Question

If two samples are drawn randomly from the same population and sample A has n=350 and sample B has n=500, which sample will have a larger standard error of the mean?
Group of answer choices

Sample B

Sample A

The standard errors will be the same

Answer 1

Answer:  Sample A

Reason:

The standard error of the mean has the formula $\frac{\sigma}{\sqrt{n}}$ where $\sigma$ (greek letter sigma) is the standard deviation and n is the sample size.

As n gets bigger, the standard error $\frac{\sigma}{\sqrt{n}}$ gets smaller, and vice versa. This assumes sigma is fixed. A larger sample indicates the error goes down to narrow in better on the population mean.

Based on what I mentioned, this tells us that sample A has the larger standard error since n = 350 is smaller than n = 500 for sample B.