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Chapter 3: Problem 66

A sample is given. Indicate whether each option is a possible bootstrap sample from this original sample. Original sample: 85,72,79,97,88 . Do the values given constitute a possible bootstrap sample from the original sample? (a) 79,79,97,85,88 (b) 72,79,85,88,97 (c) 85,88,97,72 (d) 88,97,81,78,85 (e) 97,85,79,85,97 (f) 72,72,79,72,79

Short Answer

Expert verified
(a), (b), (e) and (f) constitute possible bootstrap samples from the original sample. Sample (c) is not because number of values is less than original sample. Sample (d) is not because it contains values not present in the original sample.

Step by step solution

01

Evaluate sample (a)

Check if all of the values in sample (a) are present in the original sample. Also ensure sample (a) has the same number of values as the original sample. All values 79, 79, 97, 85 and 88 are present in the original sample and the count is also 5, which is equal to count of original sample. Hence this is a possible bootstrap sample.
02

Evaluate sample (b)

Check if all of the values in sample (b) are present in the original sample. Also ensure sample (b) has the same number of values as the original sample. All values 72, 79, 85, 88 and 97 are present in the original sample and the count is also 5, which is equal to count of original sample. Hence this is a possible bootstrap sample.
03

Evaluate sample (c)

Check if all of the values in sample (c) are present in the original sample. Also ensure sample (c) has the same number of values as the original sample. All values 85, 88, 97 and 72 are present in the original sample, but the count is 4, which is less than count of original sample. Hence this is not a possible bootstrap sample.
04

Evaluate sample (d)

Check if all of the values in sample (d) are present in the original sample. Also ensure sample (d) has the same number of values as the original sample. The values 81 and 78 are not present in the original sample. Hence this is not a possible bootstrap sample.
05

Evaluate sample (e)

Check if all of the values in sample (e) are present in the original sample. Also ensure sample (e) has the same number of values as the original sample. All values 97, 85, 79, 85 and 97 are present in the original sample and the count is also 5, which is equal to count of original sample. Hence this is a possible bootstrap sample.
06

Evaluate sample (f)

Check if all of the values in sample (f) are present in the original sample. Also ensure sample (f) has the same number of values as the original sample. All values 72, 72, 79, 72 and 79 are present in the original sample and the count is also 5, which is equal to count of original sample. Hence this is a possible bootstrap sample.

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