Which statement regarding sampling error is correct?

Which statement regarding sampling error is correct?

• A. It is negligible in large samples
• B. It decreases with smaller samples
• C. It is a result of inaccurate sampling methods
• D. It is reduced when the sample size is larger

Answer: (D)

Sampling error refers to the difference between the sample statistic and the population parameter it estimates. This error is a natural part of the sampling process and occurs because a sample is only a subset of the entire population. As the sample size increases, the sampling error tends to decrease. This is due to the fact that larger samples tend to better represent the population, leading to more accurate estimates of population parameters. When the sample size is larger, the effects of random variability are minimized, which typically results in a sample mean that is closer to the true population mean. Larger samples provide more information and, thus, reduce uncertainty. This phenomenon is grounded in the Central Limit Theorem, which states that as the size of a sample increases, the sampling distribution of the sample mean approaches a normal distribution, allowing for better reliability and validity of the estimates being made. In contrast, smaller samples are more prone to higher variability and greater potential for error in reflecting the population parameters. Hence, the assertion that sampling error is reduced when the sample size is larger accurately describes the relationship between sample size and the precision of estimates derived from that sample.

Sampling error refers to the difference between the sample statistic and the population parameter it estimates. This error is a natural part of the sampling process and occurs because a sample is only a subset of the entire population. As the sample size increases, the sampling error tends to decrease. This is due to the fact that larger samples tend to better represent the population, leading to more accurate estimates of population parameters.

When the sample size is larger, the effects of random variability are minimized, which typically results in a sample mean that is closer to the true population mean. Larger samples provide more information and, thus, reduce uncertainty. This phenomenon is grounded in the Central Limit Theorem, which states that as the size of a sample increases, the sampling distribution of the sample mean approaches a normal distribution, allowing for better reliability and validity of the estimates being made.

In contrast, smaller samples are more prone to higher variability and greater potential for error in reflecting the population parameters. Hence, the assertion that sampling error is reduced when the sample size is larger accurately describes the relationship between sample size and the precision of estimates derived from that sample.