Question

part 1 of 2
the following table shows the results for a cancer screening test with rats. what is the likelihood of getting false positives and false negatives for the data in the table? what risk does a false
value present? explain

the likelihood of a false positive is about
(round to the nearest tenth as needed.)
% , and the likelihood of a false negative is about
%

Explanation:

Step1: Calculate false positive rate

False positive is when a rat without cancer tests positive.
Formula: $\text{False Positive Rate}=\frac{\text{False Positives}}{\text{Total Rats without Cancer}}\times100\%$
False positives = 20, total rats without cancer = 150
$\text{False Positive Rate}=\frac{20}{150}\times100\%=\frac{2000}{150}\% \approx 13.3\%$

Step2: Calculate false negative rate

False negative is when a rat with cancer tests negative.
Formula: $\text{False Negative Rate}=\frac{\text{False Negatives}}{\text{Total Rats with Cancer}}\times100\%$
False negatives = 22, total rats with cancer = 712
$\text{False Negative Rate}=\frac{22}{712}\times100\%=\frac{2200}{712}\% \approx 3.1\%$

Answer:

The likelihood of a false positive is about $13.3\%$, and the likelihood of a false negative is about $3.1\%$