We have seen that the bootstrap entails sampling with replacement from the original obse...

We have seen that the bootstrap entails sampling with replacement from the original observations.

a. If the original sample is of size n, how many samples with replacement are there?

b. Suppose for pedagogical purposes that n = 3 and we have the following observations: 1, 3, 4. List all the possible samples with replacement.

c. Now suppose that we want to find the bootstrap distribution of the sample mean. For each of the preceding samples, calculate the mean and use these results to construct the bootstrap distribution of the sample mean.

d. Based on the bootstrap distribution, what is the standard error of the sample mean? Compare this to the usual estimated standard error,