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3.2.8 Suppose that a medical test has a 92% chance of detecting a disease if the...
In a laboratory, blood test is 95% effective in detecting a certain disease, when it is,...
In a laboratory, blood test is 95% effective in detecting a certain disease, when it is, in fact, present. However, the test also yields a false positive (test is positive but patient does not have the disease) result for 1% of the healthy people tested. 0.5% of the population actually has the disease. Given this information, calculate the following probabilities: The probability that the test is positive. Given a negative result, the probability that the person does not have the...
3. It is estimated that 2% of the meinbers of a certain population are infected with...
3. It is estimated that 2% of the meinbers of a certain population are infected with Hepatitis C virus. A diagnostic test for detecting Hepatitis C yields 4% false positive and 5% false negative results. (a) Find the probability that a person randomly chosen from this popu- lation has a positive result of the diagnostic test for Hepatitis C (b) Find the probability that a random person who has a positive result of the diagnostic test, actually has Hepatitis C.
3. It is estimated that 2% of the members of a certain population are infected with...
3. It is estimated that 2% of the members of a certain population are infected with Hepatitis C virus. A diagnostic test for detecting Hepatitis C yields 4% false positive and 5% false negative results. (a) Find the probability that a person randomly chosen from this popu- lation has a positive result of the diagnostic test for Hepatitis C. (b) Find the probability that a random person who has a positive result of the diagnostic test, actually has Hepatitis C
3. It is estinated that 2% of the members of a certain population are infected with...
3. It is estinated that 2% of the members of a certain population are infected with Hepatitis C virus. A diagnostic test for detecting Hepatitis C yields 4% false positive and 5% false negative results. (a) Find the probability that a person randomly chosen from this popu- lation has a positive result of the diagnostic test for Hepatitis C. Find the probability that a random person who has a positive result of the diagnostic test, actually has Hepatitis C. (b)
2. A rare disease affects 1% of the population. A test has a sensitivity of 98%,...
2. A rare disease affects 1% of the population. A test has a sensitivity of 98%, i.e., it will give a positive result 98% of the time that a person actually has the disease. The same test also has a specificity of 95%, i.e., it will give a negative result 95% of the time when a person does not have the disease. Denote the event that a randomly person has a disease by D, and the event that a randomly...
It has been found that 0.01% of the world population has a certain disease. If a...
It has been found that 0.01% of the world population has a certain disease. If a person has the disease, there is a 95% chance they will test positive for the disease. If a person does not have the disease, there is a 5% chance they will test positive for the disease. (a) What is the probability that a person chosen at random will both have the disease and test positive? 0.000095 (or 9.5 x 10-5) (b) What is the...
[Base Rate Fallacy] Suppose a particular disease has a prevalence of 0.5 % people. A medical...
[Base Rate Fallacy] Suppose a particular disease has a prevalence of 0.5 % people. A medical test to detect this disease has a false-positive rate of 5 % and diagnoses correctly every person who has the disease. What is the probability that a randomly selected person found to have a positive result actually has the disease? Give your answer to three decimal places.
Problem 1 [Sans R (a). Say a test can detect a disease with a type I...
Problem 1 [Sans R (a). Say a test can detect a disease with a type I error rate (false positive) of 10 % and a type II error rate (missed positive) of 0.1 %. If a person is randomly chosen from the population, the chance of having this disease is 0.1 %. If a random person is chosen from the population and tests positive for this disease, what is the probability they have this disease? (b). Say a test can...
3) Suppose the probability of having a disease is .001, and a blood test is 100%...
3) Suppose the probability of having a disease is .001, and a blood test is 100% effective in detecting the disease when the person has the disease. However, the test yields a "false positive" for 1% of healthy persons tested. What is the probability a person has the disease given that his test result is positive? Is the answer approximately a).44 b).01 c).09 d).90
Question 10: (10 marks) blood test is 95 percent effective in detecting a certain disease when it is, in fact, also...
Question 10: (10 marks) blood test is 95 percent effective in detecting a certain disease when it is, in fact, also yields a "false positive" result for 10 percent of the healthy persons A laboratory present. However, the test tested. (That is, if a healthy person is tested, then, with probability 0.10, the test result will imply he or she has the disease.) If 0.7 percent of the population actually has the disease, what is the probability a person has...
3. It is estimated that 2% of the meinbers of a certain population are infected with Hepatitis C virus. A diagnostic test for detecting Hepatitis C yields 4% false positive and 5% false negative results. (a) Find the probability that a person randomly chosen from this popu- lation has a positive result of the diagnostic test for Hepatitis C (b) Find the probability that a random person who has a positive result of the diagnostic test, actually has Hepatitis C.
3. It is estimated that 2% of the members of a certain population are infected with Hepatitis C virus. A diagnostic test for detecting Hepatitis C yields 4% false positive and 5% false negative results. (a) Find the probability that a person randomly chosen from this popu- lation has a positive result of the diagnostic test for Hepatitis C. (b) Find the probability that a random person who has a positive result of the diagnostic test, actually has Hepatitis C
3. It is estinated that 2% of the members of a certain population are infected with Hepatitis C virus. A diagnostic test for detecting Hepatitis C yields 4% false positive and 5% false negative results. (a) Find the probability that a person randomly chosen from this popu- lation has a positive result of the diagnostic test for Hepatitis C. Find the probability that a random person who has a positive result of the diagnostic test, actually has Hepatitis C. (b)
2. A rare disease affects 1% of the population. A test has a sensitivity of 98%, i.e., it will give a positive result 98% of the time that a person actually has the disease. The same test also has a specificity of 95%, i.e., it will give a negative result 95% of the time when a person does not have the disease. Denote the event that a randomly person has a disease by D, and the event that a randomly...
It has been found that 0.01% of the world population has a certain disease. If a person has the disease, there is a 95% chance they will test positive for the disease. If a person does not have the disease, there is a 5% chance they will test positive for the disease. (a) What is the probability that a person chosen at random will both have the disease and test positive? 0.000095 (or 9.5 x 10-5) (b) What is the...
Problem 1 [Sans R (a). Say a test can detect a disease with a type I error rate (false positive) of 10 % and a type II error rate (missed positive) of 0.1 %. If a person is randomly chosen from the population, the chance of having this disease is 0.1 %. If a random person is chosen from the population and tests positive for this disease, what is the probability they have this disease? (b). Say a test can...
3) Suppose the probability of having a disease is .001, and a blood test is 100% effective in detecting the disease when the person has the disease. However, the test yields a "false positive" for 1% of healthy persons tested. What is the probability a person has the disease given that his test result is positive? Is the answer approximately a).44 b).01 c).09 d).90
Question 10: (10 marks) blood test is 95 percent effective in detecting a certain disease when it is, in fact, also yields a "false positive" result for 10 percent of the healthy persons A laboratory present. However, the test tested. (That is, if a healthy person is tested, then, with probability 0.10, the test result will imply he or she has the disease.) If 0.7 percent of the population actually has the disease, what is the probability a person has...
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