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 0.15 gallons. a previous study found that for an average family the standard deviation is 1.9 gallons and the mean is 16 gallons per day. if they are using a 90% 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

To determine the average water use, 109 people must be sampled.

1.9 gallons is the standard deviation.

E = 0.15 gallons maximum error

1.9 gallons on average

90% is the critical value.

1.645 is the 90% confidence interval.

sample size requirement,

n = (((z ÷ 2) × σ) ÷ E)²

n = (((1.645 ÷ 2) × 1.9) ÷ 0.15)²

n = ((0.8225 × 1.9) ÷ 0.15)²

n = (1.5627 ÷ 0.15)²

n = (10.418)²

n = 108.53 ≈ 109

As a result, the minimal sample size necessary to determine the mean water use = 109.

It is determined by dividing the average standard error by the squared of the sample size, and it decreases with increasing sample size. In other words, when the sample size is sufficiently big, the population mean approaches the population mean.

To learn more about the sample interval at

brainly.com/question/13664567?referrer=searchResults

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