In order to evaluate the performance of a certain brand of alkaline battery, researchers at a consumer testing organization took a random sample of 152 new 1.5 volt AA batteries. Each of the batteries was subjected to the same pattern of discharge, which was designed to simulate typical moderate use. A battery's lifetime was obtained as the time for the output to drop to 0.9 volt. The mean lifetime of these 152 batteries was 46.7 hours and the standard deviation was 13.3 hours. The industry standard for lifetime of such batteries is 45 hours.
(a) Using a 0.06 level of significance what kind of evidence do these data give that this brand of battery has mean lifetime that exceeds the industry standard?
(b) What is the P-value of the above testing procedure?
(c) What is the general meaning of the P-value of a hypothesis testing procedure?