Question

Suppose the average commute time of your employees is unknown. The standard deviation of their commute time is estimated as 27.6 minutes.

How many employees must be included in a sample to create a 99 percent confidence interval for the average commute time with a confidence interval width of no more than 17 minutes?

Note that the correct answer will be evaluated based on the z-values in the summary table in the Teaching Materials section.

Remember to round your answer up to an integer.

Answer 1

Solution :

Given that,

standard deviation = = 27.6

width = 17

margin of error = E = width / 2 = 17 / 2 = 8.5

At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z _0.005 = 2.576

Sample size = n = ((Z_/2 * ) / E)²

= ((2.575 * 27.6) / 8.5)²

= 69.9 = 70

Sample size = n = 70 employees .