Question

Assume we have gathered data for one quantitative variable from a random sample of a population. For each statement below, indicate whether it is True or False.

a) If we take additional samples of the same size from the same population, the value of the variable will vary from sample to sample.
b) If we generate bootstrap samples of the same size from our original sample, the values of our bootstrap sample means will vary from sample to sample.
Options:
a) True, True
b) False, True
c) True, False
d) False, False

Answer 1

The value of a variable will vary from sample to sample, whether you take additional samples from the same population or generate bootstrap samples from the original sample.

Step-by-step explanation:

a) True. If we take additional samples of the same size from the same population, the value of the variable will vary from sample to sample. This is because there is inherent variability in the population, and each sample represents a different subset of the population.

b) True. If we generate bootstrap samples of the same size from our original sample, the values of our bootstrap sample means will vary from sample to sample. Bootstrap sampling involves sampling with replacement, which means that each bootstrap sample will have slightly different data points, leading to variation in the sample means.