Question

QUESTION 5

1. Imagine a test that's 100% sensitive and 80% specific and it's testing for something that has a 5% chance of occurring. What's the chance that a test result will come back positive (remember, there are two ways to get a positive result: a true positive and a false positive). Express your answer as a value between 0 and 1 to two decimal places.

QUESTION 6

1. Suppose you're hiring a new worker for your business. You'd like someone reliable. Suppose you use administer a test to job-seekers many other employers use to determine if applicants have this trait. The test is 90% senstitive and 95% specific. If 60 unreliable people apply and 20 reliable people apply, how many positive results will you have?

QUESTION 7

1. Just like the last question, suppose you're hiring a new worker for your business. You'd like someone reliable. Suppose you use administer a test to job-seekers many other employers use to determine if applicants have this trait. The test is 90% senstitive and 95% specific. If 60 unreliable people apply and 20 reliable people apply, how many negative results will you have?

QUESTION 8

1. As Bayes' Theorem illustrates, when you're testing for a rare event (e.g. a rare disease), it's unlikely that a positive result will translate into a high likelihood that the event happened. This is true even for tests which seem very accurate. This counter-intuitive result only works for rare events; why?

   		Because it results in a lot of false negatives.
   		Because it results in a lot of false positives.
   		Because it causes specificity to fall.
   		Because it causes sensitivity to fall.

10 points   

1. Let's use the same numbers from the previous question again: 99% sensitive and 95% specific with 2% of employees on drugs. What the probability that an employee doesn't use drugs assuming the test came back negative? Express your answer as a probability from 0 to 1 to the 4th decimal place. Include a zero before the decimal point.

QUESTION 10

1. Suppose you're testing your employees for drug use. You decide to run a test which is 99% sensitive and 95% specific. If 2% of employees use drugs, what the probability that an employee uses drugs assuming the test came back positive? Express your answer as a probability from 0 to 1 to the 4th decimal place. Include a zero before the decimal point.

Answer 1