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

Answer:

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

Step-by-step 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:

$P(Negative|No\ Hepapatits\ C)=\frac{n(Negative\cap No\ Hepapatits\ C)}{n(No\ Hepapatits\ C)} \\=\frac{10}{1163}\\ =0.0086$

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)

                              $=1000\times0.0086\\=8.6$

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