The following samples were selected by two researchers.Which is associated with a smaller standard error of the mean?
Researcher A: n = 18, = 8, = 2.4
Researcher B: n = 12, = 8, = 2.4
A)Researcher A
B)Researcher B
C)They both have the same standard error.

Question

The following samples were selected by two researchers.Which is associated with a smaller standard error of the mean?
Researcher A: n = 18,  = 8,  = 2.4
Researcher B: n = 12,  = 8,  = 2.4
A)Researcher A 
B)Researcher B 
C)They both have the same standard error.

Quizplus · Accepted Answer

The standard error of the mean is inversely proportional to the sample size, which means that larger sample size results in a smaller standard error. Thus, since researcher A has a larger sample size (n = 18) than researcher B (n = 12), researcher A's sample is associated with a smaller standard error of the mean. The mean and standard deviation values in the samples do not affect the size of the standard error, only the sample size does.

The Following Samples Were Selected by Two Researchers