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

Answer:

The option D) 1.50 is correct

That is the standard error of the sample mean is 1.50

Step-by-step 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 $SE_{mean}=\frac{\sigma}{\sqrt{N}}$

Substitute the values in the above formula we get

$SE_{mean}=\frac{15}{\sqrt{100}}$

$=\frac{15}{10}$

$=1.50$

∴ $SE_{mean}=1.50$

∴ The standard error of the sample mean is 1.50

Hence the option D) 1.50 is correct