Question

A population that consists of 500 observations has a mean of 40 and a standard deviation of 15. A sample of size 100 is taken at random from this population. The standard error of the sample mean equals:

a. 2.50.
b. 12.50.
c. 1.343.
d. 1.50.

Answer 1

The option D) 1.50 is correct

That is the standard error of the sample mean is 1.50

Explanation:

Given that a population that consists of 500 observations has a mean of 40 and a standard deviation of 15.

A sample size is 100 taken at random from the given population.

To find the standard error of the sample mean :

From the given Mean=40 and
`\sigma =15`

For N=100

The formula for standard error is
`SE_(mean)=(\sigma)/(√(N))`

Substitute the values in the above formula we get

`SE_(mean)=(15)/(√(100))`

`=(15)/(10)`

`=1.50`

∴
`SE_(mean)=1.50`

∴ The standard error of the sample mean is 1.50

Hence the option D) 1.50 is correct