A carpenter is making doors that are 2058 millimeters tall. If the doors are too long they must be trimmed, and if they are too short they cannot be used. A sample of 15 doors is made, and it is found that they have a mean of 2048 millimeters with a variance of 676. Is there evidence at the 0.025 level that the doors are too short and unusable?
State the null and alternative hypotheses for the above scenario.