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 0.15 gallons. A previous study found that for an average family the variance is 3.61 3.61 gallons and the mean is 17.3 17.3 gallons per day. If they are using a 90% 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

Answer 1

ANSWER:

Given data,

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 variance is 3.61 gallons and the mean is 17.3 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

The maximum error =E = 0.15 gallons

The variance = ^2 = 3.61 gallons

The mean 17.3 gallons

level of confidence = c = 90% = 90/100 = 0.90

= 1-c = 1-0.90 = 0.1

/2 = 0.1/2 = 0.05

Critical value

Z_/2 = Z_0.05 = 1.64

Formula for Sample size is

Sample size = n = ((Z_/2)^2 * (^2)) / (E^2)

Sample size = n = ((1.64)^2 * (3.61)) / (0.15^2)

Sample size = n = 431.5

Sample size = n = 432 (Rounded to next integer)

Therefore 432 sample is required to estimate the mean usage of water.

------------------------------------------------------------------------The End ---------------------------------------------------------------------------------

If you have any doubt please ask me friend and if you are satisfied with my solution please give me thumb up.