Lumber companies dry freshly-cut wood in kilns before selling it. As a result of the drying process a certain percentage of the boards become "checked," which means that cracks develop at the ends of the boards. The current drying procedure for 1" x 4" red oak boards is known to produce cracks in 16% of the boards. The drying supervisor at a lumber company wants to test a new method to determine if fewer boards crack. From the problem above, suppose the drying supervisor uses the new method on an SRS of boards and finds that the sample proportion of checked boards is 0.11, which produces a P-value of 0.027. (2 points each)
a. Interpret the P-value in the context of the problem
b. What conclusion would you draw at the a = 0.05 level? At the a = 0.01 level?