Exercise 829 Algorithmic The traveltowork time for residents

{Exercise 8.29 (Algorithmic)}

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 6.30 minutes for the population standard deviation.

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.

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

Given a=1-0.95=0.05, Z(0.025) = 1.96 (from standard normal table)

So n=(Z*s/E)^2

=(1.96* 6.3/2)^2

=38.11828

Take n=39

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So n=(Z*s/E)^2

=(1.96* 6.3/1)^2

=152.4731

Take n=153