Bootstrap and testing hypotheses
We begin the bootstrap hypothesis testing problems with the t-test to compare means and the F-test to compare variances. It is understood that, since we are assuming normal distribution for the two populations under comparison, the distributional properties of the test statistics are well known. To carry out the nonparametric bootstrap for the t-statistic based on the t-test, we first define the function, and then run the bootstrap function boot on the Galton dataset. The Galton dataset is available in the galton data.frame from the RSADBE package. The galton dataset consists of 928 pairs of observations, with the pair consisting of the height of the parent and the height of their child. First, we define the t2 function, load the Galton dataset, and run the boot function as the following unfolds:
> t2 <- function(data,i) {
+ p <- t.test(data[i,1],data[i,2],var.equal=TRUE)$statistic
+ p
+ }
> data(galton)
> gt <- boot(galton,t2,R=100)...
