To develop an intuition as to how the t-test can confirm and calculate these statistics from so little data, we can apply an approach called resampling. Resampling is based on the premise that each sample is just one of an infinite number of possible samples from a population. We can gain an insight into the nature of what these other samples could have been, and therefore have a better understanding of the underlying population, by taking many new samples from our existing sample.
There are actually several resampling techniques, and we'll discuss one of the simplest—bootstrapping. In bootstrapping, we generate a new sample by repeatedly taking a random value from the original sample with replacement until we generate a sample that is of the same size as the original. Because these values are replaced between each random selection, the same source value can appear multiple times in the new sample. It is as if we were drawing a random card from a deck of playing cards repeatedly...
