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 6.30 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.

Explanation / Answer

here fore 95% CI, z =1.96

margin of error E =2

and standard deviation =6.3

hence sample size =(z*std deviation/E)2 =38.12

rounding it up will give sample size =39

B)here margin of error E =1

hence sample size =(1.96*6.3/1)2 =152.47

rounding it up will give sample size =153

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