Question

QUESTION)

The herpes simplex virus that causes cold sores, HSV-1, is surprisingly common. In fact, it's estimated that approximately 68% of adult Americans are carriers. One test for the virus has a sensitivity of 75% and a specificity of 98%. A researcher plans to study medical records of 10,000 Americans who have been tested for HSV-1.

How many of the 10,000 medical records were true positive results?

QUESTION)

The herpes simplex virus that causes cold sores, HSV-1, is surprisingly common. In fact, it's estimated that approximately 68% of adult Americans are carriers. One test for the virus has a sensitivity of 75% and a specificity of 98%. A researcher plans to study medical records of 10,000 Americans who have been tested for HSV-1.

How many of the 10,000 medical records were true negative results?

QUESTION)

The herpes simplex virus that causes cold sores, HSV-1, is surprisingly common. In fact, it's estimated that approximately 68% of adult Americans are carriers. One test for the virus has a sensitivity of 75% and a specificity of 98%. A researcher plans to study medical records of 10,000 Americans who have been tested for HSV-1.

If a person tests positive for carrying the HSV-1 virus, what's the probability that they are actually a carrier?

Leave your answer in decimal form and round it to 4 decimal places.

QUESTION)

The herpes simplex virus that causes cold sores, HSV-1, is surprisingly common. In fact, it's estimated that approximately 68% of adult Americans are carriers. One test for the virus has a sensitivity of 75% and a specificity of 98%. A researcher plans to study medical records of 10,000 Americans who have been tested for HSV-1.

If a person tests negative for carrying the HSV-1 virus, what's the probability that they are actually a carrier?

Leave your answer in decimal form and round it to 4 decimal places.

Please. show me your all works. Thanks.

Answer 1

The sensitivity is 75% and the specificity is 98%

Positive Test percentage is 68%.

Let a be true positive

b be false positive

c be false negative

d be true negative

In order to calculate the true positive we have the followinf equations

0.68 = a+b

0.75 = a/(a+c)

0.98 = d/(b+d)

a+b+c+d = 1

Solving the 4 equations we have

a = 0.6781

Out of 10000 Americans who have been tested HSV-1 the number of true positives are 6781.

The true negative is d can be solved using the above equations as 0.0931

Thus, out of 10000 Americans who have been tested HSV-1 the number of true negatives are 931.

If the test actually tested positive then the probability that they are actually a carrier is

0.6781/0.68 = 0.9972

If a person tests negative then the probability that they actually are a carrier is

0.2269/0.32 = 0.7091