Question

It is estimated that approximately 8.1% of Americans are afflicted with diabetes. Suppose that a certain diagnostic evaluation for diabetes correctly diagnoses 95% of all adults over 40 with diabetes as having the disease and incorrectly diagnoses 3.5% of all adults over 40 without diabetes as having the disease. Use this information and a theoretical group of 10,000 Americans to construct a table for this testing scenario. Round all answers and results to two decimal places. Test Positive Test Negative Total Have Diabetes Do not have Diabetes Total 10,000 What percentage of Americans who test positive for diabetes would we expect to actually have the disease? What percentage of Americans who test negative for diabetes would we expect to actually have the disease? What percentage of Americans who test positive will not have the disease?

Answer 1

Answer:

Multiple answers

Step-by-step explanation:

Considering that 8.1% of Americans have the disease:

If our theoretical group is of 10,000. We know that the 8.1% of our group have diabetes, so we multiplify 10,000 × .081(the percentaje) = 810. This is the total of adults in our group that have diabetes.

Now:

• Test Positive:

1. We know that the test correctly diagnoses 95% of adults with diabetes. In our case the total of adults with diabetes is 810, so we multiplify 810 × .95(percentaje) = 769.50.  
2. We know too that the test incorrectly diagnoses 3.5% of the adults. In our case the total of adults with diabetes is 810, so we multiplify 810 × .035(percentaje) = 28.35.
3. The total of adults the test diagnoses positive with diabetes should be the correctly and incorrectly we calculate previously. 769.50 + 28.35 = 797.85

• Test Negative:

1. The total of test negative diagnoses should be the total of our group less the positive diagnoses. 10,000 - 797.85 = 9,202.15

• Total do not have diabetes:

1. The total of adults do not have diabetes is the total of our group less the total of adults in our group that have diabetes. 10,000 - 810 = 9190

We expect that only the 95% of test positive for diabetes have the disease.

1. 810 × .95(percentaje) = 769.50.

We expect that only the 5% (100% - 95% of test positive) of the 8.1% of americans afflicted with diabetes of negative test actually have the disease. 8.1 × .05(percentaje) = .40%, 9,202.15 ×.004(percentaje) = 36.80.

The 3.5% of Americans who test positive will not have the disease because this is the percentaje that the test incorrectly diagnoses.