SOLUTION: I am in need of help please. Suppose you are told that a 95% confidence interval for the average price of a gallon of regular gasoline in your state is from $3.15-$ 3.45. Use th

Algebra ->  Probability-and-statistics -> SOLUTION: I am in need of help please. Suppose you are told that a 95% confidence interval for the average price of a gallon of regular gasoline in your state is from $3.15-$ 3.45. Use th      Log On


   

Question 752937: I am in need of help please.
Suppose you are told that a 95% confidence interval for the average price of a gallon of regular gasoline in your state is from $3.15-$ 3.45. Use the fact that the confidence interval for the mean has the form X-E to x+E to compute the sample mean and the maximal margin of error E.
Thank you-
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let

L = lower bound of confidence interval

U = upper bound of confidence interval


We're given that L = 3.15 and U = 3.45

So

L = X - E

3.15 = X - E


and

U = X + E

3.45 = X + E

The equations are

3.15 = X - E
3.45 = X + E

Add them up to get

6.60 = 2X + 0E

6.60 = 2X

2X = 6.60

X = 6.60/2

X = 3.30

The sample mean is xbar = 3.30

3.15 = X - E

3.15 = 3.30 - E

3.15 - 3.30 = -E

-0.15 = -E

-E = -0.15

E = 0.15

The margin of error is 0.15


So the sample mean is $3.30 and the margin of error is $0.15 (15 cents)