Question

A researcher selects two samples of 64 participants each. In the first sample, the population mean was 10 and the variance was 16. In this second sample, the population mean was 25 and the variance was 9. Which sample will be associated with a larger standard error of the mean?

Answer 1

Answer:Sample 1

Explanation:

Given

N=sample size=64

for first sample

mean $(\mu )=10$

variance$(\sigma ^2)=16$

standard deviation$(\sigma )=4$

Standard error of the mean$=\frac{\sigma }{\sqrt{N}}$

$=\frac{4}{\sqrt{64}}$

$=\frac{4}{8}=0.5$

For second sample

mean $(\mu )=25$

variance$(\sigma ^2)=9$

standard deviation$(\sigma )=3$

Standard error of the mean$=\frac{\sigma }{\sqrt{N}}$

$=\frac{3}{\sqrt{64}}$

$=\frac{3}{8}=0.375$

It is observed error for sample 1 is more than error in sample 2 thus

Thus sample 1 is associated with a larger standard error of the mean