To calculate the sample size required for estimating the mean usage of water with a maximum error of 0.11 gallons and a 98% level of confidence, we can use the formula:
n = (Z^2 * σ^2) / E^2
Where:
n = sample size
Z = z-score for a 98% confidence level, which is 2.33
σ = standard deviation of 2.6 gallons
E = maximum error of 0.11 gallons
Plug in the values:
n = (2.33^2 * 2.6^2) / 0.11^2
n = (5.4289 * 6.76) / 0.0121
n = 36.670664 / 0.0121
n = 3029.34132231
Since the sample size must be a whole number, round up to the next integer:
n = 3030
Therefore, the water works commission needs a sample size of 3030 households to estimate the mean household usage of water with a maximum error of 0.11 gallons and a 98% confidence level.
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 0.11
gallons. A previous study found that for an average family the standard deviation is 2.6
gallons and the mean is 19
gallons per day. If they are using a 98%
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