If all possible samples of size n are drawn from a large population with a mean of 20 and a standard deviation of 5, then the standard error of the sample mean equals 1.0 only for samples of size:
A) 15
B) 20
C) 25
D) 30
E) 35

Question

Quizplus · Accepted Answer

The formula for standard error of the mean is:

SE = σ/√n

Where σ is the population standard deviation and n is the sample size.

We are given that σ = 5 (population standard deviation) and we need to find the sample size (n) for which SE = 1.

1 = 5/√n

Squaring both sides:

1 = 25/n

n = 25

Therefore, the standard error of the sample mean equals 1.0 only for samples of size 25.

If All Possible Samples of Size N Are Drawn from a Large