![Q5. [20pts+5] Sasha has been randomly selected to take a screening test for a rare disease that affects 1% of the population. The test is known to report false positive results 2% of the time (conditional on being healthy) and to report false negative results 5% of the time (conditional on being sick). Note: A positive result indicates that you have the disease, a negative result, that you are healthy a) Answer the following (You can draw a two-way table with one variable being the true health status and the other variable being the test result) i. What is the probability of Sasha being healthy AND getting a negative result? ii. What is the probability of Sasha being healthy AND getting a positive result? ii. What is the probability of Sasha being unhealthy AND getting a negative result? iv. What is the probability of Sasha being unhealthy AND getting a positive result? Conditional on receiving a positive test, what is the probability that Sasha is unhealthy? b) c) [BONUS] If Sasha takes a second test to confirm the first results, what is then the probability of being unhealthy conditional on the second test being also positive?](http://img.homeworklib.com/questions/7a324da0-0b00-11ec-8cb0-cb867d54ed71.png?x-oss-process=image/resize,w_560)
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Q5. [20pts+5] Sasha has been randomly selected to take a screening test for a rare disease...
A screening test for a rare from of TB has a 7% false positive rate (i.e....
A screening test for a rare from of TB has a 7% false positive rate (i.e. indicates the presence of the disease in people who do not have it). The test has an 18% false negative rate (i.e. indicates the absence of the disease in people who do have it). Suppose that 3% of the population have the disease. (i) Partition the sample space into those who have the disease, B1, and those who don’t have the disease, B2. Find...
Screening Test Results for Greyscale Disease Disease positive Disease Negative Positive Test Result 14 50 Negative...
Screening Test Results for Greyscale Disease Disease positive Disease Negative Positive Test Result 14 50 Negative Test Result 6 212 Total How many False Negatives are there?.
A screening test for a rare form of TB has a 7% false positive rate (i.e. indicates the presence of the disease in people who do not have it). The test has an 8% false negative rate (i.e. indicates th...
A screening test for a rare form of TB has a 7% false positive rate (i.e. indicates the presence of the disease in people who do not have it). The test has an 8% false negative rate (i.e. indicates the absence of the disease in people who do have it). In a population of which 0.6% have the disease, what is the probability that someone who tests positive has the disease?
4. Generalize the Bayesian analysis of medical screening given in class. Let a rare disease D...
4. Generalize the Bayesian analysis of medical screening given in class. Let a rare disease D occur with probability P(D) = δ, with δ small. The test for this disease is accurate such that the probability of a correct result is 1-e, with e small. Derive formulas for the probabilities of a true positive P(D|+) and a false positive, P(D'l+). For this screening to be useful at a given δ, what is required of e ?
4. Generalize the Bayesian analysis of medical screening given in class. Let a rare disease D...
4. Generalize the Bayesian analysis of medical screening given in class. Let a rare disease D occur with probability P(D) with δ small. The test for this disease is accurate such that the probability of a correct result is 1-e, with e small. Derive formulas for the probabilities of a true positive P(D|+) and a false positive, P(D|+). For this screening to be useful at a given δ, what is required of ε ?
In screening for a certain disease, the probability that a healthy person wrongly gets a positive...
In screening for a certain disease, the probability that a healthy person wrongly gets a positive result is 0.05. The probability that a diseased person wrongly gets a negative result is 0.002. The overall rate of the disease in the population being screened is 1%. If my test gives a positive result, what is the probability I actually have the disease?
Only 1 in 1,000 is afflicted with a rare disease for which a diagnostic test has...
Only 1 in 1,000 is afflicted with a rare disease for which a diagnostic test has been developed. When a person has the disease , the test returns a positive result 99% of the time. However, when a person does not have the disease, the test shows a positive result only 2% of the time. When a person's test results are positive, in order to validate the results, a second test is given. The second test has the same accuracy...
18. Drug Screening If one of the test subjects is randomly seleci the subject had a...
18. Drug Screening If one of the test subjects is randomly seleci the subject had a positive test result or does not use drugs. 19. Drug Screening if one of the subjects is randomly selected, find the probability that the subject had a negative test result or does not use drugs. Whiarre is randomly selected, find the probability that the Negative Test (Drug Use Is Not Indicat Table 4-1 Pre-Employment Drug Screening Results Positive Test Result (Drug Use Is Indicated)...
The screening process for detecting a rare disease is not perfect. Researchers have developed a blood...
The screening process for detecting a rare disease is not perfect. Researchers have developed a blood test that is considered fairly reliable. It gives a positive reaction in 94.4% of the people who have that disease. However, it erroneously gives a positive reaction in 3.9% of the people who do not have the disease. Consider the null hypothesis "the individual does not have the disease" to answer the following questions. a. What is the probability of a Type I error?...
Suppose that your company has just developed a new screening test for a disease and you...
Suppose that your company has just developed a new screening test for a disease and you are in charge of testing its validity and feasibility. You decide to evaluate the test on 1000 individuals and compare the results of the new test to the gold standard. You know the prevalence of disease in your population is 30%. The screening test gave a positive result for 292 individuals. Two hundred eighty-five (285) of these individuals actually had the disease on the...
4. Generalize the Bayesian analysis of medical screening given in class. Let a rare disease D occur with probability P(D) = δ, with δ small. The test for this disease is accurate such that the probability of a correct result is 1-e, with e small. Derive formulas for the probabilities of a true positive P(D|+) and a false positive, P(D'l+). For this screening to be useful at a given δ, what is required of e ?
4. Generalize the Bayesian analysis of medical screening given in class. Let a rare disease D occur with probability P(D) with δ small. The test for this disease is accurate such that the probability of a correct result is 1-e, with e small. Derive formulas for the probabilities of a true positive P(D|+) and a false positive, P(D|+). For this screening to be useful at a given δ, what is required of ε ?
18. Drug Screening If one of the test subjects is randomly seleci the subject had a positive test result or does not use drugs. 19. Drug Screening if one of the subjects is randomly selected, find the probability that the subject had a negative test result or does not use drugs. Whiarre is randomly selected, find the probability that the Negative Test (Drug Use Is Not Indicat Table 4-1 Pre-Employment Drug Screening Results Positive Test Result (Drug Use Is Indicated)...
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