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

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