A psychiatric researcher wishes to evaluate a new diagnostic instrument for psychotic illness. The test is comprised of 20 questions regarding individual psychiatric symptoms.
A positive test is one in which a score of at least 16 of the 20 symptoms. The sensitivity of the test was determined to be 0.96, while the specificity is 0.99. The following gives the psychotic disease prevalence rates for two subpopulations of people:

General Population: 0.001

Homcless : 0.1

Compute predicitve values of a positive and negative test for each of the above subpopulations.

Suppose that predictive value of a positive test of greater than 0.5 is deamed acceptable. Under this criterion, what subpopulations should recieve the test.

Suppose that we have a sample of 1000 homeless with positive test results.

i. How many of those people do you expect to actually have psychotic illness?

 ii. How many of those people do you expect not to have psychotic illness?