Suppose that a new rapid eld test for Type II diabetes has the following properties. (During test development, these properties were veried with more extensive testing.)

P (test indicates Type II diabetes | person actually has Type II diabetes) = 0.90 P (test indicates Type II diabetes | person actually does not have Type II diabetes) = 0.05

Suppose that 20% of individuals in a certain population have Type II diabetes.

1. Draw the appropriate tree diagram and nd the probability that the test indicates a randomly chosen person from this population has Type II diabetes. Attach the tree diagram

2. Show the details for the calculation of P(test +). Show full working including text/calculations.

3. Find the probability that a person really does have Type II diabetes given the test indicates that the person has Type II diabetes. Provide full explanation as to how you got the answer; give the formula and show all intermediate steps.

4. Find the probability that a person really does not have Type II diabetes given the test indicates that the person has Type II diabetes. Provide full explanation as to how you got the answer; give the formula and show all intermediate steps.

5. What is the probability that the test indicates a randomly chosen person from this population does not have Type II diabetes? Show full working including text/calculations.

6. Find the probability that a person really does have Type II diabetes given the test indicates that the person does not have Type II diabetes. Provide full explanation as to how you got the answer; give the formula and show all intermediate steps.