Question

The Energy Information Administration (EIA) sampled 900 retail gasoline outlets and reported that, the national average gasoline price for regular-grade gasoline to be $4.113 per gallon with a standard deviation of $0.11 per gallon. Construct a 95% Confidence Interval for mean price of regular-grade gasoline price.

Answer 1

Solution :

Given that,

Point estimate = sample mean =     = 4.113

Population standard deviation =    =0.11

Sample size n =900

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* ( 0.11 / 900)

= 0.007
At 95% confidence interval
is,

- E < < + E

4.113 - 0.007 <   <4.113 + 0.007

4.106 <   < 4.120