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

The standard error of the mean is 15

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}}=(\sigma)/(√(n))`

Now substitute the values in the formula we get

`\sigma_{\overline{X}}=(120)/(√(64))`

`=(120)/(8)`

`=15`

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

∴ The standard error of the mean is 15