Question

A simple random sample of 64 observations was taken from a large population. The population standard deviation is 120. The sample mean was determined to be 320. The standard error of the mean is _____.

Answer 1

Answer:

The standard error of the mean is 15

Step-by-step explanation:

Given that a simple random sample of 64 observations was taken from a large population.

Hence it can be written as n=64

The population standard deviation is 120.

It can be written as $\sigma_{\overline{X}}=120$

The sample mean was determined to be 320.

It can be written as $\overline{X}=\mu =320$

To find the standard error of the mean :

The formula for the standard error of the mean is given by

$\sigma_{\overline{X}}=\frac{\sigma}{\sqrt{n}}$

Now substitute the values in the formula we get

$\sigma_{\overline{X}}=\frac{120}{\sqrt{64}}$

$=\frac{120}{8}$

$=15$

$\sigma_{\overline{X}}=15$

∴ The standard error of the mean is 15