I'm just learning about bootstrapping, and I'm trying to build up some intuition for when it's appropriate. I found an example here which describes a procedure to obtain a 90% confidence interval about the population mean (I assume there's a typo in the article, since it says "sample mean"), where the sample consists of the numbers:
1, 2, 4, 4, 10
I see that one can sample with replacement some large number of times, and then look at the distribution of means that results. My question is whether there's a simpler way to answer that question in this case. For example how does the result from this bootstrapping procedure relate to the sample variance (12.2) which we can calculate directly?
I understand that there are many cases where we can't directly compute a quantity of interest, but we can readily apply the bootstrapping procedure to estimate it. I'm just trying to understand how contrived some of the examples I'm reading about are.