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, 110, 37.2, 50, 101.8, 39, 80, 35, 88, 34, 82, 65, 61, 63, 66, 88, 70, 79, 75

You find that the mean commuting time is 70 minutes, with a standard deviation of 20. [You don't need to calculate this, but you can test it, using Excel!]  

a) Calculate your standard error of the mean.
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; for the latter, use Excel tinv) Show your work.

Answer 1

Given n = 25 , xbar = 70 , s = 20

a) standard error of mean = s/√n = 20/√25

Standard error of mean = 4

b) 95% confidence interval for mean commuting time

xbar - t​​​​​​a/2*( s/√n) < < xbar + t​​​​​​a/2*(s/√n)

For a = 0.05 , d.f = n - 1 = 24

t​​​​​​a/2 ,n-1 = t​​​​​​0.025 , 24 = 2.06

70 - 2.06*(20/√25) < < 70 + 2.06*(20/√25)

61.76 <   < 78.24

This is 95% confidence interval for population mean