Question: The production manager of the Nagel Beverage Company is responsible for monitoring the filling operations of its soft drink cans. The filling machine has an adjustment that allows the operator to adjust the mean fill level. However, no matter what the mean setting, the filling in individual cans will vary with respect to the mean volume. The machine has been carefully tested and is known to fill cans with a standard deviation s =0.2 ounces.

The machine is set to fill cans at an average of 12 ounces. However, due to wear and tear of its mechanical parts it is possible that after running for several hours, the actual mean fill rate may be higher or lower than 12 ounces. In such case the production stops and machine is recalibrated. Since stopping the production is a costly decision, the manager will ask for recalibration only if he is fairly confident that the mean fill volume (m) is not 12 ounces any more. To decide if recalibration is needed or not, every few hours, a sample of 100 filled cans is selected and the volume in each can is measured in the company’s quality lab. In a recent sample of 100 cans, an average volume () of 12.09 ounces was observed.

(a) Construct a 95% confidence interval for m indicating the current mean fill volume of the machine. What does this interval means?

(b) Based on your answer to part (a), should the production manager order recalibration of the machine or let the filling operation continue?

(c) How many cans should be sampled if you would like to estimate m to be within ±0.02 ounces?