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 6.46 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 3 minutes, what sample size should be used? Assume 95% confidence.

Explanation / Answer

population standard deviation. = 6.46

let tthe sample size be n

standard deviation of sample mean = 6.46/n

standard error if we assume 95% confidence interval is = 2*1.96*standard deviation of sample mean

a)margin of error of 5 minutes

so 2*1.96*6.46/n = 5

n =   2*1.96*6.46/5 = 5.064

n = 25.65 ~ 26

b)margin of error of 3 minutes

so 2*1.96*6.46/n = 3

n =   2*1.96*6.46/3 = 8.441

n = 71.25 ~ 71

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