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.

Step-by-step 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.