You notice that your fellow students consume a large amount of bottled water and decide that it might be possible to defray the cost of your college education by selling bottled water. You and your best friend begin to bottle spring water that you buy in bulk. Your bottling machine is a bit old and tends to drift away from the actual 20 oz that you want in each bottle (over and under) so not every bottle has exactly 20 oz. In order to prove to the inspector who just showed up to make sure that you are within the approved ranges for bottling, you take a sample of 20 bottles and compute a mean of 19.94 oz with a standard deviation of .26 oz. Construct a 95% confidence interval of the true amount of water that is in your bottles.

If the inspector says you must have more than 19.85 oz in the bottles to pass, will you?

Why would you use a 95% confidence interval rather than a 99% interval for this test?