Final answer:
Estimates of population variance and standard deviation are generally larger than from a sample due to sampling error, which is inherent when the sample is not perfectly representative of the population. Larger and randomized samples minimize but do not entirely eliminate this error.
Step-by-step explanation:
The question pertains to why estimates of the population variance and standard deviation are generally larger when calculated from a sample, rather than when using the entire population. The correct answer is A) Due to sampling error. This occurs because a sample is unlikely to be perfectly representative of the population, leading to unavoidable sampling errors. As the sample size increases, the error generally decreases, making the estimate more reliable. However, sampling error can never be completely eliminated, unless the sample contains the whole population.
Using a small sample size can result in chance error, which can be large and negatively affect the representation of the population. Conversely, bias happens when the sample is not randomly selected, which is another issue that can lead to inaccurate estimations. Therefore, larger and randomized samples are preferred to achieve better population parameter estimations.
To understand the differences between samples, consider that Doreen's and Jung's sleep study samples might be closer to the actual population average if they were larger. However, due to sampling variability, different samples from the same population can yield different results.