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 0.1 gallons. A previous study found that for an average family the variance is 5.76 gallons and the mean is 17.9 gallons per day. If they are using a 99% 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,

variance = ² = 5.76

Population standard deviation = = ² = 5.76 = 2.4

Margin of error = E = 0.1

At 99% confidence level the z is,

= 1 - 99%

= 1 - 0.99 = 0.01

/2  = 0.005

Z_/2 = 2.576

sample size = n = [Z_/2* / E] ²

n = [2.576 * 2.4 / 0.1 ]²

n = 3822.20

Sample size = n = 3823