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 $3.21 to $3.67. 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

Solution:

Given that,

Confidence interval = ( 3.21, 3.67)

The sample mean is ,

= ( Lower confidence interval + Upper confidence interval ) / 2

= ( 3.21+ 3.67) / 2

= 6.88 / 2

= 3.44

The margin of error is,

E = Upper confidence interval -

= 3.67 - 3.44

= 0.23

In the form of ,

- E < < + E

3.44 - 0.23 < < 3.44 + 0.23