To find the sample size required to estimate the mean usage of water with a maximum error of 0.14 gallons at 85% confidence level, we can use the formula:
n = (Z^2 * σ^2) / E^2
Where:
n = sample size
Z = Z-score for 85% confidence level, which is 1.44
σ^2 = variance = 1.44 gallons
E = maximum error = 0.14 gallons
Plugging in the values:
n = (1.44 * 1.44) / 0.14^2
n = 2.0736 / 0.0196
n = 105.714
Rounded up to the next integer, the sample size required is 106.
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 0.14
gallons. A previous study found that for an average family the variance is 1.44
gallons and the mean is 16.7
gallons per day. If they are using a 85%
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.
1 answer
1 answer