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I've been assigned this question as "homework":

Run a simulation study to examine the performance of the bootstrap for obtaining 95% confidence intervals on the mean of a univariate sample of data.

You should look at confidence interval coverage (what proportion of times does the confidence interval contain the true mean?) and Monte Carlo variation (by how much do the upper and lower confidence limits vary between simulations?).

You may choose which bootstrap methods to evaluate.

The confusing thing is that we've been given no data to use in our simulations. How would I interpret the assignment given this fact?

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    $\begingroup$ well, you could make it up... $\endgroup$ – conjugateprior Mar 24 '12 at 13:45
  • $\begingroup$ @ConjugatePrior I could make up a set of sample data, say ${1.0,2.0,2.5,3.5,4.7,5.9}$, then bootstrap with this. But what's the true mean of my sample data? $\endgroup$ – James Highbright Mar 24 '12 at 13:51
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    $\begingroup$ How would you 'make up' a sample of data whose true mean you knew? Hint: using a piece of software $\endgroup$ – conjugateprior Mar 24 '12 at 13:55
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    $\begingroup$ Right. rnorm in R would be an example. Next question: will making up one data sample be sufficient for your task? If the answer to this is obvious, you're off and running. $\endgroup$ – conjugateprior Mar 24 '12 at 14:06
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    $\begingroup$ Sounds like you're good to go. $\endgroup$ – conjugateprior Mar 24 '12 at 14:36

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