A sample of size 36 is drawn at random from a population with a standard deviation of 12. Which of the following is the standard error of the sample mean (the standard deviation that describes the spread of the sample mean)?

Answer: A. 2

The standard error of the sample mean is σ/√n, the population standard deviation σ divided by the square root of the sample size n: 12 ÷ √36 = 12 ÷ 6 = 2. With a sample four times as large, 144, the standard error halves to 1, so doubling the precision of the estimate requires four times as many samples.

• A. Correct. 12 ÷ √36 = 2.
• B. σ² ÷ n = 144 ÷ 36 = 4 is the variance of the sample mean, without taking the square root.
• C. 12 is the standard deviation of the individual values in the population; the spread of the sample mean is smaller than this.