Question

11. If the standard deviation of the mean for the sampling distribution of random samples of size 36 from a large or infinite population is 2, how large must the sample size become if the standard deviation is to be reduced to 1.2? Show work. (8 points)

Answer 1

Standard deviation of sampling distribution = 2

Hence,

$2 = \frac{\sigma}{\sqrt{36}}$

$\sigma$ = 2*6 = 12

Let the sample size be n for SD = 1.2

Therefore,

$1.2 = \frac{12}{\sqrt{n}}$

n = 100