do only 6 and 7 and 8(a,b,c,d,e) please Ten thousand athletes are competing in t
ID: 3170194 • Letter: D
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do only 6 and 7 and 8(a,b,c,d,e) please
Ten thousand athletes are competing in the olympics. The International olympiccommittee is concerned about rumors that some the athletes have been taking the banned drug zapuwol.The loc doesn't know which athletes or even how many have actually taken zapuwol, but they plan to conduct blood tests of all 10,000 athletes to check forthis substance. The diagnostic test used by the loc is said to be "99% accurate". By this, the mean that, if an athlete has taken zapuwol, there is a 99% chance that the diagnostic test will be "positive". And if athlete has not taken zapuwol,there is a 99% chance an the diagnostic test will be "negative". suppose the truth of the matter is that 100 of the 10,000 athletes have actually taken zapuwol.The other 9900 athletes have not taken this drug. According to the 99% accuracy level of the diagnostic test 2) How many of the 100 who have taken zapuwol will test negative? 3) How many of the 9900 who have not taken zapuwolwilltest positive? 4) How many of the 9900 who have not taken zapuwol will test negative? 5) Put the above results into a two-way classification table: Test Negative Totals Test Positive Took Zapuwol Didn't take it Totals 6) of those who tested positive, what percentage actually took zapuwor? 7) Should an athlete who test positive for zapuqol using this test alone be banned from the competition?Explanation / Answer
To solve the question 6, we need to solve the question 5.
99 % of the athletes who took Zapuwol will test positive. So, Out of 100 athletes who took Zapuwol, 99 will be test positive and remaining 1 will test negative.
99 % of the athletes who did not took Zapuwol will test negative.So, Out of 9900 athletes who did not took Zapuwol, 9801 (99% of 9900) will be test negative and remaining 99 will test positive.
6. From the table 198 athletes tested positive.
Of those who test positive, percentage who actually took Zapuwol = 99/198 = 50 %
7. No, the athlete should not be banned using this test. If the athlete is tested postive, there is only 50 % chance that the athlete took Zapuwol.
8 (a) Again, we will generate the table from the given data
Suppose the population size is 100, so 5 are drug users and 95 are non-drug users.
95 % of the users will test positive. So, Out of 5 users, 4.75 will be test positive and remaining 0.25 will test negative.
95 % of the non-users will test negative. So, Out of 95 non-users, 90.25 will be test negative and remaining 4.75 will test positive.
(a) Prevalence = Total Users / Total Population = 0.05
(b) Sensitivity = A/(A+C) = 4.75/(4.75+0.25) = 0.95
(c) Specificity = D/(D+B) = 90.25/(90.25+4.75) = 0.95
(d) predictivevalue of postive test = P(Test Positive | User)/(P(Test Positive | User)+P(Test Positive | Non-User)) = 4.75/(4.75+4.75) = 0.5
(e) If the prevalence is 1 %, the chart becomes
Suppose the population size is 100, so 1 are drug users and 99 are non-drug users.
95 % of the users will test positive. So, Out of 1 users, 0.95 will be test positive and remaining 0.05 will test negative.
95 % of the non-users will test negative. So, Out of 99 non-users, 94.05 will be test negative and remaining 4.95 will test positive.
So, predictive value of postive test = P(Test Positive | User)/(P(Test Positive | User)+P(Test Positive | Non-User)) = 0.95/(0.95+4.95) = 0.161
Test Positive Test Negative Totals Took Zapuwol 99 1 100 Didn't take it 99 9801 9900 Totals 198 9802 10000Related Questions
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