Question

The water works commission needs to know the mean household usage of water by the residents of a small town in gallons per day. They would like the estimate to have a maximum error of 0.14 gallons. A previous study found that for an average family the variance is 1.44 gallons and the mean is 16.7 gallons per day. If they are using a 85% level of confidence, how large of a sample is required to estimate the mean usage of water? Round your answer up to the next integer.

Answer 1

Solution

variance=1.44

standard deviation =s =   =1.44=1.2

Margin of error = E = 0.14

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96

sample size = n = [Z/2* / E] 2

n = ( 1.96* 1.2 /0.14 )2

n =282.24

Sample size = n =283