The various answers in this thread reveal that we, as a community, use self-study for multiple purposes, of which the major ones are:
To signal a desire for conceptual help and hints rather than a full answer.
To acknowledge that the question comes from a textbook or exam.
To serve as a search term.
One discussion we could--and probably should have--concerns the merits of splitting self-study into categories along such lines. However, I'm interested in something a little different:
As a moderator, what I care most about is having the ability quickly and firmly to close peremptory or artificial questions.
A peremptory question is one that demands a particular answer: true/false, multiple choice, state a formula, etc. IMHO, those are of no interest; they almost surely have answers on the site already; and allowing them to stand would rapidly litter this site with tens of thousands of threads that reduce its value.
An artificial question is one with no context or background. It is typically fabricated as a routine exercise of an elementary concept and often requires a near-mindless application of some mathematical procedure. There is no possibility of exploring statistical issues concerning how the data were obtained, how they were measured, what decisions will be made from them, etc. As such these questions are stripped of all intrinsic interest and are just math problems in disguise.
These are intrinsic qualities of the questions: my descriptions make no reference to who might be asking them or what their motivation might be. (It sometimes takes a brief conversation via comments to establish that a question truly is artificial. The key is that the OP is unable to provide any clarifying information: "this is what my teacher said" or "that's all the textbook has" are the usual responses.)
There are mitigating circumstances. Such a question that has been augmented by a description of approaches the OP has taken to solve it by virtue of that unique, personal description can thereby become new, interesting, and on-topic.
The option we currently have to close questions as "self-study" has served well to explain the reasons for closing them. I think it is important that we continue to have some version of this reason for closure and that we continue to make it clear that such questions are unwelcome.
One thing we need to be cautious about is unilateral tagging: sometimes a genuine statistical question is originally phrased in a peremptory or overly abstract form. (This is relatively rare but it happens.) Our policy always has been to respect the OP and not apply the self-study tag ourselves. However, whether or not that tag has been applied, if a question clearly is peremptory or artificial, I do not hesitate to close it.
Maybe, then--to answer the original question in this thread--we should not be too concerned about applying the self-study tag, but should focus instead on how best to address the question itself, whether by answering, editing, commenting, or closing.