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MAT 274 - Benchmark 2

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Sandra Watson
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MAT 274 – Benchmark 2

1. 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 toldthat the blood test is 95 percent reliable, this means that the test will yield an accurate   positive result in 95% of the cases where the disease is actually present. Gestational diabetes affects 5+1=6 percent of the population in our patient’s age group, and that our
test has a false positive rate of 5+4=9 percent. Use your knowledge of Bayes’ Theorem  and Conditional Probabilities to compute the following quantities based on the information given only in part 2:
a. If 100,000 people take the blood test, how many people would you expect to test positive and actually have gestational diabetes?
b. What is the probability of having the disease given that you test positive?
c. If 100,000 people take the blood test, how many people would you expect to test negative despite actually having gestational diabetes?
d. What is the probability of having the disease given that you tested negative?
e. Comment on what you observe in the above computations. How does the prevalence of the disease affect whether the test can be trusted?

Fill in the conditional probability table here, then answer the questions in each part below:

Positive TestNegative TestTotal
Has GD0.95*6,000= 5,7003000.6*1,000= 6,000
Does Not Have GD0.9*100,000= 9,00085,00094,000
Total14,70085,300Overall Total: 100,000

V.  Comment on how prevalence of the disease affects your ability to trust the test. Discuss what factors would lead you to trust the blood test, or not trust the blood test.

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