Question

A random sample is selected from a population with astandard deviation of o= 18.a. On average, how much difference should there bebetween the sample mean and the population meanfor a random sample of n = 4 scores from thispopulation?b. On average, how much difference should there befor a sample of n = 9 scores?c. On average, how much difference should there befor a sample of n = 36 scores?

Answer 1

In order to calculate the difference between the sample mean and the population mean (that is, the standard error), we can use the formula below:

$SE=\frac{\sigma}{\sqrt{n}}$

(a)

For sigma = 18 and n = 4, we have:

$SE=\frac{18}{\sqrt{4}}=\frac{18}{2}=9$

(b)

For n = 9, we have:

$SE=\frac{18}{\sqrt{9}}=\frac{18}{3}=6$

(c)

For n = 36, we have:

$SE=\frac{18}{\sqrt{36}}=\frac{18}{6}=3$