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 0.19 gallons. A previous study found that, for an average family, the standard deviation is 3 gallons and the mean is 12.2 gallons per day. If they are using a 90% 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 :

Given that,

standard deviation =s =   =3

Margin of error = E = 0.19

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05 = 1.645

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

n = ( 1.645 * 3 / 0.19 )2

n =674.63

Sample size = n =675