A lumber company is making boards that are 2767 millimeters tall. If the boards are too long they must be trimmed, and if they are too short they cannot be used. A sample of 37 boards is made, and it is found that they have a mean of 2763.3 millimeters with a standard deviation of 15. Is there evidence at the 0.05 level that the boards are too short and unusable?
State the null and alternative hypotheses for the above scenario.
(H0: , Ha: )