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 $3.23 to $4.20. Use the fact that the confidence interval for the mean is in the form x − Eto 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

Let

L = lower bound of confidence interval

U = upper bound of confidence interval

We're given that L = 3.23 and U = 3.45

So

L = X - E

3.23 = X - E

and

U = X + E

3.45 = X + E

The equations are

3.23 = X - E
3.45 = X + E

Add them up to get

6.68 = 2X + 0E

6.68 = 2X

2X = 6.68

X = 6.68/2

X = 3.34

The sample mean is xbar = 3.34

3.23 = X - E

3.23 = 3.34 - E

3.23 - 3.34 = -E

-0.11 = -E

-E = -0.11

E = 0.11

The margin of error is 0.11

So the sample mean is $3.34 and the margin of error is $0.11 (11 cents)