Question

A firm purchases very large quantity of metal offcuts and wishes to know the average weight of an offcut. A random sample of 625 offcuts is weighted and it is found that the mean sample weight 150 grams with a sample standard deviation of 30 grams. What is the standard error of the mean? What would be the standard error if sample size was 1,225?  

 

Answer 1

Standard error $\sigma_x$ for n samples with standard deviation $\sigma$ is given by a formula

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

So for 625 samples $\sigma_x = \frac{30}{\sqrt{625}} = \frac{30}{25} = 1.2$

and for n = 1225 $\sigma_x = \frac{30}{\sqrt{1225}} = \frac{30}{35} \approx 0.857$