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 6.76 gallons and the mean is 16.1 gallons per day. If they are using a 98% 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 = 6.76

Population standard deviation = = 6.76 = 2.6

Margin of error = E = 0.1

At 98% confidence level the z is,

= 1 - 98%

= 1 - 0.98 = 0.02

/2 = 0.01

Z/2 = Z0.01 = 2.326

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

n = [ 2.326 * 2.6 / 0.1 ]2

n = 3657.35

Sample size = n = 3658