8
AssignmentMultiple Choice

Sampling Distributions – Center and Variability

Question 8 • NC-Math 4

What happens to the standard deviation of the sampling distribution as the sample size increases?

Answer
A
It increases.
B
It decreases.
C
It stays the same.
D
It may increase or decrease depending on the size of the population.

Explanation

The standard deviation of a sampling distribution of the sample mean is the population standard deviation divided by the square root of the sample size: σ/√n. As the sample size increases, √n increases, so the standard deviation decreases. Therefore, the correct choice is B, “It decreases.”

AI-written and checked against the verified answer.

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