Five hundred people used a home test for a certain disease and then all underwen
ID: 3233135 • Letter: F
Question
Five hundred people used a home test for a certain disease and then all underwent more conclusive hospital testing. The accuracy of the home test was evidenced in the following table. (a) What is the predictive value of the test? Thai is, what is the probability that a person has the disease given they have received a positive test result? (b) What is the sensitivity of the test? That is, what is the probability of testing positive given that the person has the disease? (c) What is the specificity of the test? That is, what is the probability of testing negative given that the person does not have disease?Explanation / Answer
Solution:
(a) Observed the given table and conclueded that:
Probability that a person has the disease given they have received a positive test result = 35/500 = 0.07
Hence, the predictive value of the test is 0.07 or 7%.
(b)
The probability of testing positive given that the person has the disease = 35/40 = 0.875
Hence, the sensitivity of the test is 0.875 or 87.5%
(c)
The probability of testing negative given that the person does not have the disease = 25/460 = 0.054
Hence, the specificity of the test is 0.054 or 5.4%.
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