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 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.

Answer 1

Answer: 387

Step-by-step explanation:

Given : Standard deviation: $\sigma=2.3$

Margin of error : 0.15

Critical value for 80% confidence interval = 1.2816

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

$\\\\=(\dfrac{1.2816\times2.3}{0.15})^2\\\\=386.16966144\approx387$

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