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 6.20 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

Mean = 6.20

a. Margin of error = 2 min

2 = 1.96*6.20/sqrt(n)

sqrt(n) = (6.20*1.96/2)^2 = 36.9 or 37 people

b.

1 = 1.96*6.20/sqrt(n)

sqrt(n) = (1.96*6.20/1)^2

n = 147.67 or 148

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