Question

a medical manufacturer did a trial of a new virus screening test. 100,000 people took the test, and they already knew from other testing whether or not each person was infected with the virus.

	infected (i)	not infected (ni)
test negative (–)	5,400	75,200

the manufacturer wants the false positive rate, ( p(+ | ni) ) to be less than 0.04. if the false positive rate is greater than 0.04, they will create a new test.

the manufacturer (\boldsymbol{\text{will create a new test}}), because the false positive rate is (\boldsymbol{0.02}), which is less than 0.04 / (\boldsymbol{0.09}), which is greater than 0.04 / (\boldsymbol{0.23}), which is greater than 0.04) (select the correct option from the dropdown).

Explanation:

Step1: Calculate the false - positive rate

The false - positive rate \(P(+|NI)\) is calculated as the number of false - positives (people not infected but test positive) divided by the total number of non - infected people.
The number of non - infected people is \(1800 + 75200=77000\).
The number of false - positives (test positive among non - infected) is \(1800\).
So, \(P(+|NI)=\frac{1800}{77000}\approx0.0234\)

Answer:

\(0.02\), which is less than \(0.04\)