In the context of basic probability concepts, does sampling error increase as the sample size $n$ increases?

• A. True, sampling error increases as sample size $n$ increases.
• B. False, sampling error generally decreases as sample size $n$ increases.
• C.
• D.

Answer: (B)

Verified step by step guidance

1. Understand the definition of sampling error: it is the difference between a sample statistic (like the sample mean) and the true population parameter due to random chance in selecting the sample.
2. Recall that sampling error is influenced by sample size because larger samples tend to better represent the population, reducing variability in the estimate.
3. Recognize the relationship between sample size and sampling error is typically inverse; as sample size increases, the sampling error tends to decrease.
4. Mathematically, the standard error (a measure of sampling error) is calculated as \(\text{SE} = \frac{\sigma}{\sqrt{n}}\), where \(\sigma\) is the population standard deviation and \(n\) is the sample size.
5. Since \(\text{SE}\) decreases as \(n\) increases (due to the square root in the denominator), sampling error generally decreases with larger sample sizes, making the statement that sampling error increases with sample size false.