The traveltowork time for residents of the 15 largest cities

The travel-to-work time for residents of the 15 largest cities in the United States is reported in the 2003 Information Please Almanac. Suppose that a preliminary simple random sample of residents of San Francisco is used to develop a planning value of 6.25 minutes for the population standard deviation.

a.If we want to estimate the population mean travel-to-work time for San Francisco residents with a margin of error of 2 minutes, what sample size should be used? Assume 95% confidence.

b.If we want to estimate the population mean travel-to-work time for San Francisco residents with a margin of error of 1 minute, what sample size should be used? Assume 95% confidence.

Solution

a)
Compute Sample Size
n = (Z a/2 * S.D / ME ) ^2
Z/2 at 0.05% LOS is = 1.96 ( From Standard Normal Table )
Standard Deviation ( S.D) = 6.25
ME =2
n = ( 1.96*6.25/2) ^2
= (12.25/2 ) ^2
= 37.516 ~ 38      
b)
Standard Deviation ( S.D) = 6.25
ME =1
n = ( 1.96*6.25/1) ^2
= (12.25/1 ) ^2
= 150.063 ~ 151