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If a farmer's new mastitis test has a sensitivity and specificity of 90% with a disease prevalence of 5%, what is the approximate negative predictive value (NPV) of the test?

35%

99%

To determine the approximate negative predictive value (NPV) of a diagnostic test, one must consider the sensitivity, specificity, and disease prevalence.

In this case, the test has a sensitivity of 90%, meaning that it accurately identifies 90% of cows with mastitis (true positives). The specificity is also 90%, indicating that it correctly identifies 90% of cows without the disease (true negatives). The disease prevalence is 5%, which indicates that 5% of the population has mastitis.

To find the NPV, you can use the following method:

1. Calculate the prevalence in the sample population. For a sample size of 100 (for easy calculations):

- Number of true positives (TP): 5% of 100 = 5 cows with mastitis.

- Number of true negatives (TN): 95% without disease = 95 cows without mastitis.

2. Calculate the expected results from the test:

- True positives: 90% sensitivity of 5 infected cows = 4.5 true positives.

- False negatives: 10% of 5 infected cows = 0.5 false negatives.

- True negatives: 90% specificity of 95 non-in

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3%

72%

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