In: Statistics and Probability
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
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 )