Statistics Worksheet With Answers - Stat 200 (Page 6 of 6) in pdf

Statistics Worksheet With Answers - Stat 200 Page 6

5. No diagnostic tests are infallible, so imagine that the probability is 0.95 that a certain test will diagnose a

diabetic correctly as being diabetic, and it is 0.05 that it will diagnose a person who is not diabetic as

being diabetic. It is known that roughly 10% if the population is diabetic.

What is the probability that a person diagnosed as being diabetic actually is diabetic?

Hint: This is a use Bayes’ theorem problem, which we did not cover in the lectures. There is another

way to handle this problem – mack a mock 2 by 2 table of the data based on the information you already

know. Once the table is complete, you can solve for the conditional probability. Since some of the

probabilities are small, I would sugget you make a table that is based on 100,000 people. I have started

the table for you.

Test Results

Diabetes Status

Diabetic

Not Diabetic

Diabetic

9500

500

10,000

Not Diabetic

4500

85500

90,000

14000

86000

100,000

This is a conditional probability.

Given you are diagnosed as being diabetic, what is the probability that you actually are diabetic?

P(D|Test says D) = 9500/14,000 = .6786

Statistics Worksheet With Answers - Stat 200 Page 6