Question

a medical test 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.

the manufacturer wants the false negative rate, p(-|i)) to be less than 0.03. if the false positive rate is greater than 0.03, they will create a new test.
will they need to create a new test?

the manufacturer
☑️ create a new test, because the false negative rate is

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

	will need to	will not need to

Explanation:

Step1: Calculate the false negative rate

The false negative rate \(P(-|I)\) is calculated by the formula \(P(-|I)=\frac{\text{Number of False Negatives}}{\text{Total Infected}}\).
The number of false negatives is \(5400\), and the total number of infected people is \(17600 + 5400=23000\).
So \(P(-|I)=\frac{5400}{23000}\approx0.235\)

Step2: Compare with the required rate

Since \(0.235> 0.03\) (the required rate for false negative rate to not create a new test), the manufacturer will need to create a new test.

Answer:

The manufacturer will need to create a new test.