Question

Suppose you are told that a 95% confidence interval for the average price of a gallon of regular gasoline in your state is from $3.05 to $3.92. Use the fact that the confidence interval for the mean is in the form x − E to x + E to compute the sample mean and the maximal margin of error E. (Round your answers to two decimal places.)

Answer 1

The sample mean is 3.48 and the margin of error is 0.44.

Explanation:

We know that the confidence interval is written in the form "x − E to x + E", meaning x: sample mean or estimator, and E: margin of error.

To calculate the mean, we can calculate the average of both bounds of the confidence interval:

`X=(UL-LL)/2=(3.92+3.05)/2=6.97/2=3.48`

With one of the bounds, we can calculate the margin of error E

`UL=X+E\\\\E=UL-X=3.92-3.48=0.44`