Question

A rapid antigen flu test is the least accurate type of flu test. The test accuracy rate is approximately 60%. Assume that 14% of the population will have influenza this year, and we will test 1,200 people for influenza.

Complete the table below on your own paper, and answer the questions below.

Question 1: If you test negative for influenza, what is the probability that you do not have influenza? Round your answer to the hundredths place.

If you test positive for influenza, what is the probability that you do not have influenza? Round your answer to the hundredths place.

What is the probability a person will test positive for influenza? Round your answer to the hundredths place.

Answer 1

Answer: To complete the table and answer the questions, we need to consider the test accuracy rate, the prevalence of influenza in the population, and the total number of people tested.

Let's define the following:

TP = True Positive (tested positive and have influenza),

FP = False Positive (tested positive but do not have influenza),

TN = True Negative (tested negative and do not have influenza),

FN = False Negative (tested negative but have influenza).

Given:

Test accuracy rate = 60% (0.60),

Prevalence of influenza = 14% (0.14),

Total number of people tested = 1,200.

Now, let's calculate the values for the table:

Number of people who have influenza:

Influenza population = Prevalence * Total tested

Influenza population = 0.14 * 1200

Influenza population = 168.

Number of people who do not have influenza:

Non-influenza population = Total tested - Influenza population

Non-influenza population = 1200 - 168

Non-influenza population = 1032.

True Positive (TP):

TP = Test accuracy rate * Influenza population

TP = 0.60 * 168

TP = 100.8 (Approximately 101).

False Positive (FP):

FP = Non-influenza population - TN

FP = 1032 - TN

False Negative (FN):

FN = Influenza population - TP

FN = 168 - TP

True Negative (TN):

TN = Non-influenza population - FP

TN = 1032 - FP

Question 1:

If you test negative for influenza, the probability that you do not have influenza is TN / (TN + FP).

Probability (TN) = 1032,

Probability (TN + FP) = TN + FP = 1032 + FP.

Since the table is not complete, we do not have the exact value of FP. We can only calculate the probability if we know the value of FP.

Similarly, if you test positive for influenza, the probability that you do not have influenza is TN / (TN + FP). However, since the table is not complete, we cannot provide an exact value.

Question 2:

The probability a person will test positive for influenza is TP / (TP + FN).

Probability (TP) = 101,

Probability (TP + FN) = TP + FN = 101 + FN.

Again, since the table is not complete, we do not have the exact value of FN. We can only calculate the probability if we know the value of FN.