Consider the following sample of three measurements {4,8,13}.Five bootstrap samples of this sample produced the following resamples: {4,8,8},{4,4,13},{4,8,13},{8,8,8},{8,13,13}.Based on these five resamples,find the bootstrap of the standard error of the sample median.
A)3.1937
B)1.4283
C)8.2
D)5.2222
E)10.2

Question

Quizplus · Accepted Answer

The bootstrap standard error of the sample median is the standard deviation of the bootstrap distribution of the sample median. The bootstrap distribution of the sample median is the distribution of the sample medians that would be obtained if we were to repeatedly resample the original sample with replacement. The bootstrap standard error of the sample median can be estimated by taking the standard deviation of the bootstrap resamples. In this case, the bootstrap resamples are {4,8,8},{4,4,13},{4,8,13},{8,8,8},{8,13,13}. The sample medians of these resamples are 8,4,8,8, and 10.5, respectively. The standard deviation of these sample medians is 3.1937. Therefore, the bootstrap standard error of the sample median is 3.1937.

Consider the Following Sample of Three Measurements {4,8,13}