In a population of 500 people we have a test for a disease which is specific at 70% (it can detect a person as positive in 70% of the case, the remaining 30% the test indicate a positive person and in fact it is a false positive) but higly sensitive at 100% (if somebody is positive, there is no mistake in the test, no false negative). We estimate the prevalence of the disease to be 10% of the people. Alpha is 0.05 and beta is 0.95. What is the size sample to detect this disease in the population? I believe we can do this in DOE in JMP, but I am not sure of that and which test to use.