You want to know how the commuting time of your employees compare to Departments

Question

You want to know how the commuting time of your employees compare to Departments competing for the same staff, so you get some survey data on average commuting times for 25 randomly selected people in your line of business.

Data: 59, 74, 73, 66, 80, 84, 90, 122.5, 37.2, 50, 139.3, 39, 80, 35, 88, 34, 82, 65, 61, 63, 66, 88, 70, 79, 75

You find that the mean commuting time is 72 minutes, with a standard deviation of 24.53.

a) Calculate your standard error.
b) Based on this, calculate a 95 percent Confidence Interval for the mean commuting time. (Remember, the C.I. is calculated by adding and subtracting from the observed sample mean the product of the standard error and the appropriate t-value

Explanation / Answer

a. The sample size is small (n<30) and population standard deviation is unknown. Thus, use Student's t distribution to compute standard error for 1-population mean.

Standard error=s/sqrt n, where, s is sample standard deviation, n is sample size.

=24.53/sqrt 25

=4.906

b. The 95% c.i for population mean time to commute is: xbar+-talpha/2, df=n-1*SE, where, xbar is sample mean, t is t critical at alpha/2 (alpha=0.05, alpha/2=0.025) and n-1 degrees of freedom, Se is standard error.

=72+-2.064*4.906

=(61.874,82.126)

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