Question

Positive Test Result Negative Test Result

Hepatitis C 335 10
No Hepatitis C 2 1153

Based on the results of this study, how many false negatives should you expect out of 1000 tests

Answer 1

In a sample of 1000 test the expected number of false negatives is 8.6.

Explanation:

The table provided is:

Positive Negative TOTAL

Hepatitis C 335 10 345

No Hepatitis C 2 1153 1155

TOTAL 337 1163 1500

A false negative test result implies that, the person's test result for Hepatitis C was negative but actually he/she had Hepatitis C.

Compute the probability of false negative as follows:

`P(Negative|No\ Hepapatits\ C)=(n(Negative\cap No\ Hepapatits\ C))/(n(No\ Hepapatits\ C)) \\=(10)/(1163)\\ =0.0086`

Compute the expected number of false negatives in a sample is n = 1000 tests as follows:

E (False negative) = n × P (Negative|No Hepatitis C)

`=1000*0.0086\\=8.6`

Thus, in a sample of 1000 test the expected number of false negatives is 8.6.