Bootstrap simulation and distribution of samples

#1
Hello everyone! I can not understand one thing about bootstrap method. Imagine I have a sample of 1000 measures of people's height. But I want to estimate a mean height of all country population. I decided to compute 1000 additional samples via bootstrap method (random choice with replacement) and count their mean values. So, will this sample distribution of sample mean will be normal? I think that not in all situations. So, the second question occurs. How we can find confidence interval? I have seen the variant with counting 2.5 and 97.5 percentiles to find 95% confidence interval.But I can not understand the logic of this process... How the mean value of sample means array will be related to the mean value of general sample if distribution of mean samples is not normal?
 

hlsmith

Less is more. Stay pure. Stay poor.
#2
You calculate the mean of your sample, that is the mean estimate of the target population. Next you conduct m simple random samples with replacement of the your sample (all being equal to the sample's n-value) and calculated the mean for each sample. Yes, that distribution of means serves as the possible mean distribution of the target population and the 2.5 and 97.5 percentiles serve as estimates of the 95% CI of the mean for the target population. The splendor of the BS is that it is a distribution of paramaters and, yes will be approxiamately normally distributed given you had enough BS samples. Height isnt a good example since it is usually normally distributed (based on a bunch of genes, environmental and epigenes conditions). Instead some thing skewed like length of hospital stays will better display how a dist can be skewed but the distribution of its parameters via BSing will be normal.