when testing for a fever, what is the true positive rate for a thermometer that always reads 105 F? What is the false positive rate?
**Note: the definition of fever is that the patients temperature exceeds 100 F**
To determine the true positive rate and the false positive rate for a thermometer that always reads 105°F when testing for a fever, we need to understand the concepts of true positives and false positives in the context of diagnostic testing.
True Positives: These are the cases where the test correctly identifies the condition or attribute being tested for. In this case, a true positive would occur when the thermometer reads 105°F for a person with a temperature exceeding 100°F.
False Positives: These are the cases where the test incorrectly indicates the presence of the condition or attribute being tested for. In this case, a false positive would occur when the thermometer reads 105°F for a person with a temperature below or equal to 100°F.
Given that the thermometer always reads 105°F, we can conclude the following:
True Positive Rate: The true positive rate indicates the proportion of actual positives correctly identified by the test. Since a thermometer that always reads 105°F would correctly identify any person with a temperature exceeding 100°F, the true positive rate would be 100%.
False Positive Rate: The false positive rate indicates the proportion of negatives incorrectly identified as positives by the test. Since the thermometer always reads 105°F, it will incorrectly identify anyone with a temperature of 100°F or below as having a fever. Therefore, the false positive rate would also be 100%.
In summary, for this specific thermometer, the true positive rate is 100% and the false positive rate is also 100%. However, it is important to note that this value does not reflect real-world conditions and does not provide a reliable indication of a person's actual body temperature.