# Question: the results for a blood test for a certain disease...

###### Question details

The results for a blood test for a certain disease are shown.

Blood Test

Sick POS NEG Total

Yes 34 5 39

No 1025 3795 4820

Total 1059 . 3800 4859

a. Estimate the probability that the sickness occurs.

b. Find the estimated (i) sensitivity P(POS|Yes), (ii) specificityP(NEG|No).

c. Find the estimated (i) P(Yes|POS), (ii) P(Yes| NEG)

d. Explain how the probabilities in parts b and c give four ways of describing the probability that a diagnostic test makes a correct decision.

a. The probability is approximately

b. (i) The sensitivity is approximately

(ii) The specificity is approximately

c. (i) P(Yes POS)=

(ii) P(No NEG)=

d. Describe the probabilities below. Options: one would not have the disease if the test is negative, the test would be positive if one has the disease, the test would be negative if one does not have the disease, or one would have the disease if the test is positive.

The probability in b-i is that

The probability in b-ii is that

The probability in c-i is that

The probability in c-ii is that