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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.

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If you knew that your data came from a normal distribution, you could use the sample variance and apply the usual confidence interval approach for the population mean (why don't you look it up and learn about it?). But, given that you don't know what distribution the population has and you have a small sample, bootstrapping is a good option.

Yes, this example seems somewhat contrived, but in applied work with small samples bootstrapping is a handy tool to know about.

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  • $\begingroup$ It makes sense that for many distributions we can calculate a confidence interval for the population mean from a sample. My question was about how the bootstrap result compares to quantities that we can calculate directly without resulting to taking random samples many times and combining those results. $\endgroup$ – nonagon Oct 17 '15 at 22:48
  • $\begingroup$ Try this: assume the data from your example do come from a normal population. Find the traditional confidence interval on the population mean and compare to the bootstrapped interval. $\endgroup$ – soakley Oct 18 '15 at 2:00

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