Question

The U.S. Department of Transportation reported recently that all commuters in the New York City area average 120 minutes on the road traveling to and from work each workday. Assume that the standard deviation for the amount of time all commuters in the New York City area travel to and from work each workday equals 30 minutes. If a random sample of 36 commuters in the New York City area is selected, calculate the associated standard error of the mean.

Answer 1

The standard error of the mean for a sample of 36 commuters in the NYC area is 5 minutes.

Step-by-step explanation:

To calculate the standard error of the mean, we use the formula:

Standard Error = Standard Deviation / √(Sample Size)

In this case, the standard deviation is given as 30 minutes, and the sample size is 36 commuters. Plugging these values into the formula, we have:

Standard Error = 30 / √(36)

Simplifying further:

Standard Error = 30 / 6

Standard Error = 5 minutes

Therefore, the associated standard error of the mean is 5 minutes.