How does increasing the sample size affect the standard error of the mean?

How does increasing the sample size affect the standard error of the mean?

• A. Increases the standard error.
• B. Decreases the standard error.
• C. Does not affect the standard error.
• D. Depends on the population variance.

Answer: (B)

The standard error of the mean measures how far a sample mean is expected to be from the true population mean across repeated samples. It gets smaller as you collect more data because the estimate becomes more precise. The standard error is roughly σ/√n (or s/√n with sample data). As the sample size n increases, the denominator grows, so the standard error decreases. The actual size of the standard error for a given n depends on the population (or sample) variance—the higher the variance, the larger the standard error for that n—but the direction is always a decrease when n increases.

The standard error of the mean measures how far a sample mean is expected to be from the true population mean across repeated samples. It gets smaller as you collect more data because the estimate becomes more precise. The standard error is roughly σ/√n (or s/√n with sample data). As the sample size n increases, the denominator grows, so the standard error decreases. The actual size of the standard error for a given n depends on the population (or sample) variance—the higher the variance, the larger the standard error for that n—but the direction is always a decrease when n increases.