Question

Select ALL of the following that are possible bootstraps of an original sample:

a.(7.-8. 5.7.7,5)
(b. 5,7,7,8,5,7)
c. {5.7.-8,5,5,7)
d. (5,5-9,7,5,7)
e.None of the above

Answer 1

All options except for d are valid bootstrap samples of the original sample (7, -8, 5, 7, 7, 5), as they consist of the same values, arranged or repeated any number of times. Option d is incorrect because it includes a value not present in the original sample.

Step-by-step explanation:

The question asks us to select all possible bootstraps of an original sample. Bootstrap is a statistical method that resamples a single dataset to create many simulated samples. This is often used to estimate the distribution of an estimator like the sample mean or sample variance. In bootstrapping, samples are taken with replacement, meaning that the same value can appear multiple times in a bootstrap sample.

Considering the original sample (7, -8, 5, 7, 7, 5), a valid bootstrap sample could include any arrangement and repetition of these numbers. Thus, options a, b, and c from the given dataset are all valid bootstrap samples since they consist of the same values that are present in the original dataset, repeated any number of times.

Therefore, the correct answer is e. None of the above, because all of the given options (a, b, and c) are indeed possible bootstraps of the provided original sample. Option d contains the number -9, which is not present in the original sample, therefore it is not a valid bootstrap sample.