The water works commission wishes to know the mean houshold

The water works commission wishes to know the mean houshold usage of water the residents of a small town. They believe that the mean is 17.7 gallons per day for each family. Assume a previous study found the variance to be 5.29.

How large of a sample would be required in order to estimate the mean number of gallons of water used daily per family at the 90% confidence level with an error of at most 0.14 gallons?

Solution

For a 90% confidence level, you use a z of 1.645

Sample size N = (z*standard deviation/E)^2

N = (1.645*sqrt 5.29/.14)^2

N = 731, always round up with this formula

Answer: 731