Random sampling error can be reduced by increasing sample size.

Question

BlackTom AI · Accepted Answer

Restating the claim: The statement says that random sampling error can be reduced by increasing the sample size, and we must evaluate True or False.
Option 1: True. In sampling theory, random sampling error (the variability due to the fact we sample a subset rather than the entire population) generally decreases as sample size increases. The standard error of a statistic such as the sample mean typically decreases roughly with the square root of the sample size (for example, SE ~ sigma / sqrt(n) for a known sigma), so larger samples lead to more precise estimates and smaller random error. This aligns with the idea that more data provides a more stable picture of the population.
Option 2: False. This would be incorrect because it ignores the mathematical relationship between sample size and the precision of estimates. While increasing n does not eliminate all error, it does reduce random sampling error. It’s also important to note that other types of error remain regardless of sample size: sampling bias (if the sample isn’t representative), nonresponse bias, measurement error, and model specification errors. Thus, the statement as a blanket claim is inaccurate only if one considers that other errors exist; the claim about random sampling error specifically becomes less but not zero as n grows.

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Random sampling error can be reduced by increasing sample size.

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