A statistician employed by a consumer testing organization r

A statistician employed by a consumer testing organization reports that at 95% confidence he has determined that the true average content of the Un-cola soft drinks is between 11.7 to 12.3 ounces. He further reports that his sample revealed an average content of 12 ounces, but he forgot to report the size of the sample he had selected. Assuming the standard deviation of the population is 1.28, determine the size of the sample.

Solution

CI : ( 11.7 , 12.3 )

Margin of error = ( 12.3 -11.7 ) /2 = 0.3

0.3 = (Z*SD) / sqrt(n)
=> sqrt(n) = ( 1.96 * 1.28 ) /0.3
=> sqrt(n) = 8.36
=> n = 69.93 ~ 70 Answer