As the sample size increases, the standard error decreases.

As the sample size increases, the standard error decreases.

• A. Decreases
• B. Increases
• C. Stays the same
• D. Not enough information given to answer this question

Answer: (A)

The standard error of the sample mean gets smaller as you collect more data because it measures how much the sample average is expected to wiggle around the true population mean. It’s the spread of the sampling distribution of the mean. Mathematically, the standard error is the population standard deviation divided by the square root of the sample size: SE = sigma / sqrt(n). As n grows, the sqrt(n) in the denominator increases, so SE shrinks. Even when you estimate the standard deviation from the sample (SE ≈ s / sqrt(n)), the same idea holds: increasing n reduces the estimated variability of the sample mean. For intuition, doubling the sample size reduces the standard error by a factor of about sqrt(2). This is why larger samples give more precise estimates of the population mean: the average you compute is less variable from sample to sample.

The standard error of the sample mean gets smaller as you collect more data because it measures how much the sample average is expected to wiggle around the true population mean. It’s the spread of the sampling distribution of the mean. Mathematically, the standard error is the population standard deviation divided by the square root of the sample size: SE = sigma / sqrt(n).

As n grows, the sqrt(n) in the denominator increases, so SE shrinks. Even when you estimate the standard deviation from the sample (SE ≈ s / sqrt(n)), the same idea holds: increasing n reduces the estimated variability of the sample mean. For intuition, doubling the sample size reduces the standard error by a factor of about sqrt(2).

This is why larger samples give more precise estimates of the population mean: the average you compute is less variable from sample to sample.