College

A random sample of 5 heights (in inches) are 58, 65, 67, 70, and 74. A student reported the following five heights in a bootstrap sample: 67, 67, 67, 67, and 67. What is true regarding this bootstrap sample?

Answer :

The Bootstrap sample has 67 as it mean, mode and median values.

Final answer:

This bootstrap sample, while a possible outcome due to the randomness of the sampling process, is not a good representation of the total population given the lack of diversity in the sample.

Explanation:

The question relates to a bootstrap sample in a statistical context. A bootstrap sample is supposed to be a random sample with replacement from the original data.

In the given scenario, the values in the bootstrap sample are all the same, i.e., '67'. This could occur by chance, since we are sampling with replacement. However, it doesn't provide a good representation of the overall data because it completely misses the smaller and larger values.

Hence, while it is true regarding this bootstrap sample that it can occur due to the randomness inherent to the sampling process, its usefulness in estimator calculations or predictions would be limited given the lack of diversity in the sample.

Learn more about bootstrap sample here:

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