Suppose you randomly selected 40 gas stations in the Baton Rouge area and found that the...

Suppose you randomly selected 40 gas stations in the Baton Rouge area and found that the average price of regular unleaded gas is $3.04. Assume that population standard deviation is known to be $0.25. Construct and interpret a 95% confidence interval for the true mean of the gas price.

Solutions

Expert Solution

Solution :

Given that,

Point estimate = sample mean = = $3.04

Population standard deviation = = $0.25

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 * ( / $\sqrt$ n)
= 1.96* (0.25 / $\sqrt$ 40)

= 0.0775
At 95% confidence interval estimate of the population mean
is,

- E < < + E

3.04 - 0.0775 < <3.04 + 0.0775

2.9625 < < 3.1175
( 2.9625,3.1175 )

orchestra answered 1 year ago

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