Sample size will depend upon the expected prevalence proportion (p) that you want to estimate. use the formula n= [3.84 * p * (1-p)] / (l * l), where l is the allowable error in your estimate, taken usually as 10 to 20% of p. The value 3.84 corresponds to 95% confidence in your estimate. Replace it with square of 2.58, if you want 99% confidence. If sample is not a random sample, multiply by the design effect, taken usually between 1.5 and 2. If you expect some non-response from your study subjects, divide by the response rate proportion.

It depends on what testing you plan to do. You need to evaluate the power of such test. Why not use G*Power

http://www.gpower.hhu.de/en.html

The problem is too complex to be answered with broad generalizations like “20% of the population.” Some things to consider:

What is your population size? If the population is a few hundred, then you should sample the population. If the population is in the millions, then it is probably unrealistic to sample 20%.

What is your disease incidence? If you are trying to estimate a disease that afflicts 0.00001% of the population you need a different sample size than for a disease that afflicts 50%.

What accuracy do you need? Are you interested in a disease that affects 0.00001% of the population and you need this estimate accurate to 0.001% of the estimated mean? Or are you interested in a disease that affect 50% of the population and you are willing to accept any answer within 40% of this value?

An extension of the previous issue: what is the minimum difference that you want to detect. Do you care if males are infected 30% of the time and females are infected 20% of the time, and you cannot tell the difference? Do you care if males are infected 30.01% of the time and females 29.99% of the time? The latter will require a much larger sample size.

Another angle on same issue: Do you care if you fail to detect the disease and it is present? So the disease is present at 0.01%. I take a random sample of 10 individuals and I fail to detect the disease. No one should be surprised, because it would be very unlikely that a sample size of ten would detect the disease.

What is your experimental design?

Is this survey one question: Are you ill (  ) yes   (  ) no?

You could have a pooled design: What is your family size?  Followed by: Are you or anyone in your family currently ill?  (   ) yes   (  ) No

Alternatively, you could have fifty questions. Everything from age, income, gender, smoking, work environment, diet, etc….    What are the factors that increase disease risk?

Please play with GPower. It probably won’t answer your question, but it will help you understand the problem. Also try playing with the Excel macro pooledinfrate http://www.cdc.gov/westnile/resourcepages/mosqSurvSoft.html. This program was designed to estimate prevalence of disease in mosquitoes. It can deal with pooled samples, but works fine if pool size = 1. You can plug in numbers and see how confidence intervals change with changes in sample size.