Question

A sample of 1000 students whose mean weight is 119 lbs (pounds) from a school in Tamil Nadu State was taken and their average weight was found to be 120 lbs with a standard deviation of 30 lbs. Calculate the standard error of the mean

Answer 1

Given n = 1000

${\displaystyle \overline{x}}$ = 119 lbs  ......(pounds)

Since σ is unknown

So we consider ${\displaystyle \overline{\sigma }}$ = s and µ = 120 lbs

S.E = ${\displaystyle \frac{\overline{\sigma }}{\sqrt{\text{n}}}}$

= ${\displaystyle \frac{\text{s}}{\sqrt{\text{n}}}}$

= ${\displaystyle \frac{30}{\sqrt{1000}}}$

= ${\displaystyle \frac{30}{31.623}}$

= 0.9487

Therefore the standard error for the average weight of large group of students of 120 lbs is 0.9487