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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 0.11
gallons. A previous study found that for an average family the standard deviation is 2.3
gallons and the mean is 19.9
gallons per day. If they are using a 80%
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

The formula to calculate the sample size needed to estimate a population mean with a specified margin of error is:

n = (Z*σ/E)^2

Where:

Z = the Z-score for the desired level of confidence

σ = the standard deviation of the population

E = the maximum error (margin of error) allowed

n = the sample size

Substituting the given values:

Z = 1.28 (for an 80% level of confidence)

σ = 2.3 gallons (from the previous study)

E = 0.11 gallons (the maximum error allowed)

n = (1.28*2.3/0.11)^2

n = 89.13

Rounding up to the next integer, the sample size required is 90. Therefore, the water works commission needs a sample of 90 households to estimate the mean household usage of water in the small town with a maximum error of 0.11 gallons and an 80% level of confidence.

Explanation: