The travel-to-work time for residents of the 15 largest cities In the United Sta

Question

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. 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 05% confidence.

Explanation / Answer

Q1.
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
= 37.52 ~ 38      
Q2.
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 =1
n = ( 1.96*6.25/1) ^2
= (12.25/1 ) ^2
= 150.06 ~ 151      

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