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 $3.36 to $3.82. 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

Answer: The sample mean = $3.59 and the margin of error is 0.23.

Explanation:

The confidence interval for mean is given by :-

`\overline{x}\pm\ E`, where
`\overline{x}` is the sample mean and E is the margin of error .

Given : A 95% confidence interval for the average price of a gallon of regular gasoline in your state is from $3.36 to $3.82.

Lower limit of confidence interval :
`\overline{x}-\ E=3.36` (1)

Upper limit of confidence interval :
`\overline{x}+\ E=3.82` (2)

Adding (1) and (2) , we get

`2\overline{x}=7.18\\\\\Rightarrow\ \overline{x}=3.59`

From (1) , we have

`3.59-E=3.36\\\\\Rightarrow\ E=3.59-3.36=0.23`

Hence, the sample mean = $3.59 and the margin of error is 0.23.