Question

The water works commission needs to know the mean household usage of water by the residents...

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.

Homework Answers

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

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