My question revolves around the accuracy of a estimator which is obtained with bootstrap. This example is taken from "An introduction to bootstrap" Efron & Gong:

A small experiment, in which 7 out of 16 mice were randomly selected to recieve a medical treatment, while the remaning 9 were assigned to the non treatement group. Threatment was intended to prolong survivial after a test surgery. Did the treatment prolong surivival?

Let $\bar{x} = 86.86$ be mean of the threatment group and $\bar{y} = 56.22$ mean of the control-group.

the difference $\hat{\theta}= \bar{x} - \bar{y} = 30.63$. How accurate is these estimates?

Using bootstrap to estimate the standard error resulted in 28.93.

The argument that I dont understand is :

since 30.63/ 28.93 = 1.05 estimated standard errors greater than 0. therefore the results are insignificant.

The problem is that they are implicitly assuming that the expected value of $\Theta = \hat{X} -\hat{Y}$ is in fact $\hat{\theta}=30.63$ why?

The standard error,28.93, tells how far we would expect any realization from $\Theta$ are from its mean. The actual mean could in fact be, say, 55.


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