'Bootstrapping' is a really useful tool in Statistics that was developed relatively recently. Made possible with improved computing power, it is introduced in Section 3.3.Given the original sample data below, select which options are possible bootstrap samples that could have been selected from the original sample.There may be one or more correct answers. You must select all of the correct answers and none of the incorrect answers to gain full marks.Original Sample Data:[50,71,55,65,63] [64,66,51,72,55] [56,51,65,71,55] [72,64,51,56,66] [55,63,65,50,55] [56,51,64,71,55] [72,65,71,50,63] None above

The question is asking for possible bootstrap samples from the original sample data. Bootstrap sampling is a method that involves drawing samples from the original data, with replacement. This means that each time we draw a sample, it is put back into the original dataset before the next draw. Therefore, any sample that contains the same numbers as the original data, in any order, and possibly with repetitions, is a valid bootstrap sample.

Given the original sample data: [50,71,55,65,63]

The possible bootstrap samples could be:

[50,71,55,65,63] - This is the same as the original sample.

[64,66,51,72,55] - This is not a valid bootstrap sample because it contains numbers (64, 66, 51, 72) that are not in the original sample.

[56,51,65,71,55] - This is not a valid bootstrap sample because it contains numbers (56, 51) that are not in the original sample.

[72,64,51,56,66] - This is not a valid bootstrap sample because it contains numbers (72, 64, 51, 56, 66) that are not in the original sample.

[55,63,65,50,55] - This is a valid bootstrap sample. It contains numbers from the original sample and has repetitions, which is allowed in bootstrap sampling.

[56,51,64,71,55] - This is not a valid bootstrap sample because it contains numbers (56, 51, 64) that are not in the original sample.

[72,65,71,50,63] - This is not a valid bootstrap sample because it contains numbers (72) that are not in the original sample.

None above - This is not a valid answer because there are valid bootstrap samples in the options.

So, the correct answers are [50,71,55,65,63] and [55,63,65,50,55].