Q. 60 - The Practice of Statistics for AP

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.

Step-by-Step Solution

Answer

The standard error of the mean is $4.8925$.

Step 1: Given information

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

Step 2: 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 $4.8925$.