To calculate the sample size required to estimate the mean usage of water with a maximum error of 0.14 gallons at a 90% confidence level, we can use the formula:
n = (Z^2 * σ^2) / E^2
Where:
n = sample size
Z = Z-score for a 90% confidence level = 1.645
σ = standard deviation = 2.2 gallons
E = maximum error = 0.14 gallons
Plugging in the values, we have:
n = (1.645^2 * 2.2^2) / 0.14^2
n = (2.702025 * 4.84) / 0.0196
n = 13.0749 / 0.0196
n = 666.736
Since we need to round up to the next integer, the sample size required to estimate the mean usage of water is 667 households.
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 standard deviation is 2.2
gallons and the mean is 15.4
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.
1 answer