Respuesta :
The overall accuracy of the screening test for a newly discovered disease is being evaluated for this case is 87.78% approximately.
What is the accuracy of a test?
Accuracy of a test is the ratio of the correct results to the total results the test gives.
Thus, we have:
[tex]\rm Accuracy =\dfrac{\text{Total number of correct results}}{\text{Total number of results}} = \dfrac{TP + TN}{TP + FP + TN + FN}[/tex]
where T represents True, F represents False, N represents Negative, and P represents Positive. The negativity and positivity are the results of the test.
For this case, we're specified that:
- The test is happening for diagnosis of a newly discovered disease.
- Total number of tests done = total number of workers administered = 900
- True positive (TP)= test result positive (ie test saying that the person has disease) when disease is actually present (that actual presense is known by some other method, and here we're evaluating the quality of 'disease testing procedure' in consideration) = 150 in count.
- False Negative (FP)= test result negative (no disease detected by the test) when person is diseased in reality = 60
- False positive (FN) = test result positive when person has no disease in reality = 50
- As total 900 tests were done, so we get: True negative(TN) = 900 - TP - FP - FN = 640
(as each test result would be one of the TP, TN, FP, FN and these four no test result can lie in more than one of these categories).
Now, we have:
true results = TP + TN = 640 + 150 = 790
total results = 900
Thus, we get:
[tex]\text{Test accuracy} = \dfrac{TP + TN}{TP + FP + TN + FN} = \dfrac{790}{900} \approx 0.8778 = 87.78%[/tex]
Thus, the overall accuracy of the screening test for a newly discovered disease is being evaluated for this case is 87.78% approximately.
Learn more about accuracy of a test here:
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