Suppose next that we have even less knowledge of our patient, and we are only given the accuracy of the blood test and prevalence of the disease in our population. We are told that the blood test is 94 percent reliable, this means that the test will yield an accurate positive result in 94% of the cases where the disease is actually present. Gestational diabetes affects 4+1 percent of the population in our patient’s age group, and that our test has a false positive rate of 4+4 percent. Use your knowledge of Bayes’ Theorem and Conditional Probabilities to compute the following quantities based on the information given only in part 2: If 100,000 people take the blood test, how many people would you expect to test positive and actually have gestational diabetes? What is the probability of having the disease given that you test positive? If 100,000 people take the blood test, how many people would you expect to test negative despite actually having gestational diabetes? What is the probability of having the disease given that you tested negative? Comment on what you observe in the above computations. How does the prevalence of the disease affect whether the test can be trusted?
Suppose next that we have even less knowledge of our patient, and we are only given the accuracy of the blood test and prevalence of the disease in our population. We are told that the blood test is 94 percent reliable, this means that the test will yield an accurate positive result in 94% of the cases where the disease is actually present. Gestational diabetes affects 4+1 percent of the population in our patient’s age group, and that our test has a false positive rate of 4+4 percent. Use your knowledge of Bayes’ Theorem and Conditional Probabilities to compute the following quantities based on the information given only in part 2: If 100,000 people take the blood test, how many people would you expect to test positive and actually have gestational diabetes? What is the probability of having the disease given that you test positive? If 100,000 people take the blood test, how many people would you expect to test negative despite actually having gestational diabetes? What is the probability of having the disease given that you tested negative? Comment on what you observe in the above computations. How does the prevalence of the disease affect whether the test can be trusted?
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section: Chapter Questions
Problem 27T
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- Suppose next that we have even less knowledge of our patient, and we are only given the accuracy of the blood test and prevalence of the disease in our population. We are told that the blood test is 94 percent reliable, this means that the test will yield an accurate positive result in 94% of the cases where the disease is actually present. Gestational diabetes affects 4+1 percent of the population in our patient’s age group, and that our test has a false positive rate of 4+4 percent. Use your knowledge of Bayes’ Theorem and Conditional Probabilities to compute the following quantities based on the information given only in part 2:
- If 100,000 people take the blood test, how many people would you expect to test positive and actually have gestational diabetes?
- What is the probability of having the disease given that you test positive?
- If 100,000 people take the blood test, how many people would you expect to test negative despite actually having gestational diabetes?
- What is the probability of having the disease given that you tested negative?
- Comment on what you observe in the above computations. How does the prevalence of the disease affect whether the test can be trusted?
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