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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 0.15 gallons. A previous study found that for an average family the standard deviation is 2.3 gallons and the mean is 17.6 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.

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JeanaShupp

Answer: 387

Step-by-step explanation:

Given : Standard deviation: [tex]\sigma=2.3[/tex]

Margin of error : 0.15

Critical value for 80% confidence interval = 1.2816

Required minimum sample size : [tex]n=(\dfrac{z_{\alpha/2}\cdot \sigma}{E})^2[/tex]

[tex]\\\\=(\dfrac{1.2816\times2.3}{0.15})^2\\\\=386.16966144\approx387[/tex]

Hence, the minimum sample size required to estimate the mean usage of water = 387

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