As the sample size increases, the variability of the sample mean _____

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BlackTom AI · Accepted Answer

The question asks: As the sample size increases, the variability of the sample mean _____.

Because the core idea is about how sampling variability changes with larger samples, the standard result is that the variability of the sample mean decreases as n grows. This is quantified by the standard error of the mean, which is sigma divided by the square root of n (SE = sigma/√n) when sigma is the population standard deviation. As n increases, the denominator √n grows, making SE smaller, so the sample mean tends to be closer to the true population mean across repeated samples.

If we consider common misinterpretations: some might think variability stays the same regardless of sample size, which is incorrect because SE explicitly depends on n. Others might suggest variability increases with n, which contradicts the mathematical relationship and empirical intuition that more data stabilizes the estimate.

In this case, the provided correct answer is Decreases, reflecting the inverse square-root relationship between sample size and the variability (uncertainty) of the sample mean. However, the answer options list is empty in the input, so there are no alternative choices to evaluate here. The key takeaway remains: increasing sample size reduces the variability of the sample mean due to the standard error diminishing as n grows.

STAT 1450.02 SP2025 (28132) Checkpoint 15.1 - 15.3

As the sample size increases, the variability of the sample mean _____

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