A carpenter is making doors that are 20582058 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 1111 doors is made, and it is found that they have a mean of 20452045 millimeters with a variance of 6464. Is there evidence at the 0.050.05 level that the doors are too short and unusable?

State the null and alternative hypotheses for the above scenario.