The standard testing method for HIV has a sensitivity of 0.997 and a specificity
ID: 2921882 • Letter: T
Question
The standard testing method for HIV has a sensitivity of 0.997 and a specificity of 0.985. In other words, a person who is infected with HIV will test positive 99.7% of the time, while a person that is NOT infected will test negative 98.5% of the time. It is estimated that the proportion of infection in the U.S. is 0.006, or 0.6% of the adult population. 1. If a person tested with this exam tests positive, what is the probability that they are in fact HIV positive? 2. If a person tested with this exam tests negative, what is the probability that they are in fact HIV negative? 3. Comment on these numbers. Do they seem higher than they should be, lower than they should be, or do they seem satisfactory? If someone you know 4. In Singapore, the HIV infection rate is 0.001. If a person in Singapore tests 5. In Belize, the HIV infection rate is 0.03. If a person in Belize tests positive 6. It is estimated that in South Africa, the adult HIV infection rate is 0.173. tests positive, do you think they should get tested again? positive for HIV, what is the probability that they are in fact HIV positive? for HIV, what is the probability that they are in fact HIV positive? If a person in South Africa tests positive for HIV, what is the probability they are actually infected? If a person in South Africa tests negative, what is the probability that they are actually NOT infected? 7. How does the infection rate affect the accuracy of the test results? It isExplanation / Answer
6) probability of tested positive =P( have HIV and tested postive+not have HIV and tested postive)
=0.173*0.997+(1-0.173)*(1-0.985)=0.1849
therefore probability actually infected given tested postive ==0.173*0.997/0.1849=0.9329
probability of tested negative =1-P( tested positive) =1-0.1849 =0.8151
therfore probability actually not infected given tested negative =(1-0.173)*0.985/0.8151=0.9994
7)as percentage of people usinfg these drugs is higher for Marijuana; we are more confidenct that person is using Marijuana then Heroine. However as overall percentage is comparatively low for both of them in population ; we should bot be very much confident and retest needs to be done to incresae relaibility of that.
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