In: Statistics and Probability
The water works commission needs to know the mean household usage of water by the residents of a small town in gallons per day. Assume that the population standard deviation is 2.3 gallons. The mean water usage per family was found to be 20.5 gallons per day for a sample of 1559 families. Construct the 90% confidence interval for the mean usage of water. Round your answers to one decimal place.
lower endpoint = ?
upper endpoint =?
Solution :
Given that,
= 20.5
= 2.3
n = 1559
At 90% confidence level the z is ,
= 1 - 90% = 1 - 0.90 = 0.10
/ 2 = 0.10 / 2 = 0.05
Z/2 = Z0.05 = 1.645
Margin of error = E = Z/2* (/n)
= 1.960 * (2.3 / 1559)
= 0.1
At 90% confidence interval estimate of the population mean is,
- E < < + E
20.5 - 0.1< < 20.5 + 0.1
20.4 < < 20.6
lower endpoint = 20.4
upper endpoint = 20.6