Answer :
Bootstrap sampling involves creating new samples from an existing data set that can include repeated values from that set. For the given data, samples (a), (b), and (d) are correct bootstrap samples because they only include values from the original data set.
The subject of this question is bootstrap sampling, which is a statistical technique used to estimate properties of an estimator (e.g., its variance) by resampling from the given data. Each bootstrap sample should consist of a random selection from the original data set, with the possibility of the same data point being selected more than once. For this problem, the sample is the set of male heights given: 62, 63, 65, 66, 70, 75.
The key point to notice here is that each bootstrap sample must contain only values from the original data. Therefore options (a), (b), and (d) are possible bootstrap samples, as they consist of values from the original data set. (c) and (e) cannot be bootstrap as they contain values (73 and IRRI respectively) not found in the original data set.
The options (a), (b), and (d) could be possible bootstrap samples for the given data. This answer in 100 words is that a bootstrap sample for a given set of data should contain only values from that data set, and can include repetitions.
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