I don't know whether the study is valid or not.
I just want to point out that in the science of sampling, the sample size is independent of the population size - assuming that the sample is random, and the population is normally distributed.
Those are two BIG assumptions, which is why I can't comment on the study. I just want to point out that IF those assumptions are true, then 838 is a valid sample size.
COLIN POWELL can stop reading now.
Normally distributed means that STDs are found everywhere, and are just as likely to be found among north and south, east and west, urban and rural, young and old, rich and poor, educated and uneducated, moral and slutty, Black and white, etc.
We know this isn't true, because the study suggests that STDs are more common among Blacks than Whites, and more common among older women than teens. So, the study was limited to Black teens, thereby eliminating the race and age parameters. Problem is, what makes white teens different than Black teens? Unless it is something that no white teen has and all Black teens have, then there is reason to doubt that there is a normal distribution of Black teens.
For example, STD might be more common among Christian Black teens than among Muslim Black teens, or more common among Double Dutch jumpers than among Hop Scotch jumpers. If there is some correlation between STDs and some other factor besides race, then it is important that that other factor be uniformly distributed through the population. In my examples, the distribution of Christians is fairly uniform, while the distribution of Muslims is not. Similarly, Hop Scotch is played all over, while Double Dutch is not.
Back to sampling - the sampler has to ensure that the sample is random and normally distributed partly by taking enough samples in enough places in a random manner. The less confidence there is that the population distribution is random, the larger the sample size needs to be.
Without reading the actual study, I can't determine the validity of the study. Furthermore, the usual way to determine the validity of the study is to have someone else repeat the study and get the same results.
Call me when that happens.