As the sample size decreases, the _____.

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BlackTom AI · Accepted Answer

The question given is: 'As the sample size decreases, the _____.'

Because the answer options are not provided, we cannot evaluate specific choices. Nevertheless, we can discuss the key statistical principle that typically completes this sentence.

Conceptual foundation: standard error of the mean (SEM) measures how precisely the sample mean estimates the population mean. It is calculated as SEM = sigma / sqrt(n), where sigma is the population standard deviation and n is the sample size.

Reasoning about the effect of sample size: as n decreases, the denominator sqrt(n) becomes smaller, which makes the fraction sigma / sqrt(n) larger. Thus, the standard error of the mean increases when the sample size is smaller. This leads to wider confidence intervals and greater variability in sample means from sample to sample.

If the question intended to contrast SEM with standard deviation: standard deviation (SD) is a property of the data itself and does not change with sample size, whereas SEM is inherently dependent on n. Therefore, with smaller samples, SEM increases while SD remains a property of the underlying data.

If the question were about margin of error in estimates: a smaller n yields a larger margin of error because the SEM is larger, reflecting less precision.

Limitations due to missing options: without the provided list of answer choices, we cannot map each potential option to this reasoning or identify distractors. If options were present, each would need to be assessed in light of whether it references SEM, SD, bias, or other sample-size–dependent quantities, and the correct relationship would be SEM increasing as n decreases.

In summary, the core idea is that standard error of the mean increases when the sample size decreases, because the estimate becomes less precise as fewer observations are used to estimate the population mean.

22803 Quantitative Skills in Accounting and Finance - Autumn 2025 Quiz 3

As the sample size decreases, the _____.

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