Question

Bootstrap Sample Given the sample data from Exercise 2, which of the following are not possible bootstrap samples?

a. 12, 19, 13, 43, 15

b. 12, 19, 15

c. 12, 12, 12, 43, 43

d. 14, 20, 12, 19, 15

e. 12, 13, 13, 12, 43, 15, 19

Short answer

Parts b, d, and e are not possible bootstrap samples.

Step-by-step solution

Given information

Refer to Exercise 2, for the American Airlines flights leaving JFK airport, the sample of taxi-out times (min) is taken is given as:12, 19, 13, 43, 15

Describe the criteria of the bootstrap sample

Criteria of bootstrap sampling are stated as follows:

1. The sample size of the bootstrap sample needs to be the same as the sample size of the original data set.

2. The bootstrap sample should be drawn with replacement from an original sample.

3. All the observation values of the bootstrap sample should come from an original data set.

Check whether the samples are possible bootstrap samples or not

The original sample is 12, 19, 13, 43, 15, and the sample size of this sample is 5.

a. The given sample is 12, 19, 13, 43, 15 and sample size of this sample is 5.

The given sample is the same as the original sample. More importantly, the sample size is the same as the sample size of the original data and all the numbers are taken from the original data set.

Therefore, this is a bootstrap sample.

b. The given sample is 12, 19, 15 and the sample size of this sample is 3.

All the numbers of this sample are taken from the original data set but the sample size of this the sample is not the same as the original sample.

Therefore, this is not a bootstrap sample.