Question

Assume that there is a test for a person having antibodies for COVID-19 disease. Let A denote a

test result that shows that a person has antibodies for COVID-19 disease.

Let B denote that a person truly has antibodies for COVID-19. Such a person is thought to be

immune to again contracting and spreading COVID-19 because that person already had the

disease.

Assume that the sensitivity of a test for antibodies is .938 and that the specificity of the test

is .956.

Here is what I would like you to do:

1. In the first column in Excel, create a column for Pr(B) -- this probability denotes the fraction

of the general population that has antibodies. The first entry in this column is 0 and increase this

value by .01 in successive rows until you reach 1.00. That is, the entries in the first column are 0,

.01, .02, .03, ..., .99, 1.00.

2. In the second column in Excel, use Bayes Theorem to compute Pr(B|A) for all of the rows in

the first column.

3. Use the graphing tool in Excel to create a graph with the first column values on the horizontal

axis and the second column values on the vertical axis.

4. What is the probability that a person truly has antibodies given that a test shows the person has

antibodies when

5% of the population has antibodies ____________?

10% of the population has antibodies ___________?

20% of the population has antibodies ___________?

40% of the population has antibodies ___________?

80% of the population has antibodies ___________?

There is no summary answer sheet for this assignment; just highlight the appropriate rows in

Excel in yellow that answer the foregoing questions. Also, make sure your Excel file has the

graph I asked you to create in Excel.

5. Redo everything above but with sensitivity of .90 and specificity of .80. Put your work in the

third and fourth columns in Excel and draw a new graph. Now, what is the probability that a

person truly has antibodies given that a test shows the person has antibodies when

5% of the population has antibodies ____________?

10% of the population has antibodies ___________?

20% of the population has antibodies ___________?

40% of the population has antibodies ___________?

80% of the population has antibodies ___________?

Highlight the appropriate rows in Excel in light blue that answer the foregoing questions.

6. At the bottom of your spreadsheet, write a few sentences indicating what we must know in

order to make accurate statements about the question: What is the probability that a person truly

has antibodies given that a test shows the person has antibodies?

Answer 1

a)Sensitivity=0.938, Specificity=0.956

b)Sensitivity=0.9, Specificity=0.8