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.

a. 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.
b. If we want to estimate the population mean travel-to-work for San Francisco residents with a
margin of error of 30 seconds, what sample size should be used? Assume 99% confidence.

Explanation / Answer

Margin of Error (half of confidence interval) = 2
The margin of error is defined as the "radius" (or half the width) of a confidence interval for a particular statistic.
Level of Confidence = 95
?: population standard deviation = 6.25
('z critical value') from Look-up Table for 95% = 1.96

significant digits = 2

Margin of Error = ('z critical value') * ?/SQRT(n)
n = Sample Size

Algebraic solution for n:
n =[('z critical value') * ?/Margin of Error]^2
= [ (1.96 * 6.25)/2 ]^2

Sample Size = 38

Margin of Error (half of confidence interval) = 1
The margin of error is defined as the "radius" (or half the width) of a confidence interval for a particular statistic.
Level of Confidence = 95
?: population standard deviation = 6.25
('z critical value') from Look-up Table for 95% = 1.96

significant digits = 2

Margin of Error = ('z critical value') * ?/SQRT(n)
n = Sample Size

Algebraic solution for n:
n =[('z critical value') * ?/Margin of Error]^2
= [ (1.96 * 6.25)/1 ]^2

Sample Size = 151

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