Consider the following sample of four measurements {2,5,11,14}.Five bootstrap samples of this sample produced the following resamples: {2,5,5,14},{5,11,11,11},{2,11,14,14},{2,2,14,14},
{5,5,11,14}.Based on these five resamples,find the bootstrap of the standard error of the sample mean.
A)0.6452
B)4.5667
C)8.6
D)1.4427
E)2.0813

Question

Quizplus · Accepted Answer

To calculate the bootstrap standard error of the sample mean, we need to find the standard deviation of the sample means of each resample. 
The sample means for each resample are as follows:
- {2,5,5,14}: mean = 6.5
- {5,11,11,11}: mean = 9.5
- {2,11,14,14}: mean = 10.25
- {2,2,14,14}: mean = 8
- {5,5,11,14}: mean = 8.75

Next, we calculate the standard deviation of these means:
sd = sqrt(((6.5-8.4)^2 + (9.5-8.4)^2 + (10.25-8.4)^2 + (8-8.4)^2 + (8.75-8.4)^2)/4) = 1.4427

Therefore, the answer is D) 1.4427.

Consider the Following Sample of Four Measurements {2,5,11,14}