 straight cold days in september？
2. (15 points) After arriving in the new city and experiencing some really cold weather, Aaron starts to wonder if maybe the seasons work diferently there. He still thinks september is spring with 9o% conidence, but acknowledges a 1o% chance that somehow september is still the dead of winter in the new city. Aaron believes that in the winter, the probability of a warm day is 3o% and the probability of a cold day is 7o%.
over the next 5 days, Aaron observes cold, warm, cold, cold, warm. suppose Aaron is a Bayesian updater. After these observations, what does Aaron now believe is the probability that it is spring in september？
3. (2o points) After living in the new city for two weeks, Aaron now believes the probability it is warm is 7o% and the probability it is cold is 3o%. Today Aaron checks the weather forecast and it says it will be cold tomorrow. suppose that the forecast is correct 9o% of the time. That is, the probability that the forecast says it will be warm given that it actually will be warm is o.9, and the probability that the forecast says it will be cold given that it actually will be cold is o.9.
Now suppose Aaron sufers from conirmation bias. He is pretty sure that it is going to be warm, so he misinterprets cold forecasts as warm forecasts 2o% of the time but always correctly interprets warm forecasts. He is aware of his own conirmation bias. If his interpretation is that he has seen a warm forecast, what is his updated belief about the probability that it is going to be warm tomorrow？
2023-08-31