Question

What effect does increasing the sample size have on a distribution of sample means?
a.it will not make any difference
b.it will have less variation
c.it will have more variation?

Answer 1

Correct Answer:
Option B. It will have less variation

The standard deviation of distribution of sample means is given by:

$s= \frac{S}{ \sqrt{n} }$

Here, 
s = Standard deviation of distribution of sample means
S = Population standard deviation
n = Sample Size

From equation we can see that Standard deviation of distribution of sample means is inversely proportional to the square root of sample size. This means if sample size is increased, the standard deviation of distribution of sample means will decrease. Hence a larger sample size will have less variation as compared to a small sample size.

Therefore, option B is the correct answer.