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 6.81 minutes for the population standard deviation. Round your answers to nearest whole number.

a. If we want to estimate the population mean travel-to-work time for San Francisco residents with a margin of error of 5 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 2 minutes, what sample size should be used? Assume 95% confidence.

Explanation / Answer

solution=

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 6.81 minutes for the population standard
deviation.
a. If we want to estimate the population mean travel-to-work for San Francisco residents with a margin of error of 5 minutes, what sample size should be used? Assume 95% confidence.
Since E = z*s/sqrt(n), n = [z*s/E]^2 = [1.96*6.81/5]^2 = 7

b. If we want to estimate the population mean travel-to-work for San Francisco residents with a margin of error of 2 minutes , what sample size should be used? Assume 95% confidence.
n = [1.96*6.81/(2)]^2 = 45 when rounded up

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