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 $3.06 to $4.06. 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.)

x = $

E = $

Answer 1

Answer

we know that lower limit x-E and upper limit is x+E

using the given confidence interval range

x-E = 3.06

and x+E =4.06

adding both equations, we get

x-E +x+E = 3.06+4.06

here -E and +E will cancel out

2x = 7.16

or x = 7.16/2 = 3.56

and this gives

x+E = 4.06

or E = 4.06 - x

setting x value = 3.56

we get

E = 4.06 - 3.56 = 0.5

So, mean is 3.56 and margin of error = 0.50