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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.)

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Answer:

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

Step-by-step 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:

[tex]X=(UL-LL)/2=(3.92+3.05)/2=6.97/2=3.48[/tex]

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

[tex]UL=X+E\\\\E=UL-X=3.92-3.48=0.44[/tex]

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