30 CHAPTER 2 Sampling from Populations1 is A
2 is B
3 is C
4 is D
5 is E
6 is FThe variable of interest is the patient ’ s age, so again:
A is 26
B is 17
C is 45
D is 70
E is 32
F is 9A bootstrap sample will sample six times with replacement from
the six patients, and mean age will be computed for each bootstrap
sample. There are 6^6 = 46,656 possible bootstrap samples when order
is counted. This is a little too much for a human to handle, but not so
large to cause diffi culty for today ’ s computers. To get the bootstrap
distribution for the mean, we would enumerate all 46,656 possible
bootstrap samples get the age distribution for each of these bootstrap
samples. For each bootstrap sample we compute, its mean and the set
of all 46,656 means provides the bootstrap sampling distribution for
the mean. This is very tedious and unnecessary.
We can get a good approximation of the distribution from just 100
to 1000 randomly selected bootstrap samples. The number of randomly
selected bootstrap samples is often denoted as B. That approach is what
we call the Monte Carlo approximation to the bootstrap distribution.
For illustrative purposes, we will take B = 10 even though in practice
the number B needs to be much larger to get a good approximation to
the bootstrap distribution. The random numbers and the corresponding
patients and ages for the ten bootstrap samples are as follows: