Question

41 burgers were randomly selected from the production process at a fast-food restaurant and the mean sodium content was measured to be 420 mg. Assume that the sodium measurements are well approximated by a normal distribution with a standard deviation of 156 mg. Calculate the lower bound for the 99% Confidence Interval for the true mean sodium content.

Answer 1

Solution

c = 0.99

= 1- c = 1- 0.99 = 0.01

  /2 =  0.005 and 1- /2 = 0.995

Search the probability 0.995 in the Z table and see corresponding z value

= 2.576   

The margin of error is given by

E = Z/2 * ( / n )

= 2.576 * (156/ 41 )

= 62.7594

Lower bound=

= ( - E )

=441 - 62.7594

= 378.24