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, we need to understand the concepts of true positive, false positive, and the definition of fever.
- True positive: In this context, a true positive occurs when the thermometer correctly identifies someone with a fever (temperature exceeding 100 F) as having a fever.
- False positive: A false positive happens when the thermometer incorrectly identifies someone without a fever as having a fever.
In the given scenario, the thermometer always reads 105 F.
Since the definition of fever is a temperature exceeding 100 F, it is clear that the thermometer will always show a higher temperature than the threshold for fever. Therefore, in this scenario, there will be no false negatives (people with a fever who are wrongly identified as not having a fever).
However, the false positive rate will be 100%. This is because a false positive is defined as the proportion of people without a fever who are wrongly identified as having a fever. In this case, the thermometer always reads 105 F, regardless of whether the person actually has a fever or not. So, even individuals without a fever will be identified as having a fever, resulting in a false positive rate of 100%.
To summarize:
- True positive rate: 100% (as there will be no false negatives)
- False positive rate: 100%