Question

They would like the estimate to have a maximumm error of 0.14 gallons. a previous study found that for an average family the variance is 1.69 gallons and the mean is 15.9 gallons per day. If they are using a 85% level of confidence how large is the sample is required to estimate the man usage of water round to next integer

Answer 1

Solution

standard deviation =1.69=1.3

Margin of error = E =

At 85% confidence level the z is ,

= 1 - 85% = 1 - 0.85 = 0.15

/ 2 = 0.15/ 2 = 0.075

Z_/2 = Z_0.075 = 1.44( Using z table ( see the 0.025 value in standard normal (z) table corresponding z value is 1.96 )

sample size = n = [Z_/2* / E] ²

n = ( 1.44* 1.3 / 0.14 )²

n =179

Sample size = n =179