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 time for San Francisco residents with a margin of error of 22 minutes, what sample size should be used?
b. If we want to estimate the population mean travel-to-work time for San Francisco residents with a margin of error of 11 minute, what sample size should be used?