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 )

= 0.0072
At 95% confidence interval estimate of the population mean
is,

- E <   < + E

4.113- 0.0072 <   < 4.113+ 0.0072

4.1058 <   < 4.1202

( 4.1058 , 4.1202 )