The standard error of the sample mean is calculated as:

Standard Error = Population Standard Deviation / √Sample Size

Given:

• Population standard deviation (σ) = 100
• Sample size (n) = 1,000

Calculation: √1,000 ≈ 31.6228 Standard Error = 100 / 31.6228 ≈ 3.16228 ≈ 3.16

Why other options are incorrect:

• A (0.1): This would be 100/1,000, which is incorrect because we need to divide by the square root of the sample size, not the sample size itself.
• C (27.6): This is too large and doesn't correspond to any standard calculation.
• D (0.01): This would be 100/10,000, which incorrectly uses the population size instead of the sample size.

Key Concept: The standard error measures the precision of the sample mean as an estimate of the population mean. As sample size increases, the standard error decreases, making the sample mean a more precise estimate of the population mean.