Question

Amedical research lab proposes a screening test for a disease. In order to try out this test, it is geiven to 100people 60 of whom are known to have the disease and 40 of whom are known not to have the disease. A positive test indicates the disease and a negative test indicates no disease. Unfortunately, such medical test can produce two kinds of error:
(1)A false negative test: for the 60 people who do have the disease, this screening test indicates that 2 do not have it.
(2)A false positive test: For the 40 people who do not have the disease, this screening test indicaites 10 do have it.

Answer 1

QUESTION IS: A: which of the false test do you think is more serious?
B: suppose the test is given to a person not in the original group of 100 people. It is not known whether this person has the disease but the test result is positive. What is the probability that the peroson really does have the disease?
C: suppose the test is given to a person whose disease status is unknown. If the test reslut is negative, what is the probability that the person does not have the disease?



thank you ...it is confused me ......x0x

Answer 2

A. A false negative is more serious, the reason being that a person with the disease who gets a false negative might not get more testing and the opportunity for early treatment might be missed.

B. For people who have the disease, the event 'false negative (FN)' and the event 'true positive (TP)' are mutually exclusive. Therefore
P(FN) + P(TP) = 1
From the results of the initial testing: P(FN) = 2/60 = 1/30
\[P(TP)=1-P(FN)=1-\frac{1}{30}=you\ can\ calculate\]

C. For people who do not have the disease, the event 'false positive (FP)' and the event 'true negative (TN)' are mutually exclusive. Therefore
P(FP) + P(TN) = 1
From the results of the initial testing: P(FP) = 10/40 = 1/4
\[P(TN)=1-P(FP)=1-\frac{1}{4}=you\ can\ calculate\]