190. One-Sample Two-Tail Z-Test for Mean

Example

A café’s automatic dispenser is calibrated to pour 250 mL per cup. The manufacturer specifies that pour volume has a known standard deviation of 9 mL. After a maintenance visit, the owner wants to check whether the machine has drifted off target in either direction. A simple random sample of 36 pours has a mean volume of 245.8 mL. At 𝛼 = 0.05, test whether the mean pour volume differs from the calibrated setting.

𝐻0:𝜇=250𝐻𝑎:𝜇250