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 gallons. A previous study found that for an average family the standard deviation is 2.5 gallons and the mean is 15.2 gallons per day. If they are using a 80% 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

SOLUTION:

From 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 standard deviation is 2.5 gallons and the mean is 15.2 gallons per day. If they are using a 80% level of confidence, how large of a sample is required to estimate the mean usage of water?

Standard deviation = = 2.5

Mean = 15.2

Maximum error = E = 0.15

80% level of confidence

80% = 80/100 = 0.80

= 1-0.80 =0.2

/2 = 0.2/2 = 0.1

Critical value = z_/2 = z_0.1 = 1.282

Sample size = n= ( (z_/2 * ) / E)²

n= (21.366)² = 456.5059

Sample size = n= 457 (round to next integer)