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 0.14
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.
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.
Answers
GPT 3.5
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.
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.