<p>The key difference here is that the asker's intention was to get maths help. The asker knew how to compute a confidence interval. They were asking how to solve for $\theta$ in an equation. As you say, it's a lot of work to come up with general rules, but I can see a couple of guidelines that would help you here. </p>

<p>Firstly, think about the type of person who is best suited to answering that question. On the one hand, it's possible that someone who uses statistics often might not know how to solve for $\theta$ in that problem. They might use a solver program instead. Lots of statisticians would be able to solve it, but there's no branch of statistics where that kind of manipulation is fundamental. On the other hand, solving an equation involving surds and powers of $\theta$ is an important skill in mathematics. There are areas of mathematics where an ability to solve a problem like that is a prerequisite. So one criterion might be that a question is only relevant on CrossValidated if the required technique for solving the problem is more important in statistics than in other branches of mathematics. </p>

<p>Secondly, think about what the most likely answer is, and think about how you could generalise that answer. In this case, the asker is asking for an algorithm for solving an equation in one unknown involving surds. That could generalise to other equations involving surds, but it couldn't generalise, for example, to solving for parameters given a boundary of the confidence interval if the equation for that endpoint of the confidence interval doesn't involve surds. The answer is going to be more applicable to other algebra problems than it will be to other confidence interval problems. So again, it belongs with the other algebra questions. </p>

<p>There's a lot of information that's relevant to statistics in Glen_b's answer, but most of that information isn't actually answering the question. He's providing warnings about things the asker might have overlooked. This is useful information, but the asker's intention wasn't to get that information - if it was, the question would have had an explicit "Is this a statistically valid method?" part to it. </p>
