Question

A diagnostic test for a certain disease has 95% sensitivity and 95% specificity. Only 1% of the population has the disease in question. If the diagnostic test reports that a person chosen at random from the population tests positive, what is the conditional probability that the person does, in fact, have the disease? Are you surprised by the size of the answer? Do you consider this diagnostic test reliable?

Name: A diagnostic test for a certain disease has 95% sensitivity and 95% specificity. Only 1% of the population has the disease in question. If the diagnostic test reports that a person chosen at random from the population tests positive, what is the conditional probability that the person does, in fact, have the disease? Are you surprised by the size of the answer? Do you consider this diagnostic test reliable?
Uploaded: 2023-03-25T03:24:32-08:00
Duration: 4 min 35 s
Channel: Sri K

          A diagnostic test for a certain disease has 95% sensitivity and 95% specificity. Only 1% of the population has the disease in question. If the diagnostic test reports that a person chosen at random from the population tests positive, what is the conditional probability that the person does, in fact, have the disease? Are you surprised by the size of the answer? Do you consider this diagnostic test reliable?

A diagnostic test for a certain disease has 95% sensitivity and 95% specificity. Only 1% of the population has the disease in question. If the diagnostic test reports that a person chosen at random from the population tests positive, what is the conditional probability that the person does, in fact, have the disease? Are you surprised by the size of the answer? Do you consider this diagnostic test reliable?

Added by Sean R.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Sri K

03/25/2023

Step 1

Sensitivity: The probability that the test is positive given that the person has the disease is 95%. Mathematically, this can be written as P(T+|D+) = 0.95. Show more…

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A diagnostic test for a certain disease has 95% sensitivity and 95% specificity. Only 1% of the population has the disease in question. If the diagnostic test reports that a person chosen at random from the population tests positive, what is the conditional probability that the person does, in fact, have the disease? Are you surprised by the size of the answer? Do you consider this diagnostic test reliable?