Question

in 2022, a study at get well pediatrics found that 20% of its patients were allergic to pet dander. the study also showed that 20% of patients who were allergic to pet dander tested negative, while 5% of the patients who were not allergic tested positive. the relative frequency table summarizes the data.

	allergic to pet dander	not allergic to pet dander	total
negative	4%	76%	80%
total	20%	80%	100%

determine the ratio of false positives to true positives.

Explanation:

Step1: Identify false positives and true positives

False positives: patients not allergic to pet dander but tested positive. From the table, this is 4%.
True positives: patients allergic to pet dander and tested positive. From the table, this is 16%.

Step2: Calculate the ratio

Ratio of false positives to true positives = $\frac{\text{False Positives}}{\text{True Positives}} = \frac{4\%}{16\%} = \frac{4}{16} = \frac{1}{4}$

Answer:

$\frac{1}{4}$ (or 1:4)