Question

60. 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

The standard error of the mean is $4.8925$.

Step-by-step solution

Given information

The mean is $\overline{x}=31.25$ minutes, and the standard deviation is $s_x=21.88$ minutes.

Explanation

Utilizing the formula $\overline{E}=\frac{s_x}{\sqrt{n}}$, to determine the standard error of mean.
Where, Mean $\overline{x}$is $31.25$. The Standard deviation $s_x$is $21.88$.
And the Sample size $n$is $20$.
$\overline{E}=\frac{s_x}{\sqrt{n}}$
$=\frac{21.88}{\sqrt{20}}$
$=4.8925$
Therefore, the standard error of the mean is $4.8925$.