"Appropriate sample" is just another way of saying a reasonably good approximation of the population. The most basic significance tests (t-tests, ANOVAs, etc.) are extensions of z-scores, which take for granted knowledge of the population. Sample statistics are just ideally, approximately as good.
That said, most inferential statistics are flawed from the get-go. The logic behind "reject the null" fails to adequately take into account that there are multiple "alternatives" one can accept. However, data from the whole population is always superior from that taken from at best ideally representative samples of the population.
I believe that you do not have to make significance tests for the data taken from whole population when you want to do the one sample t-test for an example. But when you do other tests, such as paired sample t-test or independent samples t-test, you have to use the significance level, because you are not talking on one population.
I think the answer to your question depends on the goal of the research you're conducting. If you truly have data on every single individual in a population, and your goal is to simply describe the population, then you need no significance tests.
If your goal is to compare two groups within the population, and be able to say with certainty that there's a statistical difference between the groups, then you do need a statistical test.
You should also consider whether or not you need to determine statistical differences or meaningful differences. Many meaningful differences may not be statistically significant, and many statistical differences may not be meaningful in the real world.
The whole population is made up of gender and, may be, educational background, age etc. Supposing one wants to find, for instance, the variable which impacts most on conception of the whole population. The one will have to find the statistical differences existing within and between the groups. So, either it is a sample size or the whole population, everything will depend on the research questions/ hypotheses.