A lumber company is making boards that are2754.0 millimeters tall. If the boards are too long they must be trimmed, and if they are too short they cannot be used. A sample of21 boards is made, and it is found that they have a mean of2750.0 millimeters with a standard deviation of16.0. Is there evidence at the0.025level that the boards are too short and unusable? Assume the population distribution is approximately normal.

a) State the null and alternative hypotheses.

b) Find theP-value for the hypothesis test. Round your answer to four decimal places.

c) Make the decision to reject or fail to reject the null hypothesis.