**Core Concept:** Hepatitis C virus (HCV) infection is a common cause of chronic liver disease. Hepatitis C serological tests are used to detect anti-HCV antibodies in the blood. The interpretation of test results depends on the prevalence of infection in the tested population.

**Why the Correct Answer is Right:**

In this question, we are dealing with the performance characteristics of a diagnostic test, specifically the sensitivity and specificity. **Option C** is correct:

- Sensitivity (true positive rate) = (number of true positives) / (number of true positives + false negatives) = (180) / (180 + 150) = 0.90 (or 90%)
- Specificity (true negative rate) = (number of true negatives) / (number of true negatives + false positives) = (150) / (150 + 180) = 0.80 (or 80%)

**Why Each Wrong Option is Incorrect:**

**Option A:** False positive rate (100% - sensitivity) = 100% - 90% = 10%
False positive rate means the proportion of false positives (patients who test positive but do not have the disease). In this case, only 10% of the patients tested positive but do not actually have hepatitis C.

**Option B:** False negative rate (100% - specificity) = 100% - 80% = 20%
False negative rate means the proportion of patients who test negative but actually have the disease. In this case, 20% of the patients tested negative but do have hepatitis C.

**Option D:** False positive rate X false negative rate = 10% X 20% = 2%
The calculation assumes that the false positive rate and false negative rate are independent of each other. In reality, they are not independent as the same patients may have both false positives and negatives (e.g., patients with liver diseases other than hepatitis C).

**Clinical Pearl:**

When interpreting diagnostic test results, it is essential to consider the prevalence of the disease in the population being tested. False positive and false negative rates are dependent on the prevalence of the disease in the population. False positive rate is high in low-prevalence populations, while false negative rate is high in high-prevalence populations.

**Correct Answer Explanation:**

A diagnostic test has a sensitivity of 90% and a specificity of 80%. This means the test has a high rate of correctly identifying patients with hepatitis C (90% sensitivity) and a lower rate of correctly identifying patients without hepatitis C (80% specificity).

**Correct Answer Explanation:**

The test has a sensitivity of 90% and a specificity of 80%. This means:
- The test correctly identifies 90% of patients with hepatitis C (90% sensitivity)
- The test correctly identifies 80% of patients without hepatitis C (80% specificity)

The test is **specific