Question

A city planner wants to estimate the average monthly residential water usage in the city. He selected a random sample of 40 households from the city, which gave the mean water usage to be 3411.10 gallons over a one-month period. Based on earlier data, the population standard deviation of the monthly residential water usage in this city is 387.70 gallons. Make a 95% confidence interval for the average monthly residential water usage for all households in this city.

Round your answers to two decimal places.

_____ to_____  gallons

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 3411.10

Population standard deviation =    = 387.70

Sample size n =40

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96   ( Using z table )

Margin of error = E = Z/2 * ( /n)

= 1.96 * ( 387.70 /  40 )

E= 120.15
At 95% confidence interval estimate of the population mean
is,

- E < < + E

3411.10  - 120.15 <   < 3411.10  + 120.15

3290.95 <   < 3531.25

( 3290.95 , 3531.25 )