In: Statistics and Probability
(1) A survey of 100 grocery stores revealed that the average price of a gallon of milk was $3.00, with a population standard deviation of $0.20. What is the 95% confidence interval of the true cost of a gallon of milk?
Given that,
Point estimate = sample mean =
= 3.00
Population standard deviation =
= 0.20
Sample size = n = 100
At 95% confidence level the z is ,
Z/2
= Z0.025 = 1.96
Margin of error = E = Z/2*
(
/
n)
= 1.96* ( 0.20/
100 )
= 0.039
At 95% confidence interval estimate of the population mean is,
- E <
<
+ E
3.00 - 0.039 <
< 3.00 + 0.039
2.96 <
< 3.04
The 95% confidence interval of the true cost of a gallon of milk is ,(2.96 , 3.04)