Question

Travel time to work A study of commuting times reports the travel times to work of a random sample of $20$employed adults in New York State. The mean is $\overline{x}=31.25$minutes and the standard deviation is $s_X=21.88$

minutes. What is the standard error of the mean? Interpret this value in context.

Short answer

Standard error of mean value is$4.892$.

Step-by-step solution

Given Information

It is given that $\left(\overline{x}\right)=31.25$

$\left(s_x\right)=21.88$

$n=20$

Concept Used

Formula to be used is
$S{E}_{\overline{x}}=\frac{s_x}{\sqrt{n}}$

Calculation

We can calculate standard error of mean as

$S{E}_{\overline{x}}=\frac{s_x}{\sqrt{n}}$

$=\frac{21.88}{\sqrt{20}}$

$=4.892$

Hence, standard error of mean is$4.892$