Question

I am looking for help with the following question:

In a small community with 1600 households, we want to estimate the total daily water consumption during a specified dry spell. How many households should we sample if we want to estimate the total consumption with a margin of error of 2500 gallons with 90% confidence? We do not have pilot data but guess that the household daily consumption in that community ranges from 250 gallons to 380 gallons.

Answer 1

Ans:

Range=380-250=130

The Range Rule of Thumb says that the range is about four times the standard deviation.

Standard deviation=130/4=32.5

Standard deviation for total consumption=1600*32.5=52000

Margin of error=2500

z=1.645 for 90% confidence

Sample size required,n=(1.645*52000/2500)^2=1170.735

$n\approx 1171$