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 variance is 3.61 gallons and the mean is 19.4 gallons per day. If they are using a 95% level of confidence, how large of a sample is required to estimate the mean usage of water

Answer 1

The minimum sample size required to estimate the mean usage of water = 2225.07

What is Standard deviation?

In statistics, the standard deviation (SD, also represented by the Greek letter sigma σ or the Latin letter s) is a measure that is used to quantify the amount of variation or dispersion of a set of data values.

We can find the minimum sample size required to estimate the mean usage of water as shown below:

Standard deviation $\sigma =3.61$

Margin of error E=0.15

Critical value for 95% confidence interval = 1.96

Required minimum sample size: $n=(\frac{Z_{\frac{\alpha}{2}}.\sigma }{E} )^2$

$=(\frac{1.96\times 3.61}{0.15} )^2$

=2225.07

Hence, the minimum sample size required to estimate the mean usage of water = 2225.07

Learn more about Standard deviation here:

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