Click on nine stick people to randomly select nine males from the population
Only 18% of you got the population median (the median weight of all males) correct using the sample median as an estimate. Since you don't know who got it correct or not, is it a safe bet that your estimate is "correct"?
To increase our chances of "hitting the target", we want to use an interval estimate for the median weight of all the males, rather than just using the point estimate (the sample median), but how do we know what numbers to use for the interval?
Bootstrapping to the rescue!
We can use the bootstrap method to estimate the extent of the variation between the sample medians from this population (all the male weights) to get a measure of how far "off" we could be from the true population median. We'll take your original sample and sample with re-placement nine times to create a re-sample, and then record the median of this re-sample. We'll then repeat this re-sample process 1000 times to get 1000 re-sampled medians (the bootstrap distribution).
We'll then chop off the bottom 2.5% and the top 2.5% of the re-sample medians (the bootstrap distribution), and use the middle 95% of the bootstrap distribution to construct our interval.
Now 96% of you got the population median (the median weight of all males) correct using a bootstrap confidence interval (an interval estimate)! You still don't know who got it correct or not, but it's a fairly safe bet that your interval estimate is "correct" (correct in that the interval contains the true population median, the median weight of all males).
Because we know you are dying to know what the population median (the median weight of all males) was .....
See 96% (96/100) of the bootstrap confidence intervals constructed from different samples and medians covered the population median (the median weight of all males) of 70kg. Our confidence in a particular interval comes from the fact that the method (bootstrapping) works most of the time.